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ESR of x-irradiated cyanocetylurea and dicyandiamide single crystals. Lau, Pui-Wah 1970

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ESR OP X-IRRADIATED CYANOACETYLUREA AND DICYAKD1AMIDE SINGLE CRYSTALS BY PUI-WAH LAJJ B.Sc, The Chinese University of Hong Kong, 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF Master of Science in the Department of Chemistry We accept this thesis as conforming to the required standard. THE UNIVERSITY OF BRITISH COLUMBIA June, 1970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver 8, Canada ABSTRACT X - i r r a d i a t e d cyanoacetylurea CNCH2CONHCONH2 and x-i r r a d i a t e d dicyandiaraide NCNC(NH2)2 si n g l e c r y s t a l s were studied,by E l e c t r o n Spin Resonance. Two r a d i c a l species were formed when cyanoacetylurea, CNCHgCONHCONHg, was i r r a d i a t e d with x-rays. One was a. TT-electron r a d i c a l , CNCHCONHCONHg, and the. other a <r-electron r a d i c a l , CNCHgCONHCONH . The ^ e l e c t r o n rad-i c a l was found to have a- l a r g e , i s o t r o p i c proton coupling tensor and an a n i s o t r o p i c nitrogen coupling tensor very s i m i l a r to those of H2NC0CH2C0NH . The TT-electron rad-i c a l had s i m i l a r proton and nitrogen coupling tensors as CNCHCOOH which was formed i n l - i r r a d i a t e d cyanoacetic a c i d . In x - i r r a d i a t e d dicyandiaraide c r y s t a l s , the main species formed was shown to be NCNC(NH2)NH, having a l s o a l a r g e , i s o t r o p i c proton coupling tensor, and hyperfine i n t e r a c t i o n s with two nitrogen coupling n u c l e i were a l s o observed and measured. ESR studies were c a r r i e d out both at room and at l i q u i d n i t rogen temperatures. The e f f e c t of temperature on the spectra i s discussed/. IHDO-SCP-LCAO-MO c a l c u l a t i o n s were c a r r i e d out f o r * • * a model compound HCONH , with the amide proton assuming d i f f e r e n t inplane and out of plane p o s i t i o n s . The spin density was found to vary over a wide range and could i be used to i n t e r p r e t the large proton coupling of the i i dicyandiaraide r a d i c a l . MO c a l c u l a t i o n s were al s o per-formed on the r a d i c a l NCCHCOO"". The ca l c u l a t e d r e s u l t s c o r r e l a t e f a i r l y s a t i s f a c t o r i l y with the observed ones. Comparison of the d i r e c t i o n of the unpaired e l e c -t r o n p - o r b i t a l symmetry axis with bond d i r e c t i o n s and with normals to the fragment planes showed that while e malonamide r a d i c a l , HgNCOCHgCONH was a genuine «*-electron r a d i c a l , dicyandiamide.radical, NCNC(NH2)NH was most l i k e l y a TT-electron r a d i c a l . TABLE OP CONTENTS Chapter page 1 INTRODUCTION 1 2 THEORETICAL 2 . 1 The 8pin-Hamiltonian 5 2 .2 Calculation of the Hyperfine Coupling 1 Tensor from the observed Splittings •.2>3 Theoretical Interpretation of the 8 Principal Values of the A tensor 2.4 The Semi-empirical Molecular Orbital 13 Theory 3 STUDIES ON X-IRRADIATED CYANOACETYLUREA 3 . 1 Experimental . . 1 5 3 .2 Results 16 3 . 3 Discussion 31 4 STUDIES ON X-IRRADIATED DICYANDIAMIDE ,4 .1 Experimental 36 4 . 2 Results 40 4 . 3 Discussion 45 5 MO CALCULATIONS 63; 6 CONCLUSION 76 BIBLIOGRAPHY LIST OP TABLES Tables Page 1 Proton Hyperfine Coupling Tensor f o r the 2 9 C l e l e c t r o n Radical CNCHgCONHCONH 2 Nitogen Hyperfine Coupling Tensor f o r the 2 9 ^ - e l e c t r o n Radical CNCH2C0NHC0NH 3 Proton Hyperfine Coupling Tensor f o r the 2 9 TT-electron Radical NC C HC ON HC ON H 2 4 Nitrogen Hyperfine- Coupling Tensor f o r the 30 TT-electron Radical NC C HC ON HC ON H 2 5 g-Tensor f o r Radical NCNC(NH2)NH at Liquid 60 Nitrogen Temperature 6 Proton Hyperfine Coupling Tensor f o r Radical 60 NCNC(NH2)NH at Liquid Nitrogen temperature 7 N Hyperfine Coupling Tensor f o r NCNC(NH2)NH 60 at l i q u i d Nitrogen Temperature 8 N' Hyperfine Coupling Tensor f o r NCNC(NH2)NH 61 a t . L i q u i d Nitrogen Temperature 9 g-Tensor f o r NCNC(NH2)NH at Room Temperature 62 10 Proton Hyperfine Coupling Tensor f o r NCNC(NH2)NK62 at Room Temperature 11 N Hyperfine Coupling Tensor f o r NCNC(NH2)NH 62 at Room Temperature 12 N 1 Hyperfine Coupling Tensor f o r NCNC(NH2)NH 63 at Room Temperature 13 D i r e c t i o n Cosines of the Vector along the NH 45 Bond, the normal to the -C-N plane H V 14 Spin Density D i s t r i b u t i o n s of NCNC(NH2)NH 66 Radi c a l at Room and Liquid Nitrogen Tem-peratures 15 Spin Density D i s t r i b u t i o n s (After Spin 75 Pro j e c t i o n ) . o f Cyanoacetic Acid Radical 16 Hyperfine Coupling Tensor of the N Nucleus 75 Figure LIST OF FIGURES Page .1 - Two structures of *C-H fragment 12 2 Sample Holder i n the Study of x-irradiated 17 Cyanoacetylurea 3 ESR spectrum for x-irradiated Cyanoacetylurea 21 with H P a r a l l e l to (0.000, 0.643,-0.766) 4 ESR spectrum for x-irradiated Cyanoacetylurea 22 with H p a r a l l e l to (0.940, 0.000, 0.342) 5 Angular variation of the Nitrogen Hyperfine 23 s p l i t t i n g for the Radical CNCHgCONHCONH with Hia . , ' .6 Angular Variation of the Ni.trogen Hyperfine 24 S p l i t t i n g for the Radical CNCHgCONHCONH : with HJLD 7 Angular Variation of the Nitrogen Hyperfine 25 S p l i t t i n g f or the Radical CNCHgCONHCONH with Hjjc 8 Angular Variation of the Nitrogen (inner curve)26 and the Proton (outer curve) Hyperfine S p l i t t -ings for the rad i c a l CNCHC0NHC0NH2 with Hia 9 Angular Variation of the Nitrogen (inner curve)27 and the Proton (outer curved Hyperfine S p l i t -tings for the Radical CNCHCONHCONHg with Hi.b 10 Angular Variation of the Nitrogen (inner curve)28 v i i and the Proton (outer curve) Hyperfine Splittings for the Radical CNCHCONHC0NH2 with Hie 11 Coordinates used in the ESR measurement for 37 Dicyandiamide radical . 12 Sample Holder for ESR Measurement of Dicyan- 39 ' diamide radical at Liquid Nitrogen Tem-perature 13 Room Temperature ESR spectrum for x-irradiated41, Dicyandiamide with H pa r a l l e l to b 14 Liquid Nitrogen Temperature ESR Spectrum for 42 x-irradiated dicyandiamide with Hib 15 Resonance Structures of Dicyandiamide Radical 40 16 ESR Spectrum of x-irradiated deuterated 46, dicyandiamide with H having direction cosines (0.643, 0.000, 0.766) at Room Temperature 17 ESR Spectrum of x-irradiated Dicyandiamide 47 with H having direction cosines (-0.174, 0.985, 0.000) at Liquid Nitrogen Temperature 18 Angular Variation of the N Hyperfine S p l i t t - 48 ing for the Radical CNCN(NH2)NH with HJa at Liquid Nitrogen Temperature 19 Angular Variation of the N Hyperfine S p l i t t i n g 49 for the Radical CNCN(NH2)NH with Rib at Liquid Nitrogen Temperature 20 Angular Variation of the N Hyperfine S p l i t t i n g 50 for the Radical CNCN(NH2)NH with HJ.C at Liquid Nitrogen Temperature v i i i 21 Angular Variation of the N' Hyperfine S p l i t t i n g 51 for the Radical CNCN(NH2)NH with Hja at Liquid Nitrogen Temperature 22 Angular Variation for the N' Hyperfine Spl i t t i n g .52 for the Radical CNCN(NH2)NH with H±b at Liquid Nitrogen Temperature 23 Angular Variation of the N'Hyperfine S p l i t t i n g 53 for the Radical CNCN(NH2)NH with Hj.c' at Liquid Nitrogen Temperature 24 Angular Variation of the N Hyperfine S p l i t t i n g 54 for the Radical CNCN(NH2)NH with Hja at Room Temperature 25 Angular Variation of the N Hyperfine Spl i t t i n g 55 for the Radical CNCN(NH2)NH with Hlb at Room Temperature •26 Angular Variation of the N Hyperfine S p l i t t i n g 56 for the Radical CNCN(NH2)NH with Hlc'at Room Temperature 27 Angular Variation of the N' Hyperfine Spl i t t i n g 57 . for the Radical CNCN(NH2)NH with' Hia at Room Temperature 28 Angular Variation of the Hyperfine S p l i t t i n g 58 for the Radical CNCN(NH2)NH with Hlb at Room Temperature 29 Angular Variation of the N' Hyperfine Spl i t t i n g 59 for the Radical GNCN(NH?)NH witJa Hlc' at Room i x Temperature 30 L a b e l l i n g of Atoms i n Dicyandiamide 45 31 At Room Temperature the Proton i n NH group 65 assuming d i f f e r e n t positions i n the cone 32 The L a b e l l i n g of the Conformations of HCONH 66 33 Change i n E l e c t r o n i c Energy and Spin Density 70 at H with Conformation 34. Change i n E l e c t r o n i c Energy and spin Density 71 with Conformation-35 Change i n Energy d i f f e r e n c e between the 72 s i n g l y occupied MO and