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DETERMINATION BY POLARIZED NEUTRON DIFFRACTION OF THE SPIN DENSITY
DISTRIBUTION IN A
NON-CENTROSYMMETRICAL CRYSTAL OF DPPH : C6H6
J. Boucherle, B. Gillon, J. Maruani, J. Schweizer
To cite this version:
J. Boucherle, B. Gillon, J. Maruani, J. Schweizer. DETERMINATION BY POLARIZED NEUTRON DIFFRACTION OF THE SPIN DENSITY DISTRIBUTION IN A NON-CENTROSYMMETRICAL CRYSTAL OF DPPH : C6H6. Journal de Physique Colloques, 1982, 43 (C7), pp.C7-227-C7-234.
�10.1051/jphyscol:1982731�. �jpa-00222338�
DETERMINATION BY POLARIZED NEUTRON DIFFRACTION OF THE SPIN DENSITY DISTRIBUTION IN A NON-CENTROSYMMETRICAL CRYSTAL OF DPPH:C6H6
J.X. Boucherle*, B. Gillon ** J . Maruani** and J . Schweizer*
+*DRF/DN, CENG, B.P. 85X, 38041 Grenoble Cedex, France
+ ILL, B.P. 158X, 38042 Grenoble Cedex, France
**CMOA, 23 rue du Maroa, 75019 Paris, France
Résumé. - La d e n s i t é de spin du r a d i c a l l i b r e DPPH (diphenylepicrylehydrazyle) a été étudiée dans l a forme c r i s t a l l i s é e DPPH:C6Hg, avec l e s moments paramagnétiques o r i e n - t é s , à basse température, par un champ magnétique e x t é r i e u r . Comme l a s t r u c t u r e c r i s t a l l i n e est non centrosymétrique, i l n ' e s t pas possible d ' o b t e n i r directement l e s f a c t e u r s de s t r u c t u r e magnétiques a p a r t i r des rapports de "flipping" mesurés par d i f f r a c t i o n de neutrons p o l a r i s é s . Pour c e t t e r a i s o n , l a d e n s i t é de spin a é t é représentée par un développement m u l t i p o l a i r e sur chaque atome. Les paramètres de ce développement sont déterminés directement par une comparaison avec l e s rapports de
"flipping" mesurés.
La plus grande p a r t i e de l a densité de spin est partagée entre l e s deux atomes d'azote du groupe hydrazyl (N
aet Ng) . La p a r t i e r e s t a n t e est d é l o c a l i s é e sur l e s 2 cycles phenyl et sur l e cycle p i c r y l . Ces r é s u l t a t s sont comparés aux mesures de résonance magnétique.
Abstract. - The spin d e n s i t y of the free r a d i c a l DPPH (diphenylpicrylhydrazyl) has been studied in the c r y s t a l l i z e d form DPPH CgHg with the paramagnetic moments
orientated, a t low temperature, by an external magnetic f i e l d . As the c r y s t a l s t r u c t u r e i s not centro-symmetrical, i t i s not possible to obtain d i r e c t l y the magnetic s t r u c - t u r e factors from the experimental f l i p p i n g r a t i o s measured by polarized neutron d i f f r a c t i o n . For t h i s reason we have represented the spin density by a multipole ex- pansion on the d i f f e r e n t atons, and determined d i r e c t l y the parameters of t h i s expan- sion by comparing with the observed flipping r a t i o s .
A large amount of the spin density i s shared between the 2 nitrogen atoms (% and Ng) of the hydrazyl group. The remaining part i s delocalized on the 2 phenyl and the p i c r y l r i n g s . These r e s u l t s are compared to magnetic resonance d a t a .
