Copyrigbt
(f969).1
[Rcprinted froor the Jourorl of tbc Aocricrn Cbeoicd Socicty, 9L,2245
lg6g by the Americeo Cbenricrl Society sld rcpriotcd by pcrmisrio! of tbc copyrigbt otaer.
Vanadium Nuclear Spin,Lattice Relaxation
in pi,Tropyliumvanadium(- I) Tricarbonyl
GeorgeM. Whitesidesand H. Lee Mitchell
Relaxationin
VanadiumNuclearSpin-Lattice
z-Tropyliumvanadium(-I
) Tricarbonyl'
George M. Whitesidesand H. Lee Mitchell2
Confributionfrom the Departmentof Chemistrv, MassachusettsInstitute of
Technology,Cambridge,Massachusetts 02139. ReceicedOctober 7, 1968
solutions is a broad
Abstract: The rH nmr spectrum of zr-tropyliumvanadium( I) tricarbonyl (1) at 30' in nonviscous
this specdoublet; in viscoussolutions the spectrum is a relatively sharp singlet. The temperaturedependenceof
specthat
the
observed
establish
Nujol
and
ciclooctane
of
in
mixturis
dependence
its
viscosity
trum in toluene-drand
5rV-rH
vanavalue
for
the
the
of
Combination
spin-spin coupling.
tral line shapesin nonviscousmedia are due to
rH linl shape of 1 in cyclooctatresolution at 30o with an estimate
clium spin-littice relaxation time inferred from the
vanadium quadru'
of its rotational correlation time under thesecircumstancesleads to an approximate value for the
=
*
MHz(e'zqQlh)
0.5
Z.O
pole coupling constant in I of
T\ T m r inv es t iga ti o n so f th e d y n a m i c s o f metal atom
l\
m i -cor aC,
t i oH"
n between carbon atoms in lluxional
m e ta l c o mp l e x e s h a v e l e d to the
1 r- and
d i s c ov er y of a v a ri e ty o f n e w ty p e s o f s tructural l y
3 n ts .3 T i re spectral
si g nif ic ant m olec u l a r re a rra n g lme
b
a s e d ,a l th o u gh w i dcl y
a
re
whic
h
t
he
s
e
s
tu
d
i
e
s
d a ta on
va r iegat ed, hav e n o rm a l l y s h a re d o n e fe ature i n
c o m m o n : L , i z .t,h e r e l a t i v e l yc o m p i e x " s l o w - e x c h a n g e "
Sp ec t r aobs er l, eda t l o w te rn p e ra tu re sb e c o me si mpl er
o i h i g h . , t e m p e r a t u r e sa,s t h e m a g n e t i cn o n e q u i v a l e n c e s
c h a r a c t e r i z i n gt h e s t a t i c s l o w - e x c h a n g eS t r u c t u r e sa r e
a v er aged.
o f t h e n m r s p e c t r u mo [
T h e t e m p e r a t u r ed e p e n d e n c e
l
)
t
r
i
c
a
r b o n y l a( 1 ) d e s c r i b e d
a.-rropyliumvanadiunr(
b y F r i t z a n d K r e i t e r a p p e a r e dt o p r o v i d e a n o t a b l e
eiccption to this general pattern of behavior:3 the
- 5 0 o i n tol uene
si ngie s har p peak o b s e rv e d fo r 1 a t
(Gfvrcor,
\\_-//
I
b e c onr espr ogr es s i v e l ym o re c o n tp l e x a t h i g her temp e r a t u r e s ,u l t i m a t e l y b e c o m i n g w h a t a p p e a r st o b e a
6 ro adened doub l e t a t ro o m te m p e ra tu re a nd above'
S i n c ea s i n g i e - c r y s t aXl - r a y s t u d y o f t h i s c o m p l e x h a d
p rev ious lyloc at e d th e I' a n a d i u m a to m o n th e C z axi s
b f t n. planar CrH r ri n g ,6 F ri tz a n d Kre i te r advanced
the intriguing proposal to account for the nmr data
th at t he s y m m et r i c a ls tru c tu re e s ta b l i s h e db y t he X -ray
w o r k e x i s t e di n t e m p e r a t u r e - d e p e n d e en qt u i l i b r i u m i n
s o l u t i o nw i t h o n e o r m o r e s p e c i e si n w h i c h t h e C 7 r i n g
s y m m e t r yw a s n o t p r e s e r v e d . I n t h i s p a p e r w e w i s h t o
tH nmr line
r l p o r t . u i d . n . . w h i c h e s t a b l i s h etsh a t t h e
te
m
p
e
ra
tu
rei s i n fact
a
m
b
i
e
n
t
1
a
t
fo
r
shape obs el, ed
due to irV-rH spin-spin coupling, and that the temp er a' r ur edepend e n c e o f th e tH l i n e s h a p e refl ects
v a r i a t i o n si n t h e r a t e o f ; i V s p i n - l a t , t i cree l a x a t i o n . T h e
w ell- def inedand ri g i c l g e o m e try o f 1 p e rm i ts a com( 1 ) S u p p c r t e cb
i y t h e U . S . A r m y R e s e a r c hO f f i c e ( D u r h a m ) , G r a n t s
A R O ( D ) 3 l - 1 2 4 - - 1 3a5n d A R o ( D ) - 3 1 - 1 2 4 - G 6 9 1 .c o m p u t a t t o n sw e r c
c u r r i e c !o u r i n p i . r r ra t t h c M I T C o m p u r a t i o n c e n t e r , C a m b r i d g c ,N l a s s '
( 2 ) N a r i o n a l I r r s t i r u t c so f H c a l t h P r e d o c t o r a lF e l l o w , 1 9 6 G 1 9 6 9 .