the highest f u l l y occupied MO with conformation 36 Change i n Energy di f f e r e n c e s between the s i n g l y 73 occupied MO and the highest f u l l y occupied MO with conformations 37 The L a b e l l i n g , Coordinates, and Angles i n 74 Cyanoacetic Acid r a d i c a l used i n the C a l c u l a t i o n ACKNOWLEDGEMENT I would like to express ray sincere appreciation to Professor W.C. Lin for his guidance and encouragement throughout the course of this study. Never can I forget the hours he spent on counselling and discussions. I would also like to thank Dr. P.G. Herring for hi$ advice, especially on MO calculations, and for allowing me to use his self-consistent f i e l d programs. I am indebted to Dr, P.C. Chieh for the determination of the c e l l constants and the identi f i c a t i o n of the crystal axes for cyanoacetylurea. Acknowledgement must .a.lso be expressed to Drs. M.D. Sastry; R.S. Eachus, D. Chadwick, M.R. Mustafa, and Mr. D. Kennedy for their helpful discussions. CHAPTER 1 INTRODUCTION In the past decade, e l e c t r o n spin resonance (ESR) studies of x-ray or Tf -ray i r r a d i a t e d s i n g l e c r y s t a l s of organic and inorganic compounds have been of considerable i n t e r e s t . This i s p a r t l y due to the fact that x- or X -ray i r r a d i a t i o n provides a very convenient means f o r the gen-e r a t i o n of "stable" free r a d i c a l s whose molecular e l e c t r o n i c structures can be understood mainly from a study of the hyperfine structures of t h e i r respective ESR spectra. The spectroscopic s p l i t t i n g f a c t o r , or more simply, g-factor, and l i n e - w i d t h studies supply f u r t h e r valuable information about the molecular e l e c t r o n i c structures of, and the i n t e r a c t i o n among r a d i c a l s . ( " S t a b i l i t y " here, of course, means s t a b i l i t y toward reaction).. The fact the r a d i c a l s formed by such means are trapped r i g i d l y i n the l a t t i c e of a c r y s t a l , i n a manner compatible with the c r y s t a l symmetry, a l s o provides an added a t t r a c t i o n that the anisotropy of the hyperfine i n t e r a c t i o n makes i t possible to study of the unpaired e l e c t r o n d e n s i t i e s (or s p i n d e n s i t i e s ) i n the non-s o r b i t a l s of the c o n s t i t -uent atoms. In contrast to t h i s , ESR spectra of f r e e l y tumbling molecules, such as that of r a d i c a l s i n s o l u t i o n s , r e v e a l d i r e c t l y only the spin d e n s i t i e s i n the s - o r b i t a l s . A f a i r l y comprehensive review of ESR of the s o - c a l l e d oriented free r a d i c a l s can be found i n an a r t i c l e published i n 1964 by J.R. Morton (1). Unfortunately, no f u r t h e r c o m p a r a b l e w o r k h a s a p p e a r e d s i n c e t h e n . T h i s i s i n c o n -t r a s t w i t h t h e c a s e o f t h e e l e c t r o n p a r a m a g n e t i c r e s o n a n c e ( e p r ) o f t r a n s i t i o n m e t a l c o m p l e x e s o n w h i c h r e c e n t r e v i e w a r t i c l e s c a n b e f o u n d (2 ) . P e r h a p s t h e t i m e h a s nr/t y e t come f o r a s e n s i b l e , u n i f i e d p r e s e n t a t i o n o f t h e r e s u l t s e x -c e p t , may b e , f o r r a d i c a l s i n v o l v i n g o n l y c a r b o n a n d h y d r o g e n . A n y a t t e m p t a t s u c h a p r o j e c t now may t h e n b e a t b e s t a m e r e c o l l e c t i o n o f u n r e l a t e d m a t e r i a l . A n a r t i c l e b y R o g e r s a n d K i s p e r t (2) roust h o w e v e r b e m e n t i o n e d w h i c h a t t e m p t s t o r a t i o n a l i z e t h e m e c h a n i s m o f t h e f o r m a t i o n o f r a d i c a l s b y i r r a d i a t i o n r a t h e r t h a n t h e i n t e r p r e t a t i o n o f t h e m o l e c u l a r e l e c t r o n i c s t r u c t u r e . M o s t o f t h e e a r l i e r w o r k o n E S R o f o r i e n t e d o r g a n i c f r e e r a d i c a l s h a d b e e n o n c o m p o u n d s i n v o l v i n g c a r b o n a n d h y d r o g e n . F o r s u c h r a d i c a l s , t h e t h e o r y i s b e t t e r u n d e r -s t o o d . One c a n g e t a f a i r l y c o m p l e t e p i c t u r e f r o m r e a d i n g a n i n t r o d u c t o r y t e x t b o o k s u c h a s t h a t o f C a r r i n g t o n and. M c L a c h l a n (4 ) . A m o r e r e c e n t t r e n d o f t h i s t y p e o f worB: h a s b e e n t o w a r d s t h e s t u d y o f c o m p o u n d s i n v o l v i n g f l u o r i n e a n d n i t r o g e n . W i t h f l u o r i n e - c o n t a i n i n g r a d i c a l s , t h e m a i n i n t e r e s t h a s b e e n , t h e h y p e r f i n e i n t e r a c t i o n o f t h e u n p a i r e d e l e c t r o n w i t h t h e f l u o r i n e n u c l e i . A s h o r t s u r v e y o f E S R w o r k o n f l u o r i n e c o n t a i n i n g r a d i c a l s h a s b e e n : g i v e n i n a r e c e n t t h e s i s b y M . R . M u s t a f a . ( 5 ) W i t h n i t r o g e n -c o n t a i n i n g r a d i c a l s , b e s i d e s h y p e r f i n e i n t e r a c t i o n s d u e t o > n i t r o g e n n u c l e i , t h a t d u e t o p r o t o n s a t t a c h e d t o n i t r o g e n i B a l s o o f i n t e r e s t . I n t h i s w o r k , we s h a l l m a i n l y c o n c e r n o u r s e l v e s u i t h r a d i c a l s o f t h e t y p e R N H , i t i s n o t i m m e d -i a t e l y o b v i o u s w h e t h e r t h e u n p a i r e d e l e c t r o n w o u l d o c c u p y 5 a (T- or a 7" -MO. Smith and Wood (6) studied the ESR of the r a d i c a l HCONH i n a flow system and found that the i s o t r o p i c com-ponent of the proton hyperfine coupling tensor was 30.55 gauss They considered the unpaired electron to be i n a77VMO with the proton being i n the nodal plane. The spin density at the proton was then due to spin p o l a r i z a t i o n very much l i k e that found i n the now we l l known and we l l studied r a d i c a l s of the type R-j^CH, a t y p i c a l example of which i s CH(C.00H)2 (7). Lontz observed a r a d i c a l of i r r a d i a t e d penta-fluoro-propionamide and interpreted i t as CF^E^C-ONR" (8). In one o r i e n t a t i o n , the proton s p l i t t i n g was found to be 18 gauss ( the spectra of t h i s r a d i c a l being observ-able only f o r a few o r i e n t a t i o n s ) . Presumably, t h i s r a d i c a l i s also to be interpreted as a i r - e l e c t r o n r a d i c a l . In contrast to t h i s , Cyr and L i n found a r a d i c a l i n x - i r r a d i a t e d single c r y s t a l s of malonamide which was shown to.be NHgCOOHgCONH ( 9 ) . The proton coupling was however found to be very large (of the order of 80 gauss) and nearly i s o t r o p i c . They postulated that the unpaired el e c t r o n occupied a<5~-MO and the r a d i c a l was to be r e -garded as a °~-electron r a d i c a l . This implies that the spin density at the proton i s due to dir e c t e d overlap of the hydrogen Is o r b i t a l with the <f-orbital of the nitrogen. The authors have not discussed the pos s i b i l i t y ; / that the unpaired e l e c t r o n might, occupy a 77"-MO, but with the attached proton being i n an out-of-plane p o s i t i o n . This point w i l l , be brought up again l a t e r . 4' In t h i s t h e s i s I wish to report the study of the. ESR of two more r a d i c a l s of the type R N H . The f i r s t i s a r a d i c a l formed'in x - i r r a d i a t e d cyanoacetyluxea,CNCJLjCONHCONH and i s to be interpreted as CNCHgCONHCONH, which can be formed by the loss of one hydrogen atom from the o r i g i n a l -CONHg group. The second r a d i c a l i s believed to be ...' NCNC(NH2)NH formed i n x - i r r a d i a t e d dicyandiamide, NCNC(NH 2^ by the loss of one hydrogen i n one of the NH2 groups. As we s h a l l see, both r a d i c a l s have rather large and nearly i s o t r o p i c proton coupling tensors. F i n a l l y , semi-empirical u n r e s t r i c t e d Hartree Pock (UHF) calculation;.on the r a d i c a l HCONH has been made i n an attempt to investigate the molecular e l e c t r o n i c structure from a t h e o r e t i c a l approach. Although no general conclusion can yet be made regarding the e l e c t r o n i c structure of r a d i c a l s of - - % * .the type RNH, some understanding of the problem has however been attained which c e r t a i n l y paves the way f o r future i n v e s t i g a t i o n s . CHAPTER 2 THEORETICAL Since the basic theories of electron spin resonance have been described i n standard textbooks (4), (10), only those directly related to the development of this thesis w i l l be described. 