1. Introduction. - The s t a b l e aromatic free r a d i c a l a,a-diphenyl (3-picryl hydrazyl (DPPH) was among the f i r s t paramagnetic species investigated by electron spin r e s - onance (ESR) [ 1 ] , and i t s remarkable chemical s t a b i l i t y and narrowness of i t s r e s - onance l i n e have made i t a widespread standard for measuring unpaired spin concen- t r a t i o n s and effective gyromagnetic r a t i o s [ 2 ] . DPPH c r y s t a l l i z e s in several d i f f e r - ent forms, with [3a] or without [3b] the inclusion of solvent molecules. Complete X-ray determination of the c r y s t a l s t r u c t u r e a t room temperature was f i r s t performed on the best grown c r y s t a l form, the DPPH : C^Hg complex [ 4 ] , and l a t e r extended to acetone-containing DPPH c r y s t a l s [ 5 ] , revealing in both cases a r a t h e r twisted con-
formation (Fig. 1, t a b l e I I ) . O
Fig. 1 - Overall view of DPPH s t r u c t u r e as deduced from neutron d i f f r a c t i o n data a t
10K (paragraph 3)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982731
JOURNAL DE PHYSIQUE
The DPPH molecule i s one of t h e most widely i n v e s t i g a t e d molecules u s i n g mag- n e t i c resonance techniques[6]. ESR measurements on d i l u t e s o l u t i o n s have mainly y i e l d e d t h e h y p e r f i n e c o u p l i n g s of t h e c e n t r a l n i t r o g e n atoms i n a l a r g e v a r i e t y of p h y s i c a l c o n d i t i o n s . Both t h e c o n t a c t and d i p o l a r p a r t s of t h e s e couplings have been shown t o depend s i g n i f i c a n t l y on t h e s o l v e n t composition, r i g i d i t y and s t r u c t u r e , and t h e s p i n d e n s i t i e s t o be almost a s l a r g e on t h e n i t r o g e n l i n k e d t o t h e twophenyls a s on t h e n i t r o g e n l i n k e d t o t h e p i c r y l [7]. Nuclear magnetic resonance (NMR) of con- c e n t r a t e d samples has e s s e n t i a l l y provided t h e magnitudes and s i g n s of t h e h y p e r f i n e couplings of t h e r i n g p r o t o n s [8] and of t h e p i c r y l n i t r o g e n s [ 9 ] , r e v e a l i n g an e x t e n s i v e s p i n d e l o c a l i z a t i o n and p o l a r i z a t i o n on t h e whole molecule. Contact hyper- f i n e c o u p l i n g s have been determined most a c c u r a t e l y by e l e c t r o n - e l e c t r o n double resonance (ELDOR) f o r t h e hydrazyl n i t r o g e n s [ l ~ l and by e l e c t r o n - n u c l e a r double resonance (ENDOR) f o r t h e r i n g protons [ I l l . The hydrazyl n i t r o g e n s appear t o s h a r e about 70 % of t h e t o t a l s p i n d e n s i t y , t h e remaining p a r t being d e l o c a l i z e d on t h e 2 phenyl and t h e p i c r y l r i n g s , w i t h a l t e r n a t i n g p o s i t i v e and n e g a t i v e s i g n s on t h e r i n g carbons, i n agreement w i t h quantum mechanical c a l c u l a t i o n s L I Z ] .
One remarkable f e a t u r e of t h e magnetic resonance r e s u l t s f o r t h e h ~ d r a z y l n i t r o g e n s i s t h a t t h e i r h y p e r f i n e coupling t e n s o r s appear c o n s i s t e n t l y q u a s i a x i a l and n e a r l y p a r a l l e l [7], whereas, i n t h e few c a s e s where t h e exact molecular geometry has been determined from X-ray d i f f r a c t i o n d a t a [4,5], t h e corresponding t r i g o n a l planes a r e a t an a n g l e c l o s e t o 30'.
Table I shows some s e t s of v a l u e s obtained f o r t h e h y p e r f i n e c o u p l i n g s of DPPH under v a r i o u s c o n d i t i o n s . The f i r s t column summarizes t h e most a c c u r a t e v a l u e s measured f o r t h e c o n t a c t couplings u s i n g a p p r o p r i a t e techniques. The second column r e c a l l s t h e v a l u e s measured i n d i l u t e g l a s s y samples by ESR [7bl and i n pure c r y s t a l l i n e powders by NMR [8a]. The t h i r d column p r o v i d e s t h e corresponding v a l u e s f o r DPPH : CgHg i n d i l u t e [ 7 a , c ] o r pure [8c] c r y s t a l s . The s i g n s and assignments a r e confirmed by t h e t h e o r e t i c a l r e s u l t s g i v e n i n t h e f o u r t h column ; h e r e , we have used t h e UHF s p i n p o p u l a t i o n s pn c a l c u l a t e d f o r a n extended s t r u c t u r e [12bl t o g e t h e r with t h e semi- e m p i r i c a l r e l a t i o n s :
with t h e s p i n p o l a r i z a t i o n c o n s t a n t s :
A s has been shown f o r n i t r o x i d e f r e e r a d i c a l s [ 1 4 ] , t h e d i r e c t d e t e r m i n a t i o n of t h e s p i n d e n s i t y d i s t r i b u t i o n by n e u t r o n d i f f r a c t i o n techniques can r e v e a l new and important r e s u l t s , complementary t o t h o s e o b t a i n e d w i t h magnetic resonance techniques.
Contrary t o n i t r o x i d e r a d i c a l s , where t h e s p i n d e n s i t y i s c o n c e n t r a t e d on t h e N-0 group, DPPH o f f e r s a c a s e of l a r g e d e l o c a l i z a t i o n , w h i c h makes i t a s t i m u l a t i n g c h a l - lenge f o r neutron d i f f r a c t i o n . Unfortunately, a l l t h e c r y s t a l forms of DPPH a r e non- centrosymmetrical and t h i s h a s prevented any s t u d y with p o l a r i z e d neutrons t o be done so f a r .