( 3 ) F o r c x a m p l c s ,s c c F ' A ' C o t t o n , , l c c o u r t t s C h e m ' R e s ' , 1 ' 2 5 7
( 1 9 6 8 ); G . l v l . W h j t e s i d c sa n c lJ . F l e m i n g ,J . A m e r . C h e m .s o c . , E 9 ' 2 8 5 5
( 1 9 6 7 ) ; r . r . L . A n e t , H . D . l ( a e s z ,A . N { a a s b o l ,a u d s . w i n s t e i n , i b i d . ,
8 9 , 2 4 8 9( 1 9 6 7 ) ; A . D a v i s o na n c lP . E ' R a k i t a ' i b i d ' , 9 0 , 4 4 7 9( 1 9 6 8 ) '
i + l n . P . M . W e r n e ra r . dS . A . M a n a s t v r s k v i,b i d , 8 3 . 2 0 2 3t 1 9 6 1 ) '
(19fl)'
i S j H . P . F r i t z a n d C . C . I t r c i t c r , C h e m .9 e r . , 9 7 , 1 3 9 8
( 6 ) G . A l l c g r a a n < iC . P c r e g o ,R i c . S c i . ,, { , [ 2 ] 1 , 3 6 2( 1 9 6 t ) '
pari son betw eentheoreti calpredi cti onsconcer ningt he
i nfl uenceof macroscopi csol uti on vi scosi tyon t he r at e
o f n u c l e a rq u a d r u p o l a rr e l a x a t i o na, n d t [ e e x p e r i m e n t a l
r H specmeasurementsof thi s rate as refl ectedi n the
m
a
g
n
itude in
o
f
t
w
o
o
r
d
e
r
s
trum, over more than
viscosity.
Resultsand Discussion
T h e r H n m r s p e c t r u mo f L i n t o l u e n e - d s* o l u t i o n a t
i 0' i s a broad doubl et centered^t 4.22 ppm f r om Tl\ {S
h a v i n g 1 p e a k w i d t h a t h a l f - h e i g h tf o r t h e e n t i r es i g n a l
o f 2 0 . 5 H z : c o o l i n g t h e s a r n p l et o - 7 9 " r e s u l t s i n
g r a d u a lc o l l a p s eo l t h i s s i g n a lt o a s i n g l el i n e w i t h h i t l f * i a t n 4 . 7 H z ( F i g u r e l ) ; t h e a g r e e m e n bt e t w e e nt h e s c
o b s e r v a t i o n sa n d t h o s e r e p o r t e d e a r l i e r i s g o o d ' ; '
varying
Q u a l i t a t i v e l ys i m i l a r c h a n g e sa r e o b s e r v e do n
in this
l
;
o
f
s
o
l
u
t
i
o
n
c
y
c
l
o
o
c
t
a
n
e
a
of
the terirperature
Hz at
a
n
d
8
.
0
a
t
3
0
o
H
z
2
0
.
6
i
s
w
i
d
t
h
l
i
n
.
i
h
.
solvent
- 1 9 ' . T h e n m r s p e c t r u mo f I i n r l - p e n t a n es o l u t i o n
a t 3 0 o i s v e r y s i m i l a r t o t h a t o b s e r v e di n t o l u e n e a n d
c y c l o o c t a n ea t t h e s a m e t e m p e r a t u r ea, g a i n a p p e a r i n g
a s a b r o a d e n e dd o u b l e tr v i t h h a l i - w i d t h2 2 . 0 H z ( F i g u r e
l ) . H o w e v e r , i n c o n t r a s t t o t h e b e h a v i o ro b s e r v e di n
t o l u e n ea n d c y c l o o c t a n ec. o o l i n gt h e p e n t a n es a m p l et o
- 5 0 o r e s u l t si n n o s i g n i f i c a nct h a n g ei n t h e s i g n a ls h a p c
or l i ne w i dth. The l i ne shape of I i n seve r alsolvent s
d o e s n o t c h a n g e o n d e c r e a s i n gt h e e x t e r n a lm a g n e t i c
fi el d strengthfrom 23 to l 4 kG.
The magneti c fi el d i nvari ance of the spe ct r um of 1
i ndi catesthat al l protons on the C tH t ri ng havet he sanr e
chemi cal shi ft, ancl strongty suggeststhat th e obser ved
S tructure i n the room-tenl peraturespectra of t oluene
a n d p e n t a n es o l u t i o n so f t h i s c o m p o u n d i s n o t d u e t o
c o n r ; i b u t , i o n st o t h e s p e c t r af r o m i s o m e r so f t h a v i n g
an unsymmetrical CrH, ring. The contrasting
temperaruredependenceof the spectra from pent ane.
t o l u e n e , a n d c y c l o o c t a n es o l u t i o n ss i m i l a r l y i n d i c a t e s
that the spectralchangesobservedon varyi ng t he t ent p e r a t u r eo f , r . g . , t h e t o l u e n es o i u t i o na r e n o t d u e s i m p l l
io an intramolecular conformationaI or Structural
c h a n g e i 1 1 , b u t d e p e n d i n i r s e n s i t i v em a n n e r o n t t r e
n " t u r . o f t h e s o l v e n t . T a k e n t o g e t h e r ,t h e s e o b s e r v a t i o n s a r e i n c o m p a t i b l ew i t h a n e x p l a n a t i o nf o r t [ e
i n the ambi ent temperat ur espect r a
l i ne shape c' rbserved
of l w hi ch presupposes a temperatur e- dependent
eqtri l i bri um betw eep magneti cal l y nonequivalent
i s o m e r so f l .
-7-ru
p1'Iiwncanudium(-I) Tricarbttn;,I
lVhitesides,,Vitchellf s p in-Lutt ice Relu-ration in n
2246
1^**r^-4,.,
t\
/\"
\+arrr.r
,jn/
/\
/\
/\
--/t
\-.-:
/n\
/\
---/
A\
/\
,/
.
-y'/
\
l-{
20
Ht
\--*:
Figurel. tH nmr spectra
of ,r-tropyliumvanadium
tricarbonyl
at
60 lVlHzin roluene-r4
(left)andpentane
(right;solutions
asa functionof temperature.spectral
measurement
in pentane
below- 50.
is prevented
by crystallizarion
of I fromsolution.