2.1 The Spin-Hamiltonian The energy of the ground state of a paramagnetic molecule i n the presence of an external magnetic f i e l d H can usually be expressed i n the form of a spin Hamiltonian, i n which the operators act only on spin states. The effects of the orbital motion on unpaired electron are reflected i n the various parameters which appear in the spin Hamiltonian. It i s expected that these parameters are direction-dependant and should be represented by tensors. When the nuclear quadrupole effects and nuclear dipole - nuclear dipole interaction can be neglected, the spin Hamiltonian for a radical with interacting nuclear spins may be written as . where ^ i s a universal constant known as the Bohr magneton, g i s the g-tensor of the system, S i s the electron spin vector operator, A ^ i s the hyperfine coupling 6 tensor representing the i n t e r a c t i o n between the unpaired constant known as the nuclear magneton, and H i s the external magnetic f i e l d vector. The f i r s t term on the r i g h t hand side of Eq. ( 2 ) represents the coupling of the electron spin s_ with the external magnetic f i e l d H. If-there are no o r b i t a l angular momentum contribution to the unpaired electron ( i . e . the o r b i t a l angular momentum of the unpaired electron i s completely quenched), then the tensor f o r g would be i s o t r o p i c and equal to the free spin value of 2 . 0 0 2 3 . In'organic sing l e c r y s t a l s , with the exception of some s u l f u r containing compounds, the g tensor i s nearly i s t r o p i c and departs from the free spin value by + 0 . 0 0 1 or l e s s . The second term represents the hyperfine i n t e r a c t i o n between the electron spin and the nuclear spins. Hyperfine i n t e r a c t i o n tensors can always be decomposed as follows (for b r e v i t y superscript i s omitted i n the following) where a i s c a l l e d the i s o t r o p i c componant of A, U i s the un i t matrix, and electron and. the yU. nucleus, I i s the nuclear spin vector, g i s the nuclear spin g-factor, p i s another universal ( 3 ) (k. (4) 7 i n which Tr denotes the trace operation, a' i s called the anisotropic component of A. If a'is symmetrical as i s usually the case, i t can he diagonalized, and by definition the trace of a'is zero. The third term of Eq. (2) represents direct inter-action between the nuclear spin and the magnetic f i e l d . Its primary effect i s to relax the selection ruleAM-j-=0. 2.2 Calculation of the Hyperfine Coupling Tensor from the Observed Splittings. The task of a ESR experimentalist i s to determine the appropriate spin Hamiltonian and to measure the values of the parameters. When we address ourselves to the work of measuring these parameters, f i r s t of a l l , we take ESR spectra of the single crystal which contains radical(s) orientated at different orientations with respect to the magnetic f i e l d . In each orientation, we obtain the observed g value (g 0t) S) through resonance condition hv = g^H, where H i s the magnetic f i e l d strength of the single line i f there are no hyperfine splittings, and obtain the observed hyperfine s p l i t t i n g (hfs) by measuring the difference i n magnetic f i e l d strengths of appropriate lines. From the f i r s t term of Eq.(2) and the assumption the S i s quanitzed along the direction of H.g, i t can be shown (11) u ^ l ^ U k ^ i j f (5) ' 8 where the subscripts i , j , k stand for lab-fixed coordinates, g i j s c r e " b e n s o r elements of g, l i are the direction cosines of the external magnetic f i e l d H. Prom the second and third terms of Eq.(2) and the assumption I i s quantized along (S.A - g n^ nH)» i t can be shown that under the assumption g i s isotropic the following expression can be derived (11) ^ where §ij i s the Kronecker delta, A. . are the tensor elements of A, the quantity G i s set equal to ^flvxr* ^* with H Q being the average of the high - and low - f i e l d l i n e s e g-tensor, with six components, can be determined completely by (5) i f six g o l 3 S values (with different orientations with respect to H) are known. Usually more than six values are available, g i s calculated from (5) by least squares f i t t i n g . Similarly, A i s calculated from (6) by least squares f i t t i n g . It i s important to notice that due to the form of Eq.(6) the measurement of hfs versus orientation only yields the magnitude of A,. The sign remains undetermined. The determination of the sign of the tensor components i s one of the main problems in the subject and i s discussed at length i n Chapter 3 and 4. 9 2.5 Theoretical Interpretation of the Principal Values  of the A Tensor The electron - nucleus hyperfine interaction arises orbital occupied by the odd electron. If the odd electron occupies an s-orbital of a particular atom, the propability of the odd electron at the nucleus ^ (0) w i l l have a f i n i t e value. One can shmv that ^[0) gives an isotropic hyperfine interaction which can be expressed as (12) This electron-nucleus interaction, f i r s t introduced by Fermi to account for hyperfine structure i n atomic spectra, i s called Fermi contact interaction. The magnitude of the isotropic component of the hyperfine tensor can be used as a measure of the spin density in the s-orbital of the radical. This i s done by comparing the theoretical isotropic hyperfine component (obtained from a Hartree-Fock wave function) with the experimentally determined quantity. This ratio i s approximately equal to the square of the coefficient of the s-orbital i n the singly occupied MO. On the other hand, i f the unpaired electron i s s t r i c t l y i n a p- or d- orbital, 4^ (0) vanished and the isotropic component w i l l be zero. However, there i s another "mechanism" of electron-nucleus interaction: electron dipole-nuclear dipole interaction, similar to the classical from different origins depending upon the nature of (7) 1 0 dipole - dipole interaction. One can show that the three principal components of the interaction can be expressed as ( 1 2 ) where a^, a^ and a^ are the principal components of electron dipole - nuclear dipole interaction, R (with vector component X, Y, Z) i s the position vector of the electron with respe.ct to the nucleus, and the bracket,^ indicates integration over the radial part of the odd electron MO. We see that the sum of a', a/ and a' i s zero. This x y z fact means that a', a' and &! are simply the anisotropic x y z components of the hyperfine interaction. As for the case of the isotropic component, the magnitude and sign of the anisotropic component can be calculated theoretically from atomic p or d wave functions. A comparison of anisotropic component and the theorectical value gives the spin density in the particular p or d orbit a l . Consider a single example of «C-H fragment, in which a T-electron occupies the 2 p z carbon orbital, perpendicular to the plane of the three trigonal bonds of the carbon. A simple MO theory gives zero spin density at the nucleus in the nodal plane, and hence predicts zero isotropic 11 hyperfine interaction of the proton, for the proton l i e s on the nodal plane. In practice, there i s some isotropic contribution of the proton hyperfine coupling. To explain an ESR spectrum, therefore, a modified MO i s usually required. In the present case, the isotropic coupling may be explained i n terms of either valence bond or molecular orb i t a l theory (13), (14). In MO theory this fragment has ground state wave function, = ll°ici; rO)]\ «f * and two excited state wave function, 4, = l\ntt>W» T r ^ l l j g C c f ^ p ^ ( 1 2 ) here (5%-wv<( 0*^ are «C-H bonding and anti-bonding orbital respectively, while TF i s the carbon 2p z o r b i t a l . The wave function including configuration interaction' can be expressed as ± =^ + 1,^  (14) 12 A f t e r est imat ing \u and !|"2 by the per turbat ion theory, i t can be shown that a singl9 TT -e lectron induces a negative s p i n densi ty of about - 0 . 0 5 i n the hydrogen Is o r b i t a l , corresponding to a hyperf ine coupl ing of 20 - 25 gauss (negat ive) . The above r e s u l t can a lso be explained q u a l i t a t i v e l y i n the fo l lowing way. Consider the two s t ruc tures i n F i g . 