Recently a new t e c h n i q u e f o r d a t a r e d u c t i o n has been proposed [15], which makes use of a m u l t i p o l a r expansion f o r t h e s p i n d e n s i t y . This method makes i t p o s s i b l e t o s t u d y non-centrosymmetrical c r y s t a l s by p o l a r i z e d neutron d i f f r a c t i o n . We have undertaken such an experiment on a DPPH s i n g l e c r y s t a l , t h e r e s u l t s of which a r e r e p o r t e d i n t h i s p a p e r .
I n t h e following: S e c t i o n we show how m u l t i p o l a r e x ~ a n s i o n s
-
make i t p o s s i b l e t o measure s p i n d e n s i t i e s i n non-centrosymmetrical c r y s t a l s . S e c t i o n 3 d e s c r i b e s t h e d e t e r m i n a t i o n of t h e c r y s t a l s t r u c t u r e of t h e DPPH:C6H6 complex using unpolarized neutron d i f f r a c t i o n . I n S e c t i o n 4 we d e s c r i b e t h e p o l a r i z e d neutron experiments and t h e d e r i v a t i o n of s p i n d e n s i t y maps. I n t h e l a s t S e c t i o n we d i s c u s s t h e r e s u l t s of neutron d i f f r a c t i o n i n r e l a t i o n t o those of magnetic resonance.T a b l e I : C o n t a c t h y p e r f i n e c o u p l i n g a ( i n Gauss) o f t h e n i t r o s e n and hydrogen n u c l e i i n DPPH ( t h e numbersof n u c l e i a r e g i v e n i n p a r e n t h e s i s ) .
I
-
ELDOR [ l o ] and ENDOR [ I l l do n o t p r o v i d e t h e c o u p l i n g s i g n s whereas NPR [ 9 ] does 11, 111-
For N a , ~ one o b t a i n s a l s o t h e d i p o l a r c o u p l i n g b ( i n Gauss) by ESR [ 7 a , b l and f o r t h e H ' s , t h e i n t e r m e d i a t e v a l u e o f t h e a n i s o t r o p i c t e n s o r by NMR [ 8 a , c l . The measured v a l u e s f o r t h e h y p e r f i n e c o u p l i n g s o f t h e h y d r a z y l n i t r o g e n s r a n g e from a=6.3, b=5.0 t o a=8.7, b=7.0 f o r Na and a=9.4, b=5.0 t o a=13.0, b=8.0 f o r Ng [61.I V
-
UHF c a l c u l a t i o n f o r p l a n a r DPPH.2. Measurement o f s p i n d e n s i t y d i s t r i b u t i o n s i n non-centrosymmetrical c r y s t a l s
-
M u l t i p o l a r expansion
The n e u t r o n i n t e n s i t y o f a Bragg r e f l e c t i o n f o r a magnetic m a t e r i a l c o n t a i n s b o t h t h e n u c l e a r s t r u c t u r e f a c t o r FN and t h e magnetic s t r u c t u r e f a c t o r FM. A c c u r a t e d e t e r - m i n a t i o n s o f magnetic s t r q l c t u r e f a c t o r s a r e u s u a l l y performed w i t h p o l a r i z e d n e u t r o n s and t h e f l i p p i n g r a t i o t e c h n i q u e . One measures, f o r each r e f l e c t i o n , t h e r a t i o R ob- t a i n e d f o r two n e u t r o n s p i n s t a t e s up and down
I f t h e n u c l e a r c r y s t a l s t r u c t u r e o f t h e sample under i n v e s t i g a t i o n h a s b e e n determined, t h e n t h e n u c l e a r s t r u c t u r e f a c t o r FN i s known and hence FM may b e deduced from
measurement o f R .