M or e t han 99 % o f n a tu ra l l y o c c u rri n g vanadi um
cons is t sof t he is o to p e ' i rV, h a v i n g ^ S: ,1 , a n d el ectri c
q u a d r u p o l em o m e n t Q - - 0 . 3 x 1 0 - 2 4c m 2 . 7 s p i n s p i n c o u p l i n g b e t w e e n p r o t o n s a n d a n u c l e u sw i t h a
q u a d r u p o l em o m e n r o f t h i s m a g n i t u d ei s n o r m a l l y n o t
o b s e r v e di n s o l u t i o n , b e c a u s er a p i d s p i n - l a t t i c er e l a x a t i o n o f t h e q u a d r u p o l a r n u c l e u sa v e r a g e st h e c o u p l i n g
t o z e r o . N o n e t h e l e s ss, i n c et h e v a r i a t i o ni n I i n e s h a p e
o f t he pr ot on s pe c tru m o f I w i th te m p e ra tu rei s cl eai l y
rtot t he r es ult of a te mp e ra tu re -d e p e n d e netq ui l i brati on
b e t w e e n c h e m i c a l l y d i s t i n c t s p e c i e s ,a n d s i n c e t h e
str uc t ur e obs er v e d i n th e a m b i e n t-te rn p e ra ture
spectra
o f I is r em inis c e n t o f th e s p e c tra o f o th e r m ol ecul es
c h a r a c t e r i z ebdy c o u p l i n go f f l u o r i n et o a n u c l e u so f h i g h
s p i n , 3w e t h o u g h t i t w o r t h w h i l et o e x p l o r et h e p o s s i b i l i t y
th a t t his s t r uc t u re w a s i n fa c t d u e to i n c o mpl etel y
r e s o l v e dv a n a d i u m - p r o t o nc o u p l in g .
The mechanism of spin-lattice relaxation of a
quadrupolar nucleus is a well-understood and
t h o r o u g h l y d o c u m e n t e d p h e n o m e n o n . e , r 0I n b r i e f ,
th e r ot at ional and tra n s l a ti o n a ld i ffu s i o n i n s o l uti on of
th e m olec ule c on ta i n i n g th e q u a d ru p o l a r n u cl eus,and
o f ot her m olec ul e s ,g i v e s ri s e to a fl u c tu a ti ng el ectri c
fi e ld gr adient at th a t n u c l e u s . T h e c o mp o n ent of the
Fo u r ier s pec t r um o f th e s e fl u c tu a ti o n s ,.(c , r), w hose
fre q uenc yc oinc id e sw i th th e fre q u e n c yo roo f a m agneti c
d i p o l et r a n s i t i o no f t h e q u a d r u p o l a rn u c l e u s p, r o v i d e sa
sp i n- r elax at ion me c h a n i s m fo r th i s n u c l e us w hose
:ffe c t iv enes sdepe n d s b o th o n th e a b s o l u te magni tude
,r[" / ( c , r e)
and on t h e s tre n g tho f th e c o u p l i n g b e tw eenthe
:ru c leusand t he fl u c tu a ti n g fi e l d . F o r n e u tral mol e( 7 ) J . W . E m s l e y , J . F e e n e y ,a n d L . H . S u t c l i f f e ,. . H i g h R e s o l u t i o n
N u c i e a r M a g n e t i c R e s o n a n c eS p e c t r o s c o p y , "v o l . I , p e r g a m o n p r e s s ,
L t d . , O x f o r d , 1 9 6 5 ,p 5 9 0 .
( 8 ) K . J . P a c k c ra n d E . L . M u c t r c r t i e s ,J . , 4 m e r .C h e m .S o c . ,g S , 3 0 3 5
(1963); D. W. Aksnes, S. IvI. Hurchinson, ancl K. J. packer,
Mol.
n h v s . ,1 4 , 3 0 1 ( 1 9 6 8 ) ;
N . B a r t l e t r ,S . B c a t o n ,L . W . R e e v e sa, n d E . J .
\ V c l l s .C a n .J . C h e m . , 4 2 , 2 5 3 1( l 9 A l ) ; R . J . C i l l c s p i ca n d J . W .
euail,
i b i d . , 4 2 , 2 6 7 3 ( 1 9 6 4 ) ; E . L . M u e t r e r t i e sa n d K . J . p a c k e r ,J . A m e r .
(
1
9
6
4
)
;
S
o
c
.
,
8
6
,
2
9
3
p
h
i
l
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s
,r b i d . ,
E
.
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.
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r
t
i
e
s
a
n
d
W
.
D.
!hem.
8 1 , 1 0 8 4( 1 9 5 9 ) .
(9) A. Abragam, "The Principlcsof Nuclear Magnetism," Oxford
, J r r i v e r s i t yP r e s s ,L o n d o n , 1 9 6 1 ,C h a p t e r sV I I a n d
VIII; C. p. Slichter,
"Principles of Magnetic Resonance," Harper and Row, New york,
N . Y . , 1 9 6 3 ,C h a p t e r s5 . a n d 6 .
( 1 0 ) H . G . H e r t z , P r o g r . N m r S p e c t o r c . , 3 , 1 5 9( 1 9 6 7 ) ; R . A . D w e k
. : n d R . E . R i c h a r d s , D i s c u s s i o nFsa r a d a yS o c . ,4 3 , 1 9 6( 1 9 6 7 ) .
',turnal
tl'the
Americun
Chemical Society
I 9l:9
I Aprit 23, t969
c u l e s ,a n d p a n i c u l a r i y f o r t h o s e h a v i n g l e s st h a n c u b i c
symmetry around the quadrupolar nucleus, thc
d o m i n a n t m o t i o n c o n t r i b u t i n g t o n u 6 l e a rq u a d r u p o l , r e l a x a t i o ni s t h e t u m b l i n g o f t h e m o l e c u l - e
containing
this nucleus. rather than roration or translation oi
n e i g h b o r i n g s o l v e n t m o l e c u l e s .ITr '.r : F u r t h e r , i f t h c
r a t e o f t u m b l i n g i s c h a r a c t e r i z e db y a r o t a t i o n a l c o r rel ati on ti me r., J(ri cc r" , provi decithat or o2r "r<< l. r
T h u s , t h e r a t e o f s p i n - l a t t i c er e l a x a t i o nd u e t o i n t e r a c t i o n o f t h e v a n a d i u m n u c l e a r q u a d r u p o l em o m e n t
w i th fl uctuati ng el ectri c fi el d gradi entsi n solut ion of I
i s determi ned pri mari l y by tw o factors: t he st r engt h
of the coupling between the vanaciiumquadrupole
moment and these fl uctuati ons, measu r ed by t he
m a g n i t u d eo f t h e n u c l e a rq u a d r u p o l ec o u p l i n gc o n s t a n t
( e ' t q Q l h ) ,a n d t h e a m p i i t u d e o f t h e c o m p o n e n t o f t h e
r o t a t i o n a l m o t i o n h a v i n g t h e f r e q u e n c yc . r 6w
, hich in
turn i s determi ned by the rotati onal correlat ion t inr c
Tc.