1 f o r C-H fragment. F i g . 1 Two s t ructures o f - C - H fragment. The i n t e r a c t i o n between the o~ and if systems makes s t ructure (a) being s l i g h t l y prefer red because of the favorab le exchange i n t e r a c t i o n between the e lec t ron and the carbon e l e c t r o n , whose spins are p a r a l l e l . Hence, i f the odd e lec t ron has s p i n c< , there w i l l be excess |3 s p i n i n the hydrogen Is o r b i t a l , which gives r i s e negative i s o t r o p i c proton s p l i t t i n g . 13 2.4 The Seroi-eropirical Molecular Orbital Theory The serai-empirical molecular o r b i t a l theory used in this thesis i s a recent version of an approximately self-consistent f i e l d (SCF) MO, known as the intermediate-neglect ~of-diff erential-over.lap (INDO), devised by J.A. Pople and his co-workers (l6)-r(22). This theory was based on the Hartree-Fock-Roothaan equations for molecular orbitals taken as linear combinations of atomic orbitals'• 1 (LCAO), with approximations introduced in the calculation-of the' atomic and molecular integrals entering the matrix elements of the Hartree-Fock Hamiltonian operator. The approximations in detail are; 1. The overlap integrals are neglected unless^= ^ . 2 . The two-, three-, and four- center integrals of the type 0UjiV)are set equal, to zero unless^l=Aand ^*-(r . Those which remain are further simplified by the approximation {P-JLWO^YAB l / i ' M , I>OIL8) (15) where r A B i s the Coulomb integral (S AS A/, S^ S-g) i n -••...'.."•yolvirig.valen.ee s h e l l s-type orbitals of the atoms A and B. • 5 . The diagonal core-matrix elements are calculated by^separating the interaction ofJH(centered on atom A) with.the core of A and with the other atomic cores, C-V.l/8^ (16) • .cere 4 . The two-center core-matrix elements )-\^ core are approximated by 0 * * where and ^ * are empirical parameters. 14 Under these approximations, the elements of the P matrices become *j*-Up+gtMpte>i-fS-irlt*-J) ( 1 9 ) (20) with the T T ^ elements having a similar form. In the calculation of the spin density distribution of a free ra d i c a l , unrestricted MO must be used. It d i f f e r s from the restricted MO i n that the spatial wave functions of ^ spin electron and p spin electrons of "paired electrons" need not be the same. However, this type of molecular wave function i s not an eigenfunction of the operator but contains the components of several spin states with t o t a l spin S>j». In this thesis the contaminating components are annhilated by the use of a projection operator, devised by Lowdin ( 2 3 ) , modified by Adorns and Snyder (24). . . - * The INDO calculations were carried out on an IBM 360/67 computer using A program written by Drs. F.G. Herring, P.J. Black, together with Messers. David Kennedy and M.R. Mustafa. CHAPTER THREE STUDIES ON X-IRRADIATED CYANOACKTYLUREA 3.1 Experimental The.compound, cyanoaeetylurea, NCCH 2C0NHC0NH 2» was obtained from Aldrich Chemical Co., Milwaukee, Wisconsin.' Single crystals were grown from aqueous solutuious by slow cooling. They formed well defined hexagonal plates which showed the following analysis: C=38.34, H=4 .35; N=33.27. (calculated: C=37.80, H=3.97, N=33.06). The', identity of the single crystals with the or i g i n a l powder obtained from Aldrich Chemical Company was confirmed .by melting point test and IR spectroscopy. . :The crystals belong to the orthorhombic system with .the .Space group P n a2 ' a n d following c e l l dimensions: a=17.48, b=5.13, c=6.10A. The crystallograpic axes can be readily recognized, b being p a r a l l e l to two sides, of the hexagon and a being perpendicular to the hexagonal plate.* * .The .crystals were irradiated for several hours with 50 kv x-rays at room temperature. The ESR of the i r r a d -iated crystals was studied at room temperature, using a Varian 4500 ."ESR spectrometer, with 100 kH z modulation frequency. The magnetic f i e l d • strength was measured * The author wishes to thank Dr. P.O. Chieh of this Department for the determination of the c e l l constants • and the i d e n t i f i c a t i o n of the cry s t a l axes. 16 with a proton resonance magnetometer. The microwave frequency was determined using a Hewlett-Packard f r e -quency counter with a 5256 A plug-in unit. The orientation of the magnetic f i e l d was achieved by means of a rotating magnet used i n conjunction with a c y l i n d r i c a l cavity. A teflon sample holder i n shown .in Pig. 2 (a) was used for f i x i n g the cr y s t a l i n the cavity. ' • ' In taking the spectra, an axis of the crystal, which was fixed in the L-shape teflon "chair" (Pig. 2b), was placed perpendicular to the magnetic f i e l d , and the mag-net was rotated.about the v e r t i c a l axis. The same pro-cedure' was applied to two other mutually perpendicular axis by turning the "chair". The relative values of the angles were accurate 0.5 deg. while the absolute values were to be correct to within 2 deg. The spectra were taken at 5 deg. intervals for the applied magnetic f i e l d H being i n each of the three crys-tallographic planes, ab, be, and ca. 3.2 Results A study of a l l the spectra showed that they were consistent with two radicals being formed: one having proton and a nitrogen hyperfine coupling tensors very much l i k e those reported for the<r-electron radic a l in x-irradiated malonamide, end the other being aTT-electron r a d i c a l which showed the expected proton coupling with 17 Fig. 2 Sample holder in the study of x-irradiated cyano-aeetylurea. 18 a f u r t h e r s p l i t t i n g by a nitrogen nucleus. The fact that there were two r a d i c a l s present was confirmed by power s a t u r a t i o n study, and most c o n c l u s i v e l y , by annealing at 140°C f o r 12 hours. A f t e r such annealing the c r-electron .. r a d i c a l dissappeared completely, while the s i g n a l due to the TT-electron r a d i c a l was only s l i g h t l y reduced. F i g . 3 and 4- show two examples of the spectra. In both spectra, the outer pair of the t r i p l e t s are due to the 0 "-electron r a d i c a l of the type RCONH, NCCHgCONHCONH, . which was formed by the lo s s of an amide proton. The separation between, the two t r i p l e t s i s due to the proton and the t r i p l e t s p l i t t i n g i t s e l f i s due to the nitrogen. The inner p a i r of t r i p l e t s i n F i g . 3 i s due to the -fl"-elec-t r o n r a d i c a l NCCHC0NHC0NH2, the separation between the t r i p l e t i s due to the proton and the t r i p l e t , to - the nitrogen i n the CN group. In. F i g . 4, four l i n e s at the center are al s o due to the TT-electron r a d i c a l , NCCHCONHCONIL,. However, i n t h i s case, the s p l i t t i n g due to the nitrogen i s un-resolved and the four l i n e s are due to the proton alone and correspond to symmetry-related s i t e s . • • In general, f o r an orthorhorobic c r y s t a l one should observe two s i t e s f o r any o r i e n t a t i o n with H being i n one of the three c r y s t a l l o g r a p h i c planes. However, i n the present case, the two s i t e s f o r the 6~-electron r a d i c a l . were found to- be e i t h e r a c c i d e n t a l l y equivalent, or more'' 19 l i k e l y , the difference between the two sites was unre-solved. For thelfelectron r a d i c a l , although two sites were observed as far as proton coupling was concerned, the difference between the two symmetry related nitrogen tensors was also too small to resolve. The matrix elements of the coupling tensor A were calculated from Eq. (6) by a least-squares f i t t i n g . The g-tensor components were similarly calculated from Eq . ( 5 ) . The angular variation of the nitrogen hyperfine s p l i t -ting for the CT-electron r a d i c a l i s shown i n Fig. 5 , 6 and 7. The few points on' Fig. 7 are due to the fact that nitrogen hyperfine i s not resolved at a l l orientations The proton hyperfine s p l i t t i n g i s nearly anisotropic and i s riot shown i n these figures. The angular variation of both the nitrogen and the proton hyperfine s p l i t t i n g s for their-electron r a d i c a l are shown in Fig. 8, 9 and 10. In a l l these figures the continuous curves represent the values calculated from the respective tensors shown in Table-i 7and the open c i r c l e s represent the experimental points. . . Since the s p l i t t i n g due to the proton in the ^- e l e c -tron r a d i c a l i s very large, second order effect must be taken into account i n calculating the g o b s . The correct resonance magnetic f i e l d should be (25) • • . » . - ± l ^ ) { i r ^ ^ ) ( 2 1 ) where H & and are the magnetic f i e l d s of the two lines s p l i t by the proton. 