I n t h e c a s e o f c e n t r o symmetrical c r y s t a l s , f o r which FN and FM a r e r e a l , FM i s ob- t a i n e d by s o l v i n g e q u a t i o n ( 2 ) . I n t h e c a s e of non-centrosymmetrical c r y s t a l s , b o t h FN and FM a r e complex q u a n t i t i e s
[ 7 b l 7.6 (b=5.9) 9.9 (b-7.8)
[ g a l -2.2 ( x4) -1.3 ( x2)
+ 0 . 6 ( x4)
- - -
+ 1 . 4 ( x2)
[ 7 a , c l 6 . 3 (b=6.3) 13.0 (b=7.3)
[ 8 c l -2.6 ( x3)
( x 3 ) + 0 . 6 ( x2) + 1 . 1 ( x 2 )
+ 1 . 6 ( x 2 ) Hydrazyl
n i t r o g e n s
phenyl p r o t o n s
p i c r y l p r o t o n s
P i c r y 1 , n i t r o g e n s
and t h e e x p r e s s i o n f o r t h e f l i p p i n g r a t i o becomes : I101
7 ' 9 3 9.74 [ I l l 2 ' 0 1 ( x2) 1.90 ( x4) Oe6' ( x2) 0.75 ( x2)
1 - 0 2 ( x l ) 1 . 1 2 ( x 1 )
[91 -0.39 ( x l ) -0.48 ( ~ 2 )
C12bl +8.11 +9.24
11
3 a l -1.89 ( x2) -1.79 ( x2) -1.64 + 0 . 8 6 ( x2) +0.91 ( x 2 ) + 0 . 8 7 ( x 2 )[13bl -0.24 ( x3)
-
N a N~
EI o r t h o o u t e r H o r t h o i n n e r ( x 2 ) H p a r a
H meta i n n e r H m e t a o u t e r
- -
H m e t a
N
JOURNAL DE PHYSIQUE
The measurements o f R a l o n e c a n n o t p r o v i d e a knowledge o f t h e two unknown q u a n t i t i e s F h and Fi. To overcome t h i s d i f f i c u l t y we p r o p o s e t o a p p l y a model which p r o v i d e s a n a n a l y t i c a l d e s c r i p t i o n o f t h e s p i n d e n s i t y . We have chosen a n e x p a n s i o n o f t h e d e n s i - t y around t h e n u c l e i a t r e s t . Such a model, f i r s t used t o r e p r e s e n t c h a r g e d e n s i t i e s , h a s a l r e a d y proved t o b e v e r y w e l l a d a p t e d i n t h e c a s e o f s p i n d e n s i t i e s i n c e n t r o - symmetric c r y s t a l s . The expansion c o n s i s t s o f a s u p e r p o s i t i o n o f a s p h e r i c a l a t o m i c d e n s i t i e s , each d e s c r i b e d by a s e r i e s e x p a n s i o n i n r e a l s p h e r i c a l harmonic f u n c t i o n s :
The PR, a r e p o p u l a t i o n c o e f f i c i e n t s . The r a d i a l f u n c t i o n s R R ( r ) a r e o f S l a t e r t y p e :
The magnetic s t r u c t u r e f a c t o r s c o r r e s p o n d i n g t o e q s . (1) become
2aiEi.G R
F ~ ( $ ) =
1
e1
@R(H)1
PRm yRm(fi) eatoms m=-9.
03 2
w i t h mR(H) = 4 a i R J R,,r) j R ( 2 n H r ) r d r
I
-w0
To e s t a b l i s h t h e s p i n d e n s i t y map, t h e s e t o f p a r a m e t e r s ( 5 , P &m ) which c h a r a c t e r i z e t h e s p i n d e n s i t y and f i t t h e e x p e r i m e n t a l d a t a must be d e t e r m l n e d . To do t h i s , g i v e n a s e t o f p a r a m e t e r s , FA and FS, a r e c a l c u l a t e d and a v a l u e
Real
f o r t h e f l i p p i n g r a t i o o f e a c h measured r e f l e c t i o n i s o b t a i n e d from e q u a t i o n s ( 3 ) . By comparingReal
w i t h t h e measured f l i p p i n g r a t i o s Robs i t i s p o s s i b l e t o r e f i n e t h e p a r a m e t e r s ( 6 , PL,) which b e s t f i t t h e d a t a .3 . The c r y s t a l s t r u c t u r e o f t h e DPPH:CbH6 complex
DPPH i s paramagnetic and i t s magnetic s u s c e p t i b i l i t y f o l l o w s a C u r i e law, w i t h a magnetic moment o f 1 )Ig p e r m o l e c u l e . For t h e p r e s e n t i n v e s t i g a t i o n , o n e i n t e n d s t o measure t h e m a g n e t i c a m p l i t u d e FM (F = F' + iF") s c a t t e r e d by t h e component of t h e
M M M
magnetic moment a l i g n e d by a n e x t e r n a l m a g n e t i c f i e l d , and compare i t w i t h t h e nu- c l e a r a m p l i t u d e FN (F = F' + i ~ i ) s c a t t e r e d by a l l t h e n u c l e i o f t h e DPPIS m o l e c u l e . The magnetic moment i s smarl compared t o t h e n u c l e a r s i g n a l , and o n l y p a r t of i t i s N a l i g n e d by t h e f i e l d . To o b t a i n a d e g r e e o f a l i g m i e n t l a r g e enough t o make t h e magnetic s i g n a l measurable, i t i s n e c e s s a r y t o perform t h e n e u t r o n d i f f r a c t i o n ex- p e r i m e n t a t v e r y low t e m p e r a t u r e , i n o r d e r t o t a k e a d v a n t a g e of t h e i n c r e a s e o f s u s c e p t i b i l i t y w i t h d e c r e a s i n g t e m p e r a t u r e .