T h e s t r u c t u r eo f c o m p o u n d 1 i s s u c ht h a t t h e e l e c t r i c
fi el d gradi ent at the metal atom mi ght be expect edt o be
w eak; i n consequence,despi te e rel ati vel y lar ge valut _.
o f Q , t h e q u a d r u p o l ec o u p l i n gc o n s t a n t o r I m i g h t b c
s u f t r c i e n t l ys m a l l t o p e r m i t o b s e r v a b l er H - t r V s p i n s p i n c o u p l i n g . I n o r d e r t o t e s rt h e h y p o t h e s i st h a t t h c
structureobservedi n the ambi enttemperatu r espect r at t f
I is due to vanadium-protoncoupling, we havc
e x a m i n e dt h e d e p e n d e n c eo f t h e p r o t o n l i n e s h a p e o n
viscosity in hydrocarbon soiutions. A significunt
contribution to this line shapefrom partially rela.red
v a n a d i u m - p r o t o n c o u p l i n g i s e x p e c t e dt o r e s u l t i n a
c h a r a c t e r i s t i ci n v e r s e r e i a t i o n s h i pb e t w e e nl i n e w i d t h
a n d v i s c o s i t y : ei i t h e l i n e s h a p ei s d e t e r m i n e db y t h e
r a t e o f a u n i m o l e c u i a rc h e m i c a lr e a c t i o n ,t h e l i n e w i d t h
s h o u l ds h o w l i t t l e o r n o d e p e n d e n c oe n v i s c o s i t yb e y o n d
t h a t d u e t o v i s c o u sb r o a d e n i n g .
F o l l o w i n g e s t a b l i s h e dp r e c e d u r e s , t 3 ,trh{e r H l i n c
shape of I w as fi rst cal cul atcdas a functi on of t he r at c
o f ; 1 V s p i n - l a t t i c er e l a x a r i o n b y a m e t h o d w h i c h i n
effect treats the probl em as one of exchangebet wcer r
e i g h t e q u a l l y p o p u l a t e d s i t c s c o r r e s p o n d i n gt o t h e
(2,S + l )m5 substatesof a nucl cus of S : 7/ 2,€ach
h a v i n g a n " e f f e c t i v ec h e m i c a l s h i f t " d u e t o c o u p l i n g
w i th the vanadi um of msJy,11,rel ati ve to a f r equency
z e r o c o r r e s p o n d i n gt o t h e c h e m i c a ls h i f t o f t h e p r o t o n s
i n t h e a b s e n c eo f c o u p l i n g . U n d e r t h e i n f l u e n c eo [
the fl uctuati ngel ectri cfi el d gradi ent w hi ch result sf r om
the tumbling of 1, the vanadium nuclei can undergo
t r a n s i t i o n sf r o m s t a t e so f s p i n a n g u l a r m o m e n t u m t n
t o t h o s eo f m * . I o r m * 2 . M a k i n g t h e a s s u m p r i o n s
that (rorr" 3
a s y m m e t r yp a r a m e t e r4 i s z e r o ( a x i a l s y m m e t r yo f t h e
el ectri cfi el d gradi ent tensor at the vanadi um nucieus) ,
the rates at w hi ch these transi ti ons take place ar c
related to the quadrupole coupling constant and to
r " b y e q l - 3 : 1 3 ' 1 1i n t h e s ee q u a t i o n s T
, ru is the spinl a t t i c e r e l a x a t i o nt i m e o f t h e v a n a d i u m n u c l e u sa n d i s
a s s u m e dt o b e d e t e r m i n e de n t i r e l y b y t h e q u a d r u p o l a r
rel axati on mechani sm. The val i di ty of th e f ir st t lf
( l l ) C . D e v e r e l l ,D . J . F r o s t , a n d R E R i c h a r d s ,M o l . P h y s . , 9 , 5 6 - 1
( 1 9 6 5 ) ; M . S t . J . A r n o l d a n d K . J . P a c k c r ,i b i d . , l O , l 4 l ( 1 9 6 6 ) ; W . B .
M o n i z a n d H . S . G u t o w s k y , J . C h e m .P h . v s . , 3 8 I, 1 5 5 ( 1 9 6 3 ) .
( 1 2 ) T . D . A l g e r a n d H . S . G u t o w s k y , i b i d . , 4 8 , 1 6 2 5( 1 9 6 8 ) .
( 1 3 ) J . A . P o p l e ,M o l . P h y s - , I , 1 6 8( 1 9 5 8 , : M . S u z u k ia n d R . K u b o ,
i b i d . , 7 , 2 0 1( t 9 6 r ) .
( 1 4 ) H . S . G u t o w s k y , R . L . V o l d , a n d E . J . W e l l s ,J . C h e m .P h 1 ' s . ,
4 3 , 4 1 0 7( 1 9 6 5 ) .
these assumptionsis establishedexperimentally by the
observationthat the proton llne shape,and by inference
Trv, is independe n t o f th e m a g n e ti c fi e l d s tr ength.e
Th e r e is no s im p l e w a y o f c h e c k i n g th e second
a ssu m pt ion;howev e r,o n th e b a s i so f th e s tru c tureof 1
in the solid state6it is clearly physicallyreasonable.