20 The g-tensors for both and <5~- and the r r - electron radicals have principal axes a l l very nearly paral l e l to the crystallographic axes. The o~"-electron radical has the following principal g-values: g =2.0032, g,= c l D 2.0026, g =2.0018. The T-electron radical has the f o l -lowing principal g-values: ga=2,0036, gj)=2.0034, gc= 2.0020. The errors are estimated to be + 0.0005. The various tensors obtained are shown in Table 1 to 4. H : 1- ' - 5 0 gauss Tig^.ESR 1 spectrum for x-irradiated cyanoacetylurea with H.. parallel to (0,000,Ofi643,-0.766). . 50 gauss Pig. 4':.ESR-spectrum for x-irradiated cyanoacetylurea with H p a r a l l e l . to (0.940,0.000,0.342) Z5 P i g . 5 . Angular v a r i a t i o n of the.nitrogen hyperfine s p l i t t i n g f o r the r a d i c a l CNCHgCOHHCOHH with Hj.a. . . " 24 6 Angular variation of the nitrogen hyperfine s p l i t t i n g for the radical CNCHgCONHCONH with H4-D. 2 5 Fig. 7 Angular variation of the nitrogen hyperfine s p l i t t i n g for the radical CNCHgCONHCOKIi with Etc. 26 P i g . 8 Angular v a r i a t i o n of the nitrogen ( inner curve) and the proton (outer curve) hyperfine s p l i t t i n g s f o r the r a d i c a l CNCHCONHCOKH9 with Hia. F i g . 9 Angular v a r i a t i o n of the nitrogen (inner curve) and the proton (outer curve) hyperfine s p l i t t i n g s f o r the r a d i c a l CNCHC0NHC0NHo with HXb. 28 H//b F i g . 10 Angular v a r i a t i o n of the nitrogen (inner curve) and the proton (outer curve) hyperfine s p l i t t i n g s f o r the r a d i c a l CNCHC0NH00NH2 with Hlc. 29 TABLE i Proton Hyperfine Coupling Tensor for the T-electron radical CNCHQCONHCONH " * " ii Principal values (gauss) Direction Cosines.of Principal Axes with respect to a b c . 87.0 + 1.0 85.4 + 1.0 84.8 + 1.0 -0.005 :.0-.53'4 0.846 -0.052 0.845 -40.533 0.9995 0.025 -0.021 • TABLE 2 . Nitrogen Hyperfine Coupling Tensor for the ^ e l e c t r o n radical CNCH2C0NHC0NH 1 — Principal values (guass) Direction Cosines of Principal Axes with respect to a . b c 21.8 +0.5 -0.004 0.004 0.99998 7.4..+ 0.5 -0.052 0.9986 -0.004 5.7 + 0.5 0.9986 0.052 0.004 • TABLE 3 Proton Hyperfine Coupling Tensor for the T-electron Radical $' ' • NCCHC0NHC0NH2 Principal values •T (guass) Direction Cosines of Principal Axes with respect to a b c . 8.8 + 0.5 19.7+ 0.5 o J. n t; -0.336 -0.003 +0.942 +0.009 -0.009 0.99996 30 T A B L E 4 Nitrogen Hyperfine Coupling Tensor for the F-electron Radical NCCHC0NHC0NH2 Principal Values (guass) Direction Cosines of Principal axes with respect to i a b c 11.1 + 0.5 -0.008 -0.030 0.9995 . 2.6 + 0.5 0.99997 -0.003 0.007 0.4 + 0.5 0.003 0.9995 0.030 31 3.3 Discussion ThecT-electron Radical, CNCHgCONHOONH The c-electron r a d i c a l i n x-irradiated malonamide,. NH2COCH2CONH, has the following coupling tensors (9) : a proton coupling tensor with. principal values 84,80 and 80 gauss, and a nitrogen coupling tensor with prin-c i p a l values 6.9, 0.3 and 35.7 gauss. A comparison with the coupling tensors of the 6"-electron radic a l i n the present study shows that while the proton coupling tensor for the <r-electron r a d i c a l i n irradiated malonamide has some a x i a l symmetry, the present radical i s isotropic within the experimental error. The isotropic components for the two radicals, however, have comparable magnitudes The nitrogen coupling tensor i s also* more isotropic i n the present case as compared with that in malonamide. It i s not unreasonable to assume that the principal values of the proton tensor for the 6"-electron radic a l have the same sign, otherwise the A tensor of the proton would have too large an anisotropy. It i s also reason-able to assume that the signs are positive i f i t i s a (T-electron r a d i c a l . The signs of the principal values of the nitrogen hyperfine tensor are more d i f f i c u l t to speculate. Cyr and Lin'(9);have given some circums-t a n t i a l evidence for considering a l l three principal values to be positive. I s h a l l merely assume this to be the case. Based on this assumption and equations already known 3 2 i t i s possible to derive the p- and s- characters of the unpaired electron on the nitrogen atom, ( l ) Thus i f i t i s assumed that, for the (T-electron rad-i c a l i n x-irradiated cyanoacetylurea the principal values of the N coupling tensor are a l l positive and the tensor i s a x i a l l y symmetric with principal values 21.8G and <6.5;G (the average of 7.4 G and 5.7 G), then they can be resolved into an isotropic part A and an anisotropic part B as follows: " . -•The solutions of equations A > 2B = 21.8 - (22) . and A - B = 6. 6 . ( 2 3 ) are • . ' • A = 11.7 ' (24) B = 5.1 . . (250 Hence the spin density in the nitrogen 2s o r b i t a l i s and the spin density i n the nitrogen 2p o r b i t a l i s P*7 =: &L « o.29e> (27) respectively. This corresponds to a p:s rati o of.14.2. It can be shown that (27) for a non-linear triatomic the bond a n g l e , , relates to the hybridization r a t i o , by .GOS£= (St+2.yt . (28) " I f we-substitute the p:s ratio of 14.2 into (28), the CNH bond angle comes out to be 151°. This result should be compared with a p:s ratio of 24 and a CNH 3 3 bond angle of 157.5° reported for malonamide (T-electron radical. The two g-tensors for the two cases, though comparable in magnitude, seem to have no apparent cor-relation. The Tj-electron Radical CNCHC0NHC0NH2 The proton coupling tensor for the TT-electron radical is consistent with the well known -jr-electron radical of the type RCHCOR' with R'=OH or NH2. The principal g-value with principal axes perpendicular to the radical plane (g i n this case) i s close to the free spin g value of 2 . 0 0 2 3 while the remaining two principal g-values are somewhat greater than the free value. This again is what one would expect from many previous work. The theory behind this was f i r s t discussed by McConnell and Robertson(28).and w i l l be described b r i e f l y here. Consider an axia l l y symmetric planar aromatic radical where g^ and g_j_ refer to f i e l d directions perpendicular and p a r a l l e l to the plane of the aromatic ring. In the case of f i e l d direction perpendicular to the plane of the aromatic ring, two excitations are possible: the TI-* 0""* excitation with average energy ZiE^ involving excitation of the odd i r-electron into an antibonding (Torbital, rr, and the<T=»7r excitation with average energy A Eg involving excitation of the<T-bonding electrons t o y - o r b i t a l states. The result i s that g ^ w a l l change from 2 . 0 0 2 3 to ? - * . o o * 3 -ZL + H (28) 34 where J is the 2p spin-orbit coupling parameter o f the —1 -j carbon'atom, and J=28 cm" in this case. If (AEg -AE^) is in the reasonable range 1 - 0 . 1 ev, gx= 2 . 0 0 9 - 2 . 0 0 3 . In the case of f i e l d direction being paral l e l to the plane of the aromatic ring, only highly energetic (and hence r e l a t i v e l y unimportant) 0^* 1^ transitions, or very weak multicenter spin-orbit .interactions involving transitions, can contribute to g/j • This fact makes gfl close to 2 . 0 0 2 3 . The nitrogen coupling tensor i s very similar to that of NCCHCOOH, which was reported to have the following approximate principal values: A=10.6 G, A=0 G ( 2 9 ) . That t h e principal axis for the largest principal value' ( 1 1 . 1 G) of the nitrogen coupling tensor should be para-l l e l to the principal axis for the proton coupling tensor, (both p a r a l l e l to the carbon 2 p z o r b i t a l occupied by the unpaired electron).is also consistent with what one would normally expect. The calculation of the isotropic component of the tensor depends on how one would choose the relative signs of the principal values. It is reasonable to assume that the largest principal value ( 1 1 . 1 G) s h o u l d be positive. Then from our result, the isotropic component could vary from 2 ; 7 for both the smaller principal value assumed negative to 4 . 7 for a l l three principal values assumed positive. However, a choice of signs correspond-ing to principal values of +11 .1 , - 2 . 