A t v e r y low t e m p e r a t u r e s , however, t h e s t a t i c s u s c e p t i b i l i t y r e v e a l s s t r o n g de- v i a t i o n s from t h e C u r i e law, due t o a n t i f e r r o m a g n e t i c exchange c o u p l i n g between ad- j a c e n t m o l e c u l e s : f o r p u r e DPPH c r y s t a l s a maximum o c c u r s around 10K [17a], whereas f o r t h e DPPH-C6H6 complex (where t h e f r e e r a d i c a l s a r e k e p t a p a r t by t h e benzene m o l e c u l e s ) t h e s u s c e p t i b i l i t y r e a c h e s a maximum around 1K [17b] ( s e e F i g u r e 2 ) . This l a t t e r form i s t h e r e f o r e b e t t e r s u i t e d f o r a p o l a r i z e d n e u t r o n s t u d y made a t t h e helium t e m p e r a t u r e T = 4.2K.
As a l l o t h e r forms of DPPH, t h e DPPH:C H complex i s non-centrosymmetrical : i t s s p a c e group i s PC w i t h 2 m o l e c u l e s of b o t k $PPH and C H i n t h e c r y s t a l c e l l (Z = 2 ) . For t h e s p i n d e n s i t y d e t e r m i n a t i o n , t h e c r y s t a l s t r u c k r e , a s d e t e r m i n e d a t room 6 t e m p e r a t u r e by X-rays [41 i s n o t a c c u r a t e enough. I n p a r t i c u l a r one h a s t o know t h e l o c a t i o n o f t h e hydrogen n u c l e i and a l s o t h e e x a c t v a l u e s o f a l l t h e t h e r m a l Dara-
DPPH solvent free 0
Pig. 2
-
Magnetic s u s c e p t i b i l i t yx
a s a f u n c t i o n of t h e i n v e r s e of t h e temperature 1/T f o r DPPH s o l v e n t f r e e and f o r t h e DPPH:C6H6 complexC
17a,bl2
meteys a t t h e temperature f o r which t h e s p i n d e n s i t y i s measured. For t h i s r e a s o n , we have f i r s t undertaken a low temperature unpolarized n e u t r o n c r y s t a l s t u d y , on a DPPH-C6H6 s i n g l e c r y s t a l .
This experiment was performed on t h e 4 c i r c l e d i f f r a c t o m e t e r Dl5 of t h e ILL. The temperature, produced by a two s t a g e r e f r i g e r a t o r , was 10K. The l a t t i c e c o n s t a n t s a t t h i s temperature a r e r e p o r t e d i n Table 11- 1270 independent r e f l e c t i o n s were
c o l l e c t e d and c o r r e c t e d f o r a b s o r p t i o n . We have r e f i n e d t h e p o s i t i o n s and a n i s o t r o p i c thermal parameters of a l l atoms i n t h e c e l l . The f i n a l weighted agreement f a c t o r f o r a l l r e f l e c t i o n s was 3.6 %.
The main f e a t u r e s of t h e c r y s t a l s t r u c t u r e t h u s measured a r e s i m i l a r t o t h o s e r e p o r t e d by Williams ( F i g . 1, Table 11). The main d i f f e r e n c e between t h e 2 s e t s of r e s u l t s i s i n a s y s t e m a t i c c o n t r a c t i o n o f bond l e n g t h s a t 10K. The d e v i a t i o n from p l a n a r i t y of t h e environment of N i s about 3". The 2 phenyl r i n g s a r e completely p l a n a r , b u t w i t h d i f f e r e n t t w i s t t n g l e s w i t h r e s p e c t t o t h e N p l a n e .
a
DPPH- CSH6
-
al u ua u c
-rl u U
u ua rd G
d o
L:
u
a,
2
rd P
rl
phenyl c7/C7NaC
14.9'
picryl/NaNBC1 32.9" 33.7O
Table I1 : L a t t i c e c o n s t a n t s , bond l e n g t h s , p l a n a r a n g l e s and d i h e d r a l a n g l e s defin- i n g t h e s t r u c t u r e of DPPH s y n c r y s t a l l i z e d with C6H6 a s determined by X-rays a t room temperature [41 and by neutrons a t 10 K .
Referenee C41 7.764 10.648
;i
14.780
ii
109.05' 1.334
1;
1.422
fi
1.419
;i
1.370 121.8"
115.1' 118.5' a
b
C
6
-
N~Na - C7 N a
-
C13 N-
C1B
C7Na N~
1 3NaNt3 N a N ~ C 1
This work 7.542
;i
10.416 14.295
1
108 .80°
1.318 1.416 1.395
;i
1.337
;i
121.7' 116.3"
119.2"
33.6'
C7-232 JOURNAL DE PHYSIQUE
F i n a l l y , a s i t was r e p o r t e d L41 t h a t a c e r t a i n amount of benzene may e v a p o r a t e from t h e mixed c r y s t a l s , we have r e f i n e d t h e e x a c t s t o i c h i o m e t r y of t h e C6H6 mole- c u l e s , and found e x a c t l y 1 : l . As o u r c r y s t a l s had been s t o r e d a t -20°C, we concluded t h i s was enough t o p r e v e n t e v a p o r a t i o n .