I
:
Ttv
/f \f 2s+- 3 \1"q0\'"
\+o/\s'tx rl)\ h )''
(l)
* m + lX^S+ m)
_ (2rn* l)'3(.S
2Ttv(25- lX2S+ 3)
(2)
km,m*r:
k^!r,^
k^,^+2 :
k^*2,^ :
(S + mXS+ rn - IXS + rn * IXS * m * 2) (3)
- l)(2s+3)
2TLv(25
(4)
k^,r. : E k^,^'
m*m'
Wit h t hes eequat i o n s ,th e c a l c u l a ti o no f th e a mpl i tude
of the proton signal at frequency c,lfor any value of Trv
i s re duc edt o t he so l u ti o n o f e q 5 ,r5 i n w h i c h R i s a
I ( u ) e R e ( l ' [ i o r*
R + K]-''1)
(5)
d i a gonal m at r ix w h o s e e l e me n ts d e te rmi n e the l i ne
wi d t hs f or t he pr o to n re s o n a n c e si n th e a b s enceo[
co n t r ibut ions f r om re l a x a ti o n o f th e v a n a d i u m atom,
o i s a diagonal m a tri x w h o s e e l e me n tsa re th e val ues
< , ror de re d i n te rm s o f i n c re a s i n gm5, and
(-sJ v , n)
K, the m at r ix de s c ri b i n g th e ra te s o f tra n s fer o f
ma gnet iz at ionbet w e e ns i te sc o rre s p o n d i n gto d i fferent
va l u esof m s due t o v a n a d i u m s p i n -l a tti c ere l a ra ti on,i s
ca l culat edf r om eq 2 -4 .I6
Us ing eq 5 and 6 , s p e c traw e re c a l c u l a te dfo r a range
o f values of lr v ( Fi g u re 2 ).t7 In o rd e r to p re s entthe
co m plet e r ange of s p e c tra l b e h a v i o r c o mp a c tl y, these
spectraare representedin this figure by a surfacerather
th a n s epar at ely : a s e c ti o n th ro u g h th e s u rfa ce perp e ndic ulart o t he ? " ry a x i s y i e l d s th e o rd i n a ry s pectral
i .p r.s . nt at ion. T h e tru n c a te da p p e a ra n c eo f th e si ngl e
peak calculated f'or values of frv less than -0.004 sec
(:
J- o-''.'
E, t'
tt't'
i'
2jis
Figure 2. Surface representationof the calculated rH nmr line
of the surface
shipes for I as a funcrion of I,v. Two perspectives
are giverrfor clarity. A sectionthrough this surtaceperpendicular
to the ?"rv&xis grves the spectrumat that value of ?'rv. See the
accompanyingtext for a descriptionof the parametersusedin calculating th'esesptxtra.
this assumption is reasonable on physical grounds, we
were never successful in explicitly demonstrating its
validity by finding conditions under which line widths
-28
00000
7
21
0
0
0
0
15
16
2t -s2
520000
7
16 -48
-4002000
(r/ror,"]- 0 1 5 5
0-405150
0020
7
16
5-48
20
000
2r
16 -52
15
0
000
2I-28
7
0
0
000
L
(log ?",v
used. The value of the elementsof the matrix R used
in these calculations was adjusted to correspond to a
va l ue of T z : 0. 45 5s e c . T h i s v a l u e w a s o b ta i nedfrom
th e am bient t em pe ra tu rel i n e w i d th o f b e n z e n eused as
a n i nt er nal r es olu ti o n s ta n d a rd i n s o l u ti o n s o f 1 i n
cyclooctaneand carries with it the assumption that Tz
tor benzeneand Tz for 1 were equal in the absenceof
l i n e br oadeningdue to v a n a d i u m re l a x a ti o n . Al though
' 3 (1965)'
( 1 5 ) C . S . J o h n s o n ,J r . ,A d c a n . M a g n e t i cR e s o n a n c e , l 3
(lo Analogous matrices for values of s less than 7/r are given in ref
14.
(17) Calculationswcre carried out using the program NMRCTLwritten
by J. B. Lisle (c/. B.S. Thesis, MassachusettsInstiute of Technology,
cambridge, Mass., 1968). The surface graphics were produced using
t h c r o u t i n e p L o t 3 o .t s
(18) D. L. Nclson, University of Maryland, Departmentof Physics
a n d A s t r o n o m l r ,T e c h n i c a lR e p o r t 5 5 3 ,M a r c h 1 9 6 6 '
Whitesides, Mitchell
(6)
for benzeneand l w ere equal ;teat best, usi ng a sam ple
o f a m i x t u r e o f I a n d b e n z e n ei n N u j o l c o o l e dt o l 2 o t o
i ncreasethe vi scosi tv, w e observeda l i ne w i dt h of 2. 3
H z for the benzene resonanceand of 4.5 H z f or t he
si ngl e l i ne of l . H ow ever, i t w as cl ear that vanadium
rel axati on w as sti l l contri buti ng to the di ff er encein
thesel i ne w i dths, and w e bel i evethat the correct value
for G for the protons of 1 i n Lheabsenceof quadr upole
( 1 9 ) A n a t t e m p t t o s p i n d e c o u p l et h e v a n a d i u m f r o m t h e p r o t o n s b y
double irracliation was unsuccessful. Over the range of decoupling
f r e q u e n c i e se x a m i n e d , 1 5 . 5 0 - 1 6 . 0 8M H z ( ' H f r e q u c n c y6 0 M H z ) ' n o d c couplipg was obse'rved,although the rtv rcsonance frequency would
have been expccted to fall near the center of this tange (cf. O' W' Ho; . D.Gornostanw a r t h a n d R . E . R i c h a r d s ." / . C h e m .S o c . , 8 6 1 1 ( 1 9 6 5 )S
s k y a n d C . V . S t a g e r ,J . C h e m . P h v s . ' 4 6 , 4 9 5 9 ( 1 9 6 7 ) ) . H o w e v e r , t h c
ourpur power of the dccoupler (an NMR SpecialtiesHD-60A) varied
so irratically with frequency that the absenceof decoupting is not informative.
I Spin-Lat tice Rclaxation in r-Tropyliumuanadium(-
I) Tricarbonv' I
00
|
'
r rr rrrl
:
I
q
)<
o
a
o
\.