6 and +0.4 gauss w i l l 35 yield an isotropic coupling of 3.0 gauss which i s more in line with those measured in solutions for similar types of radicals and ranging from 3.0 to 3.5 gauss (30). The same procedure for calculating spin density described e a r l i e r for the (T-electron radical may be used here. Assuming that the nitrogen isotropic coupling i s 3.0 gauss, the spin densities distributed in nitrogen 2s and 2p orbitals are ( 2 9 ) J ; P = & = ( 3 0 ) Hence we may conclude that in the fr-electron radical, the unpaired electron i s mainly in the carbon 2p or b i t a l , which forms a T-MO extending not only to the CON^ but to the CN group as well. CHAPTER FOUR • STUDIES ON X-IRRADIATED DICYANDIAMIDE ' 4.1 Experimental .The compound, dicyandiamide, NCNC^HgJg v ; a s obtained, from Aldrich Chemical Co., Inc., Milwaukee, Wisconsin. Single crystals were grown from aqueous solutions by slow evaporation. Well formed crystals of approximately 5x4x3 mm were obtained. ••• The cr y s t a l belongs to the monoclinic system with Space 6 group, ^2h(c2/c)' a n c* * n e following c e l l dimensions, a= 15.00A, b=4.44A, c=13.2A, p=115° 20«. Its crystallography was described by Groth (31). A diagram of the crystalcf dicyandiamide i s given i n Fig. 11. The faces were identified by comparing the angles between pairs of faces calculated from the dimensions of the unit c e l l and those of the actual single c r y s t a l . A l l crystals showed well developed (100), (001), (110) faces. A set of reference axes con- i s i s t i n g of the crystallographic a and b axes together with c o r t h o g o n a l to a and b, was used for ESR measurement(Fig.] The crystals were irradiated for 3 hours with 40 kv x-rays at room temperature. Y - i r r a d i a t i o n gave essentially the same result. The electron spin resonance of the i r r a d -diated crystals was studied both at room temperature, and at l i q u i d nitrogen temperature. For room temperature studies, the spectrometer and the procedure were the same as that described e a r l i e r for cyanoacetylurea, except that' g values were related to that of a sample of DPPH taken as g=2.0036, and that the spectra were taken at 37 P i g . 11 Coordinates used i n the ESR measurement f o r dicyandiamide r a d i c a l . 38 10 degree i n t e r v a l s . For l i q u i d nitrogen temperature studies arf, E3 . spectrometer with 100 kc modulation of the magnetic f i e l d was used. The microwave frequency was determined using a Hewlett-Packard 5245 L frequency counter. Orientation of the s i n g l e c r y s t a l was achieved by means of r o t a t i n g the c r y s t a l attphed to a sample holder shown i n P i g . 12. The spectra were taken at 10 degree i n t e r v a l s f o r the applied magnetic f i e l d H being.in each of the three c r y s t a l l o g r a p h i c planes, ab, be 1 and c'a. The r e l a t i v e values of the angles were accurate to 1 degree while the absolute values were estimated to be correct to within 5 degree, gjvales were r e l a t e d to that of a.sample of DPPH taken as g=2.0036. Deutei'iation of the c r y s t a l s was c a r r i e d out by e-repeated treatment with 99.7$ 'D20 and a f i n a l r e c r y s t a l -l i z a t i o n from the same solvents 39 Pig . 12 Sample holder f o r ESR measurement of. dicyandiamide r a d i c a l . 40 4.2 Result A room temperature spectrum with the external f i e l d p a r a l l e l to the b axis i s shown in Fig. 13. The hyper-fine s p l i t t i n g s due to the proton and the two nitrogen nuclei^ are indicated in the figure. The unresolved struc-ture at the center of the spectrum was due to an unidentified species. Annealing at 75°C for 5 hours was found to anneal out the main species completely. The outer lines of the hyperfine structure due to the nitrogen were found to be always broader than the central lines. By cooling to l i q u i d nitrogen temperature, this variation i n linewidth was found to disappear. A l i q u i d nitrogen temperature spectrum for the same orientation (H]|b) i s shown in Fig. 14. Analysis of the l i q u i d nitrogen spectra i s straight-forward. The s p l i t t i n g due to the proton d i r e c t l y attached to the nitrogen i s about 75 0; there are two nitrogen hyperfine s p l i t t i n g s : one with 6.7 G, and the other 6 .9 G- fpj this orientation. We postulate that the f i r s t nitrogen hyperfine tensor i s due to that nitrogen in the NH group, for i t s principal components of the A tensor (see Table 11) are similar to those in NHgCOCHgCONH and NCCH2C0NH. It is also reasonable to assume that the other nitrogen s p l i t -ting i s due to N' shown i n Fig. 15, instead of that i n the NHg group, since valence bond (VB) resonant structures can easily be drawn as shown: Fig. 15 Resonance structures of dicyandiamide r a d i c a l . \ Fig. 13 Room temperature ESR specturm for x-irradiated dicyandiamide with H parallel to b. 43 An equivalent statement is that the unpaired electron coul easily delocalize to N.' and N" to form an extended bonding system. The above interpretation was substantiated by a spectrum shown in Fig* 16, which i s that of the x-irradiated deuterated compound. The pattern due to the radical NCNCCNDg^ can be seen to crowd around, the center of the spectrum, with the spl i t t i n g s indicated . The a j j / a j ) r a t i o was found to be 6.68 as compared with the-theoretical value of 6.52. •For monoclinic crystals when alH or c'l/H, spectra corresponding to two symmetry-related sites should be ob-served. This was indeed the case. Fig. 17 shows the li q u i d nitrogen spectrum when the external magnetic f i e l d has direction cosines (-0.174, 0.985, 0.0). The hyper-fine s p l i t t i n g s for the two sites are indicated in the figure. The matrix elements of the coupling tensor A were calculated from Eq.(6) by least-squares f i t t i n g . The g-tjensor components were similarly calculated from Eq.{5) with g o t ) S being calculated from Eq. (30). 3°*>s ~ JjgaH" (30) where g D i s the g-factor of DPPH taken as 2.0036, z> H i s the difference i n f i e l d strength between the DPPH line and the center of the spectrum, Pis microwave frequency. Other quantities have their usual meanings. 44. Eq.<> (30) can be derived simply as fol l o w s : -F i r s t , we have U - h^J> = hhs ,6 H (31) where i s the resonance f i e l d of DPPH, and H t h e center the spectrum of the free r a d i c a l concerned„ Prom Eq. .(31), we- have US= °d H Hj> + A H ~ *M + ^  (52) where AH = H-H-p Su b s t i t u t i o n of . \ • H> ~ 2T>(3 (33). into Eq. (32) gives (30). . The angular v a r i a t i o n of the N- and N 1-hyperfine couplings at both temperatures are shown i n Pi g . 18 to Pig . 29. Some fig u r e s contain on.-ly a few points due to the f a c t that the N-hyperfine i s not resolved at a l l o r i e n t a t i o n s . The proton hyperfine s p l i t t i n g i s nearly i s o t r o p i c and not shown here. In a l l these f i g u r e s the continuous curves represent the values c a l c u l a t e d from the respective tensors shown below, and the open c i r c l e s represent the experimental points. The various tensors thus obtained are shown i n Table 5-12. It should be mentioned that there are two sets of s p l i t t i n g s f o r or i e n t a t i o n s with alH or c?-L,H, correspond-ing to two symmetry r e l a t e d s i t e s , but only one s p l i t t i n g f o r o r i e n t a t i o n with bi.H. Four combinations of these sets are p o s s i b l e . But only two gave converging r e s u l t s i n 45 : least-squares f i t t i n g . These two represent the c o r r e c t choice of the sets of data. 4.3 Discussion The c r y s t a l structure of dicyandiamide has determined by x-ray and neutron d i f f r a c t i o n (31)-(33). The molecule i s completely planar with the exception of one proton which i s located out of plane. We are therefore i n a favorable p o s i t i o n of knowing the positions of the atoms p r e c i s e l y , i n c l u d i n g the hydrogen atoms. C a l c u l a t i o n s . have been made on the d i r e c t i o n cosines of the vectors along the N-H bond, and the normal to the plane. The r e s u l t i s tabulated i n Table 13, while the l a b e l l i n g of the atoms i s shown i n F i g . 30. F i g . 