4 .
P o l a r i z e d n e u t r o n measurements and d a t a t r e a t m e n tTIie p o l a r i z e d n e u t r o n experiment was performed a t a t e m p e r a t u r e o f 4.2K, w i t h a n a p p l i e d magnetic f i e l d of 4.65T p r o v i d e d by a cryomagnet on t h e D3 d i f f r a c t o m e t e r o f t h e ILL Grenoble. The wavelength o f t h e n e u t r o n beam was 0.90 &. The sample was a singl: c r y s t a l o f DPPH:C6H6, o f dimensions 1 x 2 ~ 6 mm, w i t h t h e l o n g dimension c l o s e t o t h e a a x i s o f t h e c e l l . The c r y s t a l was o r i e n t e d w i t h t h i s a x i s v e r t i c a l , pax- a l l e l t o t h e magnetic f i e l d . The f l i p p i n g r a t i o s o f 425 i n e q u i v a l e n t Bragg r e f l e c - t i o n s were measured, l i f t i n g when n e c e s s a r y t h e c o u n t e r above t h e h o r i z o n t a l p l a n e t o measure i n l a y e r s o t h e r t h a n t h e z e r o l a y e r .
The t r e a t m e n t o f t h e f l i p p i n g r a t i o s was conducted a s e x p l a i n e d i n S e c t i o n 11.
The s p i n d e n s i t y was expanded i n atomic m u l t i p o l e s a c c o r d i n g t o r e l a t i o n ( 4 ) , and t h e p a r a m e t e r s 5 and Pim were r e f i n e d . E x p e r i m e n t a l c o r r e c t i o n s due t o i m p e r f e c t p o l a r i z a t i o n and f l i p p l n g e f f i c i e n c y , X/2 c o n t a m i n a t i o n and n u c l e a r p o l a r i z a t i o n of hydrogen atoms w e r e . i n c l u d e d , modifying s l i g h t l y r e l a t i o n ( 3 ) . A t t h e p r e s e n t time no d i a m a g n e t i c c o n t r i b u t i o n t o t h e m a g n e t i z a t i o n d e n s i t y h a s been removed. T h i s r e - mains t o b e done.
I n t h e f o l l o w i n g , we p r e s e n t p a r t i a l r e s u l t s o n t h e s p i n d e n s i t y , o b t a i n e d w i t h m u l t i p o l e s l i m i t e d t o R = 2. No c o n s t r a i n t was imposed t o t h e c e n t r a l n i t r o g e n s , b u t t h e s p i n d e n s i t y o n t h e c a r b o n atoms was c o n s t r a i n e d t o t h e i r 2pz o r b i t a l s , perpen- d i c u l a r t o t h e r i n g . No s p i n d e n s i t y was examined on t h e NO g r o u p s . The t o t a l num- b e r o f p a r a m e t e r s t o b e r e f i n e d was 39. The l e a s t + s q u a r e reginement c o r r e s p o n d s t o
X*
= 2 - 7 6 " The s p i n d e n s i t y map, p r o j e c t e d a l o n g c , i s r e p r e s e n t e d i n F i g u r e 3 . 5. D i s c u s s i o nAs s e e n i n t h e map, t h e l a r g e s t amount of s p i n d e n s i t y i s l o c a t e d on t h e two c e n t r a l n i t r o g e n atoms.
However, and c o n t r a r y t o t h e c a s e of n i t r o x i d e r a d i c a l s [ 1 4 ] , 30 % o f t h e s p i n d e n s i t y i s d e l o c a l i z e d on t h e two phenyl and t h e p i c r y l r i n g s .
The s p i n d i s t r i b u t i o n o v e r t h e d i f f e r e n t p a r t s of t h e molecule i s i l l u s t r a t e d by t h e 3 ~ r o j e c t i o n maps g i v e n i n F i g u r e 4. The s p i n d e n s i t y of t h e h y d r a z y l (Fig. 4a) i s pro- j e c t e d p e r p e n d i c u l a r l y t o t h e p l a n e c o n t a i n i n g t h e %-NB bond and b i s - s e c t i n g t h e C7KC13 a n g l e . It i s w e l l s e p a r a t e d i n t o two Zp-type atomic o r b i t a l s and e v e n l y d i s t r i b - u t e d between them. At t h e p r e s e n t
s t a g e of d a t a r e f i n e m e n t t h e a x e s of t h e 2 s p i n d i s t r i b u t i o n s a p p e a r n e a r l y p a r a l l e l , whereas t h e l o c a l s t r u c t u r e i s t w i s t e d by over 28'
( F i g u r e 1, T a b l e 13. T h i s may be l i n k e d t o t h e v e r y low v a l u e observed by ESR f o r t h e a n g l e between t h e a x e s of t h e h y p e r f i n e c o u p l i n g t e n s o r s of t h e two c e n t r a l n i t r o g e n s [
71.