,,t
\
JJ o.r
\n,
t\
\o
l.\
tr\
F
E
1 t\r \
o.ol
rot
lt
\\
\
0.001
Figure3. tH nmrspectra
of I at 60 MHz and30' in cyclooctane(wt % Nujol) and viscosities
Nujol solvents.Compositions
(cp)
o f t hes se olv entare
s : (A) 0 , 2 .0 5 ;(B) 1 0 ,2 .5 1 ;(C ) 5 0,1l .l ; (D )
6 8 . 2 3 . 1( ;E )1 0 01, 6 5 .
b r oadening is u n l i k e l y to d i ffe r fro m rh e esti mated
0.455 sec by more than -0.2 sec. The vanadiump r o[ on c oupling c o n s ta n t -/y ,s u s e d i n th e m atri r < ,lof
e q 5 w a s s e t e q u a lt o 3 . 0 4 H z , s i n c et h i s v a l u e ,c o m b i n e d
wit h t he v alues o f I.: e s ti ma te d a s d e s c ri bed above,
r e s u l t e ciln c a l c u l a t e ds p e c t r a w h o s e w i d t h a n d s h a p e
f i t t e d c l o s e l y t h o s e o b s e r v e da t u m b i e n t t e m p e r a t u r e
i n t h e c y c l o o c t i r n es o l u t i o n . T h i s e s t i m a t ei s p r c . b a b l y
c o r r e c tt o w i t h i n - + 0 . 2 H z .
C o m p a r i s o no f t h e s p e c t r ac a l c u l a t e d( F i g u r c 2 ) w i t h
the s pec t r a obs e rv e dfo r c o n tp o u n d I a t. -1 0 "i n cycl oo c t a n e - N u j o l m i x t u r c s o f d i f f e r e n tv i s c o s i t y( F i g u r c 3 )
p e r m i t s a d e t e r m i n a t i o no f t h e d e p e n d e n c eo f I r v o n
\ . B y u s i n g o n l y m i x t u r e s o f s a t u r a t e dh . v d r o c a r b o n s
t o v a r y t h e v i s c o s i t yo, u r i n t e n t w a s t o m i n i m i z es o l v e n t solute interactions. It is clear from Figure 3 that
i n c r e a s i n gt h e s o l u t i o nv i s c o s i t yd e c r e a s etsh e l i n e r v i d t h
o f t h e C ' H z r e s o n a n c eo f 1 , a n d i n c o n s e q u e n cteh a t a n
i n c r eas ein 4 is ac c o mp a n i e db y a d e c re a s ei n ? .rv. Thi s
re s ult is of c ou rs e q u a l i ta ti v e l y th a t e x p e c ted i f the
a m bient - t em pera tu rel i n e s h a p e o t' 1 i s a re fl ecti on of
c uadrupole-broadened vanadium-proton coupling,
si nc e an inc r eas ei n th e v i s c o s i ty o f th e s o l vent resul ts
i n s lor v ert um blin g o f 1 , l a rg e r v a l u e s o f r" , a nd smal l er
valuesof f , v ( eq I ).
T he det ailed fo rm e .rp e c te dfo r th i s d e p e ndenceof
f,r. on v is c os it y i s a t p re s e n t a s u b j e c t o f some controv er s y . A lt hou g h th e re l a ti o n s h i p l /? " 1 c ( rc cc nl T
b as econ
i t he S t o k e sh y d ro d y n a mi c e q u a ti o n :ohas been
o bs er v ed t o be fo l l o w e d e x p e ri m e n ta l l y i n studi es
crr r ied out ov er n a rro w ra n g e s o f v i s c o s i ty ,i t i s cl ear
'h at t he abs olutev a l u e s o f th e c o rre l a ti o n t i mes cai cu iat edf r om t he Sto k e se q u a ti o n a re a p p ro x i matel yone
o rd er of m agnit u d e l a rg e r th a n th o s e o b s e rvedexperi m e n t a l l y r. 0 - r : ' : r ' : r ! A m o d i f i c a t i o n o f t h e S t o k e s
c q u a t i o np r o p o s e db y G i e r e r a n d W i r t z ( e q , 7 )s e e m st o
provide the most satisfactory equation presently
a v ailablef or r ela ti n g e x p e ri me n ta lu o i u .s fo r r btati onal
( 2 0 ) N . B l o e m b e r g e n ,E . i V [ . P u r c e l l , a n d R . V . p o u n d , p h y s . R e o . ,
1J , 6 7 9( I 9 4 8 ) .
( 2 1 ) D . E . V / o e s s n c rJ, . C h e m .P h y s . , 4 0 , 2 3 4 l ( 1 9 6 { ) .
( 2 : ) D . H e r b i s o n - E v a n sa n d R . E . R i c h a r c l s , M o l . p h y s , , Z , 5 1 5
( l 961).
.Iournul ol'tlte
Anterican
Clrcmical
Societ.v I 9l:9
I Aprit
23, t969
ocol
\
O.0l
T,
O.l
(sec)
Figure 4. Plot of alT rs. ?"rvtor l. Data in toluene-dr (I) rvere
obtained over the temperature range -30 to -79"; data in cy'clooctane-Nujol mixtures (C) were obtained at 30', with the exception
of the point at ,tiT : 1.02 which was obtained at 12".
c o r r e l a t i o n t i m e s t o m o l e c u l a r s i z e , m a c r o s c o p i cs o i . .r f l ( 1
l u t i o n v i s c o s i t v ,a n d t e m p e r a t u r e . : : ' : r H e r e r . 6 1 . , 1
r s o r v e natr e h a r d - s p h e r er a d i i f o r s o l u t e a n d s o i v ' c n t
'c
::
rs,rluteis
6f5,,lvenr
(/'r,,t,r,"XVsot*z)Tl
(1)
6kl(rro,,n.n,)
m o l e c u l e s( c n r ) , 1 5 i s t h e S t o k e sc o r r e i a t i o nt i m e ( s c c ) .