30 L a b e l l i n g of atoms i n dicyandiamide„ Table 13 D i r e c t i o n cosines of the vector along the NH bond, the normal to the -C-N plane. •_ ' N D i r e c t i o n Cosines with respect to a b c .:• N 5 H 1 . K 5 V K 6 H 3 normal to.CgN^Ng -0.388763 0.676960 -0.208291 -0.557630 0.656130 0.085019 -0.639867 -0.681528 0.680037 . 0.680997 0.917408 ~C\ 363724 0.701524 -0.476024 0.325763 ft' 10 G i it 1 i j *• ]*• .—1 1 - a 0> Pig. 16, ESR spectrum of x-irradiated deuterated dicyandiamide with H having direction cosines (0.643, 0.000, 0.766) at S i t e 1 S i t e 2 ^ g . 17 ESR spectrum of x - i r r a d i a t e d dicyandiamid d i r e c t i o n cc temperature. dirpp + i o r , « • •' / " w i t h H having.-: dxrectxo* o c S 1 „ e s (-0.174, 0.985, 0.00) a t l i W H n i t r o ^ 43 l i q u i d nitrogen temperature. 49 F i g . 19. A n g u l a r v a r i a t i o n o f t h e N h y p e r f i n e s p l i t t i n g . f o r t h e r a d i c a l CNCN(NH 2)NH w i t h HJJb a t l i q u i d n i t r o g e n t e m p e r a t u r e . 50 P i g . 20. Angular v a r i a t i o n of the N" hyperfine s p l i t t i n g f o r the r a d i c a l CNCN(NH^)NH with Hie 1 ' a t J' ' ' . l i q u i d nitrogen temperature. 51 52 P i g . 22. A n g u l a r v a r i a t i o n o f the N 1 h y p e r f i n e s p l i t t i n g f o r t h e r a d i c a l C N C N ( N H £ ) N H W I T H H J L b a t . l i q i ' d . n i t r o g e n t e m p e r a t u r e . 53 H // b Pig. 2 3 . Angular v a r i a t i o n of the N 1 hyperfine s p l i t t i n g f o r the r a d i c a l CNCN(NH2 )NH with Hlc 1' at l i q u i d . n itrogen temperature. 54, 55 .".'Fig. 25. A n g u l a r v a r i a t i o n o f the N h y p e r f i n e s p l i t t i n g f o r the r a d i c a l CNCN(NH )NH w i t h HJi a t roor: t e m p e r a t u r e . .56 P i g . 26. A n g u l a r v a r i a t i o n o f the N h y p e r f i n e s p l i t t i n g f o r the r a d i c a l CNGN(NH ?)Nil w i t h H l c ' a t room . - t e m p e r a t u r e . 57 58 59 60 TABLE 5 ' g-Tensor f o r r a d i c a l NCNC(NH?)NH at l i q u i d 'nitrogen • temperatu P r i n c i p a l values D i r e c t i o n Cosines of P r i n c i p a l Axes with respect to a b c' 2 . 0 0 3 9 + 0 . 0 0 0 3 1 . 0 0 . 0 0 . 0 2 . 0 0 4 0 + 0 . 0 0 0 3 0 . 0 , 1 . 0 0 . 0 2 . 0 0 3 6 + 0 . 0 0 0 3 0 . 0 0 . 0 1 . 0 TABLE 6 . Proton hyperfine coupling tensor f o r r a d i c a l NCNC(NH2')NH at l i q u i d nitrogen temperature P r i n c i p a l values (gauss) D i r e c t i o n Cosines of with respect to P r i n c i p a l Axes a b c ' . 7 2 . 5 . + 0 . 5 1 . 0 . 0 . 0 0 . 0 7 3 . 5 + 0 . 5 0 . 0 . 1 . 0 0 . 0 7 6 . 8 + 0 . 5 OoO 0 . 0 1 . 0 • TABLE 7 N Hyperfine. Coupling Tensor f o r NCNC(NH2)NH at l i q u i d nitrogen temperature • P r i n c i p a l values (gauss) D i r e c t i o n Cosines of P r i n c i p a l Axes with respect to a b c' 7 . 2 + 0 . 6 3 1 . 7 + 0 . 6 2 . 4 + 0 . 6 0 . 7 4 4 3 - 0 . 6 . 6 6 7 ' - 0 . 0 3 9 6 + 0 . 6 5 3 6 + 0 . 7 1 4 9 + 0 . 2 4 8 3 - 0 . 1 3 7 3 - 0 . 2 1 0 7 0 . 9 6 7 8 6 1 TABLE . 8 •N1 H y p e r f i n e C o u p l i n g T e n s o r f o r NCNC(NH 2)NH a t l i q u i d n i t r o g e n t e m p e r a t u r e P r i n c i p a l v a l u e s ( g a u s s ) D i r e c t i o n C o s i n e s o f P r i n c i p a l Axes w i t h r e s p e c t t o a b c« 8 o 7 + 0 . 2 0 . 7 0 3 8 ± 0 . 5 7 9 0 V 0 . 4 1 1 8 4.9 £ 0 . 2 0 . 6 8 9 8 + 0 . 6 9 5 6 0 . 2 0 0 9 6 . 1 + 0 . 2 0 . 1 7 0 1 + 0 . 4 2 5 4 0 . 8 8 8 9 1 62 TABLE 9 g - t e n s o r f o r NCNC(NH 2)NH AT ROOM TEMPERATURE P r i n c i p a l V a l u e s D i r e c t i o n C o s i n e s o f w i t h r e s p e c t t o P r i n c i p a l Axes b c » 2 . 0 0 4 3 + 0 . 0 0 0 3 1 . 0 0 . 0 0 . 0 2 . 0 0 4 2 + 0 . 0 0 0 3 0 . 0 1 . 0 0 . 0 2 . 0 0 3 8 + 0 . 0 0 0 3 0 . 0 0 . 0 1 . 0 . TABLE 10 P r o t o n H y p e r f i n e C o u p l i n g T e n s o r f o r NCNC(NH 2)NH a t room t e m p e r a t u r e . . P r i n c i p a l v a l u e s ( g a u s s ) D i r e c t i o n C o s i n e s o f P r i n c i p a l Axes w i t h r e s p e c t t o a b c« 7 4 . 6 + 0 . 5 1 . 0 0 . 0 0 . 0 7 5 . 1 + 0 . 5 0 . 0 . 1 . 0 0 . 0 - 7 7 . 3 ' + 0 . 5 0 . 0 . . ; . 0 . 0 1 . 0 TABLE 11 — — — ft N h y p e r f i n e C o u p l i n g T e n s o r f o r NCNC(NH ?)NH a t room t e m p e r a t u P r i n c i p a l v a l u e s ( g a u s s ) D i r e c t i o n C o s i n e s o f P r i n c i p a l Axes w i t h r e s p e c t t o a b • ..' c ' . - 0 . 3 + l c 2 2 7 . 8 + 1 . 2 . 9 . 3 + 1 . 2 0 . 5 5 2 1 - 0 . 6 3 3 8 - 0 . 5 4 1 7 + 0 . 6 6 9 7 + 0 . 7 2 4 0 . + 0 . 1 6 4 2 0 . 4 9 6 3 - 0 . 2 7 2 3 0 . 8 2 4 3 63 TABLE 12 N' Hyperfine Coupling Tensor f o r NCNC(NH^)NH at room teraperat P r i n c i p a l values (gauss) D i r e c t i o n Cosines of P r i n c i p a l Axes with respect to a b c' 7 . 7 + 0 . 3 0 o 8 1 8 5 - 0 . 0 3 4 8 - 0 . 5 7 3 1 6 . 4 + 0 . 3 - 0 . 0 9 0 8 . 0 o 9 7 6 1 - 0 . 1 9 7 5 5 . 7 + 0 . 3 0.5673 0 . 2 1 3 7 0 . 7 9 5 3 * Site s p l i t t i n g s not resolved. 6 4 The experimentally derived symmetry axes of the s i n g l y occupied p o r b i t a l are along. (-0.6667, 0.7149, -0.2107) at l i q u i d nitrogen temperature (Table 8) or (-0„6338, 0.7240,' -0 02723) at room temperature (Table 11). Compari-son of these d i r e c t i o n cosines with those shown i n Table 13 shows that the p-rorbital'symmetry axes was nearly per-pendicular to the CgN^Ng plane. . ' -.It would be i n t e r e s t i n g to compare these c a l c u l a t i o n s with s i m i l a r calculations . on the malonamide r a d i c a l , HgN.COCHgCONH (9 ) , which had been postulated as a ^ - e l e c -tron, r a d i c a l . . At the time when the ESR work on i r r a d i a t e d malonamide was undertaken, no c r y s t a l l o g r a p h i c data were a v a i l a b l e . C r y s t a l structure f o r malonamide has since been determined. (34). i After, comparing the d i r e c t i o n - o f the unpaired p-o r b i t a l symmetry.axis i n the malonamide ^ - e l e c t r o n r a d i c a l with bond d i r e c t i o n s , and the d i r e c t i o n normal to the -JJ5-N planes, i t was found that the p o r b i t a l symmetry a x i s pointed along an N-H bond. This c a l c u l a t i o n suggests that the r a d i c a l i s indeed a o^-electron r a d i c a l . i t should be noticed that these two r a d i c a l s (mal-onamide o""-electron r a d i c a l and dicyandiamide r a d i c a l ) , while having s i m i l a r ESR hyperfine coupling tensors could very w e l l be d i f f e r e n t i n the sense that the unpaired e l e c - v t r o n occupies d i f f e r e n t type of MO's. This point w i l l be discussed f u r t h e r i n Chapter 5 . 65 Another point worthy of note i s the temperature v a r i a t i o n of the hyperfine s p l i t t i n g i n the dicyandiamide r a d i c a l . It was noticed that at room temperature the outer l i n e s of the N " s p l i t t i n g were much broader that the c e n t r a l . l i n e , and that at l i q u i d nitrogen temperature a l l three l i n e s had the same l i n e w i d t h 0 This could be due to the motion of the EH bond ( F i g . 51)o Depending on t h e : p o s i t i o n of H, N hyperfine i n t e r a c t i o n s may be F i g . 31 At room temperature the proton i n NH group assuming d i f f e r e n t positions i n the cone. d i f f e r e n t . .The room temperature spectrum i s , therefore, the sum of spectra which have the same proton hyperfine i n t e r a c t i o n and d i f f e r e n t N hyperfine i n t e r a c t i o n . This explanation i s somewhat substantiated by an INDO c a l c u l a t i o n on HCONH model r a d i c a l . It i s found that when NH assumes d i f f e r e n t positions of the cone, the spin d e n s i t i e s on the N atom are d i f f e r e n t and hence have d i f f e r e n t N hyperfine i n t e r a c t i o n s . 66 Among other, v a r i a t i o n s i n the change o f t e m p e r a t u r e , the decrease i n N hyperfine s p l i t t i n g (A// from 31.7 to 27.8 G-, Aj_from 4.8 to 4.5 G) should be noted 0 C a l c u l a t i o n shows that v a r i a t i o n due to a change i n the in t e r n u c l e a r distances by thermal expansion (or contraction) i s neg-l i g i b l e . " From the experimental r e s u l t s given i n Table 5 to .12, the s p i n density d i s t r i b u t i o n s can. be c a l c u l a t e d by the method described i n l a s t chapter. Table (14) shows, •the r e s u l t of t h i s c a l c u l a t i o n assuming that the N- and the N'- hyperfine tensors are a x i a l i y symmetric taking .the l a r g e s t experimental p r i n c i p a l value to be Ajj, t and the average of the two smaller experimental p r i n c i p a l . values to be Ax. "/; Table 14 Spin Density d i s t r i b u t i o n s of NCNC(NH9)NH • r a d i c a l at room and l i q u i d nitrogen \ temperature H N . N' s s P s P Spin density d i s -t r i b u t i o n at l i q u i d n itrogen tempera-ture ~ 0.146 0.024 0.502 0.002 0.064 Spin density d i s -t r i b u t i o n at room temperature 0.148 0.022 0.455 0.002 0.022 • CHAPTER 5 ' MO CALCULATIONS . \.r-'o-.