However, d e p a r t u r e of hyperf i n e cou- p l i n g s from t h e l o c a l s t r u c t u r e h a s been a t t r i b u t e d i n o t h e r systems Fig.. 3 - P r o j e c t i o n of t h e s p i n d e n s i t $ d i s t r i - [ I 8 1 t o d i p o l a r i n t e r a c t i o n s of t h e b u t l o n a l o n g t h e c r y s t a l l o g r a p h i c a x i s $. Adja- c o n s i d e r e d n u c l e u s w i t h t h e s p i n d e n s i - c e n t c o n t o u r s a r e s e p a r a t e d b y 0 . 0 3 1-1 / ~ 2 . t i e s s u r r o u n d i n g n e i g h b o u r i n g n u c l e i .
B
t h e t r i g o n a l Na p l a n e
b) p e r p e n d i c u l a r l y t o t h e phenyl r i n g (C13)
c ) p e r p e n d i c u l a r l y t o t h e phenyl r i n g (C,)
A d j a ~ e n t ~ c o n t o u r s a r e s e p a r a t e d by 0.03 Y ~ / A ~ .
D e l o c a l i z a t i o n o f t h e s p i n d e n s i t y h a s been o b s e r v e d on t h e c a r b o n atoms o f t h e t h r e e r i n g s of t h e m o l e c u l e , i n a c c o r d a n c e w i t h t h e magnetic r e s o n a n c e d a t a . The p r o j e c t i o n maps o n t o t h e 2 phenyl p l a n e s ( F i g . 4b and 4 c ) show t h a t t h e s p i n d e n s i t y on t h e c a r b o n atoms i s a l t e r n a t i v e l y p o s i t i v e and n e g a t i v e , a s p r e d i c t e d by t h e o r e t i - c a l c a l c u l a t i o n s i n c l u d i n g s p i n ~ o l a r i z a t i o n [12b] a n d i n agreement w i t h NMR r e s u l t s [ 8 a , 8 c l . T a b l e 111 compares t h e s p i n p o p u l a t i o n s o f t h e 2pn o r b i t a l s f o r each carbon, a s deduced from t h e h y p e r f i n e c o u p l i n g c o n s t a n t s measured o n DPPH:C6H6 c r y s t a l s [ 8 c l by t h e u s e o f McConnellfs r e l a t i o n ( I ) , t o t h e monopole p o p u l a t i o n s Po, a f t e r normal-
i z a t i o n . A l l v a l u e s f i t i n t o t h i s scheme and t h e agreement i s q u i t e good. T h i s can b e c o n s i d e r e d a s a c o n f i r m a t i o n o f McConnellfs c o n s t a n t QCH = - 23 6 .
Moreover, t h e i n e q u i v a l e n c e of t h e two phenyl r i n g s , a l r e a d y n o t i c e d i n t h e NMR of s i n g l e c r y s t a l s [ 8 c ] , i s c l e a r l y i l l u s t r a t e d i n F i g u r e s 4b and 4c. The s p i n popu- l a t i o n s l o c a t e d o n t h e c a r b o n atoms of phenyl r i n g (C13), which makes a t i l t a n g l e of 15' w i t h r e g a r d t o t h e N, t r i g o n a l p l a n e , a r e a b o u t t w i c e a s l a r g e a s t h o s e r e l a - t i v e t o phenyl r i n g (C7),whose t i l t a n g l e i s 54". These d e l o c a l i z e d s p i n p o p u l a t i o n s i n c r e a s e w i t h t h e o v e r l a p between t h e 2pT(Na) and 2pT(C) o r b i t a l s [ 1 9 ] , t h a t i s w i t h c o s 2 a , where a i s t h e t w i s t a n g l e . Resonance r e s u l t s i n DPPH s o l u t i o n s 1111, where
C7-234 JOURNAL DE PHYSIQUE
no t i l t a n g l e c a n b e d e f i n e d , do n o t p e r m i t t o d e t e c t a n i n e q u i v a l e n c e between t h e two phenyl r i n g s .
T a b l e 111: S p i n p o p u l a t i o r s p IT o f t h e 2pT o r b i t a l o f t h e c a r b o n atoms o f DPPH : I
-
deduced from t h e e x p e r i m e n t a l c o u p l i n g s i n DPPH-C6H6 [ 8 c l by u s e o f t h eMcConnell r e l a t i o n (1)
11
-
g i v e n by t h e n o r m a l i z e d monopole p o p u l a t i o n of each atom i n t h e m u l t i p o l e r e p r e s e n - t a t i o n o f t h e s p i n d e n s i t yR e f e r e n c e s
[ I ] Holden A.N., K i t t e l C . , M e r r i t t F.R., and Yager W.A., Phys. Rev.