V sotute
i s the hard-sphere" ' /crl unre"of the soiut e. and
i
s
m a c r o s c o p i cs o i u t i o n v i s c o s i t y( p o i s e ) . B , c t h
t
h
e
4
e q 7 a n d o t h e r , m o r e c o m p l i c a t e de, q u a t i o n sw h i c h a r ' - '
s y d r o d y n a m i ca p p r o a c i - ,
u l t i m a t e l y b a s e do n t h e . S t o k e h
r e l a t er " t o t h e m o l c c u i a rs h a p ca n d r o t a t i o n a lf r i c t i o n a i
c o e { f i c i e n t sc h a r a c t e r i z i n gt h e s o l u t e a n d s o l v e n t , b L r t
not to the rotational inertia of the solutemoleculcs.
A n u m b e r o f r e c e n tt h e o r e t i c a d
l i s c u s s i o nosf t h e r c l r L t i o n s b e t w e e n m o l e c u l a r s h a p e a n c i c o n s t i t u t i o na n t i
r o t a t i o n a l m o t i o n i n s o l u t i o n h a l c t a k e n i n e r t i a le l l c c t s
into consideration and have arrived at predicticns
concerni ng the dependenceof rotati onal dif f usion r ) r 'r
t e m p e r a t u r e a n d m a c r o s c o p i cv i s c o s i t y s i g n i f i c a n t i y '
d i f f e r e n tf r o m t h o s eo f t h e . S t o k e as p p r o a c h p. a r t i c u l a r i v
w h e n a p p l i e d t o a p p r o x i n r a t e l ys p h e r i c a l m o l e c u i e s
w h i c h i n t e r a c t o n l y w e a k l y w i t h t h e s o l v e n t . r: '! { - r ' ;
F l o w e v e r ,i n g e n e r a i ,t h e s et r e a t m e n t sh a v es h a r e dw i t i r
e q 7 t h e p r e d i c t i c r nt h a t ; " s h o u i d d e p e n do n t h e m r s s
o r s i z e o f t h e s o l v e n t m o l e c u l e sa, s w e l l a s o n t h e b L r l k
vi scosi ty 4. W e w ere thus soni ew hatsurpr isedt o f inJ
that i l pl ot of ?" tv u.r. n,T i n the cycl ooct ane- lJuioi
m i , r t u r e sy i e i d s a g o o d s t r a i g h t l i n e o v e r a r a n g e o i
v i s c o s i t i e so f a p p r o x i m a t e l . vt w
" o o r d e r so f m a g n i t u c i , :
( F i * e u r e- l ) . I n p a r t i c u l a r ,t h i s a g r e e m e nits u n e x p e c t c d
o n t h e b a s i so f e q 7 , s i n c et h e c h a n g ei n t h e m a g n i t t r c i c
( 2 3 ) A . G i e r e r a n d K . W i r t z , Z , I - a t u r f o r s c f t . , 8 a . 5 3( 1
29 5 3 ) .
( 2 4 ) F o r c x a m p l e ,R . w . ! I i t c h e l l a n c iM . E i s n c r J, . C h e m .P l r . r ' s . , 3 1 .
8 6 ( 1 0 6 0 ) : W . A . S t c e l e i,b i d . , 3 8 , : 1 0 . 12, . l l l ( 1 9 6 3 ) ; W . B . N l o n r t z ,
W . A . S t e e l ca. n d J . A . D i . r o n ,i b i d . , 3 8 , 2 4 1 8( 1 9 6 1 ) .
( 2 5 ) W . T . H u n t r c s s ,J t ' . i, b i d . , 4 8 ,l 5 2 l ( 1 9 6 8 ) ; H . S h i m i z u ,i 6 n l . ,- 1 0 ,
7 5 4( l 9 6 4 ) .
( 2 6 ) T h e f e w e x p e r i m c n t a Is t u d i e sr v h i c h h a v c p r o v i d e d d e t a o f ; u t ' f i c i e n t q u a l i t y t o e v a l u a t et h e r e l a t i v e m e r i t s o f t h e h y d r o d y n a m i c . r r l , . l
f r e e - r o t a t o r a p p r o a c h e st o t h e c a l c u l . r t i o n so f r o t a t i o n a l d i f f u s i o n c o r r e l a t i o n t i m e s i n s o l u t i o n s u g g e s tt h t r t b o t h h 1 ' d r o d y n a m i ca n d i n c r t r . i l
effectsirre
i m p o r t a n t : c f . T . T , B o p p ,i b i d . , 4 7 , 3 6 : l ( 1 9 6 7 )a, n d r c f l l .
\
\
2249\
term on going from pure cyclooctane(n :
of the rsorvent
2 .0 5 c P , nlT : 0.0 0 6 8 c P/" I() to N u j o l (a : 165 cP ,
n l T : 0. 545 c P /" K ), a l th o u g h d i ffi c u l t to cal cul ate
e xa c t ly , s hould r es u l t i n d e te c ta b l en o n l i n e a ri ty i n the
p l o t of F igur e 4 . R e g a rd l e s s , th i s p l o t provi des
s a t th e structure
co n f ir r ningev iden c ew h i c h e s ta b l i s h eth
s p e c tra of I i s
te
rn
p
e
ra
tu
re
a
mb
i
e
n
t
t
he
o b s er v ed in
due to vanadium-proton spin-spin splitting, and
su gges t st hat t he te mp e ra tu re d e p e n d e n c eo f the l i ne
sh ape in t oluene s o l u ti o n i s d e te rmi n e d p ri mari l y by
ch angc s in t he s a m p l e v i s c o s i ty , ra th e r th an by a
struc t ur al or c onf o rma ti o n a l e q u i l i b ri u m i n v ol vi ng 1
i tse lf . T his lat t er p o i n t i n tu rn i s c o n fi rm e d by the
l i n ear r elat ion betw e e n ? r1 ya n d 4 7 i o b s e rv e dfor the
t o l u e n es o l u t i o n( F i g u r e4 ) .