-In order to i n v e s t i g a t e the e f f e c t of the p o s i t i o n of the proton i n RNH type r a d i c a l on the spin density at the proton, a s e r i e s of MO c a l c u l a t i o n s was .performed on a model compound, HCONH, the p o s i t i o n of the proton varying as shown i n P i g . 32. F i r s t of a l l , the p o s i t i o n of the proton was v a r i e d i n the molecular plane from +y d i r e c t i o n to -y d i r e c t i o n , with step s i z e 30° ( P i g . 32a); the conformations were .labelled . from ( l ) to (7). Secondly, the proton was .rotated about ON axis f o r each of the s t a r t -i n g p o s i t i o n s (1), (2), and (3) to generate c i r c l e s or cones shown i n P i g . 32 (b), (c) and (d) respectively.; each conformation being l a b e l l e d as shown i n the f i g u r e s . e i c a l with the proton assuming various p o s i t i o n s on a hem-isphere with N being the center and NH bond length being the radius . '•: . -'.' . - • . -,.v.'---: ...... The semi-empirical MO theory used was the s o - c a l l e d IND0-SCP-LCA0, described i n 2.3.. Except where s p e c i a l l y mentioned, the MO was u n r e s t r i c t e d , with spi n p r o j e c t i o n ; A l l bond lengths were taken from Pople's paper (22), and. the bond angles H^CO, OCN, and H^GN were a l l taken to be 120°. • ' " The v a r i a t i o n i n the s p i n density at H^ with change i n conformations i s shown i n Pi g . .33-36, together with the change i n e l e c t r o n i c energies, and the energy d i f f e r -ences between the s i n g l y occupied molecular o r b i t a l s and -the highest doubly-occupied MO, t h i s energy d i f f e r e n c e 6 9 being c a l c u l a t e d from the r e s t r i c t e d M0o The change i n the spin density at seems not to c o r r e l a t e with change i n the o r b i t a l energy d i f f e r e n c e , or with the t o t a l e l e c t r o n i c energy, e s p e c i a l l y i n the case when the plane formed by CNH^ i s perpendicular to the plane formed by HgCO, where the spin density at H-^  i s minimum. It should be noted that the spin d e n s i t i e s at H^ i n some conformations are as high as three times those of the other conformations, and that conformation with |iigh s p i n density on comes with high energy. However, the conformation with min. energy i n an i s o l a t e d r a d i c a l i s not n e c e s s a r i l y that i n the c r y s t a l l i n e s t a t e , since hydrogen bondings, or other c r y s t a l l i n e forces may con-t r i b u t e to a large extent. Hence, i t i s possible that the conformations with high spin density may e x i s t i n the c r y s t a l l i n e state* Some c a l c u l a t i o n s were c a r r i e d out on the urea rad-ical,'HgNCONH, which shows that same pattern of change, namely that the spi n density on the proton v a r i e s with the p o s i t i o n of the proton. It i s i n t e r e s t i n g to point out that the spin density on the proton i n HCONH and that . i n NHgCONH at the same conformation ( r e f e r to the p o s i t i o n of NH r e l a t i v e to the rest of the r a d i c a l ) are s i m i l a r in magnitude. That .is.,' i n the RCONH type r a d i c a l s , the i n -fluence of R, through inductive and s t e r i c e f f e c t , i s E( ev ) 70 -)CSo .•-WW -013 • on - 6°7 (^-(spin density on. H) P i g . 3 3 . Change - i n e l e c t r o n i c e n e r g y and' s p i n -: . d e n s i t y a t PI w i t h c o n f o r m a t i o n . ( I J J I I I J L |: L_ 1 2 5 4 5 6 7 r 6 3 1 0 1 2 7 -71 E(ev) I 2 F i g . 35. Change.in energy 'differences between the s i n g l y occupied MO and the highest f u l l y • occupied MO with conformations,, :. hco] h 000 J I l l L 1 I _ l l l 1 C 1 J J 1 2 . 3 4- Is 6 7 / & 9 10 I' i£ 7 73 Pi g . 3.6 . Change i n energy differences between the s i n g l y occupied MO and the highest • f u l l y occupied MO with conformations. E(T) -E(cr) (ev) r h'P-c-2 L-c o£ 0.0 I L O.oc 1 £ 13 l4r /$ 0 not an important factor,. What i s the determinant f a c t o r i s the p o s i t i o n of the proton r e l a t i v e to the re s t of the r a d i c a l . The above conclusion i s on a semi-empirical c a l c u l a t i o r with a set of empirical parameters which f i t s best the-4 r a d i c a l s Pople and h i s coworkers chose. This set of para-meters may not be the most s u i t a b l e one i n our case. INDO-SCF-LCAO c a l c u l a t i o n was also performed on the cyanoacetic a c i d r a d i c a l , NCCHCOCT, whose nitrogen hyperfine coupling has been determined (29), and i s s i m i l a r to that of NCCHCONHCONHg. In t h i s c a l c u l a t i o n , a l l bond lengths were taken from Pople's paper (22), and the bond angles were as shown i n F i g . 36. 0 1 2 0 120' "0 F i g . 37 The l a b e l l i n g , coordinates, and bond angles i n i n cyanoacetic a c i d r a d i c a l used i n the c a l c u l a t i o n . The r e s u l t of the spin density d i s t r i b u t i o n thus c a l c u l a t e d i s p a r t i a l l y reproduced i n Table 15; Table 15 Spin density d i s t r i b u t i o n ( a f t e r s p i n projection) of cyanoacetic a c i d r a d i c a l . 2s 2p *x 2 p y • 2p ' °2 0.007775 0.006705 0.008398 0.226998 C 3 -0.012634 -0.045825 -0.020781 -0.096850 N 0.005337 0.059913 0.023483 0.381224 — — From the r e s u l t i n Table 15, the i s o t r o p i c hyperfine coupling of N i s As=550.jJs = 550(0.00533^) = 2.9 G herej' i s the spin density of 2s at N atom. The a n i s o t r o p i c hyperfine coupling components of N along z d i r e c t i o n (Ajj) and perpendicular to i t (Ax) are: AII = 34.28(0.381224) = 13.1 G A J_ = -17.14(0.381224) = -615 G r e s p e c t i v e l y . In the c a l c u l a t i o n of a n i s o t r o p i c coupling'-due to the N atom the c o n t r i b u t i o n of other atoms and bonds are neglected. Table 16 summarizes the c a l c u l a t e d and the exp e r i -mentally determined hyperfine coupling tensor of the N nucleus. Table 16 Hyperfine coupling tensor of the N nucleus. A s All Ax Calculated Experimental 2.9 3.0 13.1 8.1 -6.5 , -4.1 CHAPTER 6 CONCLUSION ° I n summary, the RNH type r a d i c a l s although only f i v e have so f a r been reported, show very d i f f e r e n t e l e c -t r o n i c s t r u c t u r e s . While HCONH i n the s o l u t i o n phase and CP^CPgCONH s i n g l e c r y s t a l s have proton hyperfine cou-p-; i i t i g a t y p i c a l of TT-electrons, H2NC0CH2C0NH, CNCHgCONHCONH and N C N C ( N H 2 ) N H have very large and i s o t r o p i c proton hyper-f i n e coupling. In t h i s t h e s i s , the l a t t e r two r a d i c a l s (and a R C H C O R ' r a d i c a l CNCHCONHCONH 2 as well) were studied i n s i n g l e c r y s t a l i n d e t a i l ; furthermore, the p o s s i b i l i t y of large i s o t r o p i c hyperfine s p l i t t i n g of proton was i n -v e s t i g a t e d by . rXNBO-SCP-I iCAO' c a l c u l a t i o n s , and by the com-parion of the d i r e c t i o n of the unpaired, p - o r b i t a l symmetry axi s with bond d i r e c t i o n s , and normals to the fragment planes. It may be concluded that while malonamide rad-i c a l , H2NC0CH2C0NH, i s a ^ e l e c t r o n r a d i c a l , dicyandiamide r a d i c a l , N C N C ( N H 2 ) N H , . i s most l i k e l y a TT-electron r a d i c a l , with the unpaired e l e c t r o n perpendicular to the N C N plane; unfortunately, c r y s t a l l o g r a p h i c data f o r cyanoacetylurea i s not a v a i l a b l e and no conclusion can be made. INDO-S C P - L C A O c a l c u l a t i o n s on a model compound, HCONH, with the proton assuming d i f f e r e n t p o s i t i o n s suggest that, even i n the case of the unpaired e l e c t r o n being i n a T-MO with respect to C O N plane, when the proton assumes a n out-of -plane p o s i t i o n , the i s o t r o p i c hyperfine coupling 77 of the proton can be as large as three times that which i t assumes an in-plane p o s i t i o n . • BIBLIOGRAPHY 1 . J . R. Morton, Chem. Rev., 64, 453 (1964) 2 B. R. 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