2
(1950) 147 ; Townes C.H., and T u r k e v i c h J . , i b i d . 148.121 Buchachenko A.L., S t a b l e R a d i c a l s , 5 IV l a ( C o n s u l t a n t s Bureau, New York) 1965.
[33 ( a ) S t e r n b e r g M . , C.R. Acad. S c i .
240
(1955) 990 ; (b) Williams D.E., J. Chem.SOC. (1965)7535.
NMR E8cl (I)
+0.113 (3)
+0.065 (3)
-0.026 (2)
-0.048 (2)
-0.071 (2)
[4] Williams D.E., J. Amer. Chem. Sot. 88 (1966) 5665 ; 89 (1967) 4280.
151 K i e r s C.Th., d e Boer J.L., O l t h o f R T and Spek A.L.,-Acta C r y s t .
B32
(1976)2297 [6] MaruaniJ . ,
Magnetic Resonance and R e l a t e d T e c h n i q u e s , i n Becker P. , " ~ l e c t r o n andM a g n e t i z a t i o n D e n s i t i e s i n Molecules and C r y s t a l s " , pp. 633-692 (Plenum P r e s s , New York) 1980
n e u t r o n s ( t h i s work)
(XI)
+0.083 o r t h o
+0.083 p a r a phenyl C13
~ 0 . 0 7 4 o r t h o +0.064 o r t h o
+0.049 p a r a phenyl C7 +0.020 o r t h o
-0.015 meta
-0.039 meta phenyl C 7
-0.044 meta
-0.049 meta phenyl C l 3
+0.034 meta picryl C1
-0.005 meta
[71 ( a ) Holmberg R.W., L i v i n g s t o n R., and Smith Jr. W.T., J. Chem. Phys. 3 3 (1960) 541 ; (b) Sane K.V. and Weil J.A., P r o c . C o l l . AMPERE XI (1962) 431 ;
E)
L e f e b v r e R., Maruani J. and Marx R., 3. Chem. Phys. 41 (1964) 585.
[8] ( a ) Anderson M.E., Pake G.E. and T u t t l e Jr. T.R., J . T h e m . Phys.
2
(1960) 1581.(b) Sagdeev R.Z., Molin Yu. N . , Koryakov V . I . , Chirkov A.K. and Matevosyan R.O., Org. Magn. Reson. 4 (1972) 365 ; ( c ) ~ o s h i o k a T., Ohya-Nishiguchi H., and Deguchi Y . , B u l l
c&.
Soc. J a p a n47
(1974) 430.[9] D a l a l N.S., Ripmeester J.A., and Reddoch A.H., J. Magn. Reson. 31 (1978) 471 1101 Hyde J . S . , Sneed Jr. R.C., and R i s t G.H., J . Chem. Phys.
51
( 1 9 g ) 1404.[ I l l D a l a l N.S., Kennedy D.E., and McDowell C.A., J. Chem. Phys. 59 (1973) 3403 [121 ( a ) Walter R . I . , J. Amer. Chem. Soc. 88 (1966) 1930 ; (b) ~ u b z o v V.A.,
Koryakov V . I . , Chirkov A.K., and Mate=syan R.O., J. S t r u c t . Chem.
11
(1970) 941.[131(a) McConnell H.M. and Chesnut D.B., J. Chem. Phys. 28 (1958) 107 ; (b) Nanda D.N., Subramanian J. and Narasimhan P.T., Theor. ~ h z . Acta
22
(1971) 369.El41 Brown P.J., Capiomont A . , G i l l o n B . , and Schweizer J . , J. Magn. & Magn. Mat.
5
(1979) 289.
1151 Boucherle J. X . , G i l l o n B., and Schweizer J . , Proc. I n t . Symp. Neutron S c a t t e r - i n g , Am.Inst.Phys .-New York (1982) pp. 333
.
[161 Hansen N.K. and Coppens P . , Acta C r y s t .
A
(1978) 909.[171 ( a ) Grobet P . , Van Gerven L., and Van d e n Bosch A., J . Chem. Phys. 68 (1978) 522.
(b) D u f f y J r . W., S t r a n d b u r g D.L., and Deck J . F . , J. Chem. Phys. 6 8 7 1 9 7 8 ) 2097.
El81 ( a ) H e l l e r C. and Cole T., J. Chem. Phys. 37 (1962) 243 ; (b) Edlund O . , Lund A . , S h i o t a n i M . , Sohma J . , and Thuomas
K.-2lr;
Mol. Phys.32
(1976) 49.[ I 91 McLachlan A.D., Mol.Phys.
1
(1958) 233.