The or igin of th e d i ffe re n c e o f a p p ro x i m atel y a
fa ctor of - l obs er v e dfo r T s a t th e s a me v a l u e of l l T tn
to l u ene anc l t he c y c l o o c ta n e -N u j o l mi x tu res i s at
p r e s e n at m a t t e ro f s p e c u l a t i o n . S o m eo i t h i s d i f f e r e n c e
ma y be ac c ount eCfo r b y th e fa i i u re o f e q 7 to descri be
, o d a ta suggest
co rrelat iont im es p re c i s e l y . H o rv e v e i 'tw
t h a t t h e d i f i e r e n c ei n ? " r i 'i n t h e a l i p h e t i ca n d a r o n t a t i c
s o l v e n t sm i i y b e r e a i . F i r s t , t h e c h e n t i c a ls h i f t o f t h e
C , H , p r o t o n s o i I d i s p l e y ' sa s i g n i f i c a n tt e m p e r a t u r e
c i e p e r r c l e nict tet o l u e n es o i . i t i o n .s h i i t i n g f r o m 6 4 . 1 7 a t
8 5 " t o 6 3 . 8 8 a t - 8 5 ' : t h e c o r r c s p o n d i n gc h e m i c i i l
s h i i t c h a n g e i n a s i l t t t r a t e dh y d r o c a r b o n s o l v e n t i s
snrell. Second, l is hve to ten timcs as solubie
in toiuene as in, €.3., cyclooctanc. Both of these
t i t h t h e h 1 ' p o t h c s itsh a t 1
o b s e r v a t i o n st l r e c o n s i s t e n w
f'o rnr sa weak c o n rp l e x rv i th tc l l u e n e ' C o m p i ex formxtion',vould clearlyslow the tuntbling of 1, and
c o r r e s p o n d i n g l yl e n g t h e n r c a n d s h o r t e n 7 , . v . 2 7 I t
niight alsc afrect Tw by changing the quadrupole
c o u p l i n gc o n s t a n t . W e h a v e n o w a y o t ' d i s t i n g u i s h i n g
b e t r v eent hes e effe c ts o n th e b a s i s o f th e avai l abl e
experintentd
alta.
s s t a b l i s ht t r a t m e l t s u r e m e n t
T h e f o r e g o i n gi r r g u r n c n t e
o f t h e l i n e w i d t t r o t ' I p r o v i d e se n r e t h o do i e s t i m a t i n g
f r r ' . C o r n b i n l r t i o no f t h e e s t i m a t e cvi a i t t e f o r ? ' r ' , i-n
c y c l c o c t i t n cs' o l u t i o n w : t h t h e X - r a y s t r u c t u r a l d a t a d
p e r n r i t sa n a p p r o x i l t l i . I t c( la i c u l a t i q no i t h e v a n a c i i u m
q u a d r u p o i e c o L r p i ign c o n s t a n t o f I i n s o l u t i o n .
T r e a t i n g b o t h 1 a n d c y c l o o c t a n ea s h a r d s p h e r e s t. h e
o f' e q 7 c a n b e e s ti mated by
te rms f s olut eilno /' " ,,1 ....1
v
o
l
u
n t e sl / ^ f o r t h e s es p e c i e sl r o m
c a l c u i a t i n gt h e n r g l a r
. and assumins a closest packing
t h e i r d e n s i t i e sr e
r a d i i "( 0 . 7 ' 1
relation between V^ and the harci-sphere
L ' r , : 4 n r ' ] 3 ) . O n t h i s b a s i s ./ ' s . r r r t!e i . 5 i A a n d
,.rou. " "r.y j. - t 2 A . a n d fro m th e k n o w n :e v i s cosi ty oi
c y c l o o c t a n ea t i 0 o t h e r o t a t i c r n acl p r r e l a t i o nt i m e f o r
s o l u t i o n a t t t r i s t e n l p e r i t t u r ec a n b e
1 in cy'clooctane
e s t i n r a t e ct io b e r c ' ! 1 . 5 5 X l 0 - t t s e c t i o m e q i .
S L r b s t i t u t i ntgh i s v a l u e a n d t h e m e a s t i r e dv a l u e o f , t h e
v a n a d i u m r e l a x a t i o nt i m e I , 1 ' : 0 ' 0 5 0 s e c i n t o e q l '
t h e n a g n i t u d e o f t h e v l n a d i u n t q u a d r t t p o l ec o u p l i n g
c o n s r a n to i l i s e s t i m a t e dt o b e ( e ) q Q l h ) - r 2 . 0 N I H z .
A l t h o u g h r h e e r r o r i n t h i s n u m b e rc i u et o u n c e r t a i n t yi n
( 3 7 ) . \ n a t o g o u s a l t h o u g h s m i t l l c r c f l ' c c t so f a s s o c i a t i o n h a v e b c c n o b '
s er v t : d i n p r e " , i o u ss t u d i e s o l ' q u i . r d r u p o I gr r , : o ; 1 n c lo t h c r m o t i o n a l r e i a x a '
tiorr r;.rtcs.1r
( l S ) i . C r o s s l e - , n- n c l S . W a l k c r , J . C l r c m . P h : ' s , 4 8 ' 1 7 4 2 ( 1 9 6 8 ) ' a n d
r c l c r c n c c st h c r c i n .
( 1 9 ) T h c c i , J t r s i t (vp - 0 . 8 2 8 ' l g ; c m t ) o f l i q u i d c y c l o o c t a n e a t 3 0 ' w a s
obr;rincd I'ronr E. I(uss, Z. angin. Ph:'s.' 7, J72 (1955); the dcnsity of
s o l i d I ( p : 1 . 5 i 3 g , ' c m r , ;w a s c a l c u l a t e d l t o m t h c u n i t c e l l p a r a m e t e r s o [
rcf 6
\ t '.
the magni tudesof the proton fr and G i n the absenceot '
effectsdue to vanadi um. and i n the magni tude of t he
r o t a t i o n a l c o r r e l a t i o nt i m e , m a y b e a s m u c h a s * 0 . 5
I v I H z , i t i s w o r t h w h i l e e x p l i c i t l yp o i n t i n g o u F t h a t t h i s
t y p e o f n m r i n v e s t i g a t i o ni n c o m p o u n d sf o r w h i c h t h e
prerequi si testructural i nformati on i s avai l abl epr ovides
one of the most practicxl methods of estimating
q u a d r u p o l ec o u p l i n gc o n s t a n t so f t h i s m a g n i t u d e .
I n c o n c l u s i o n . t h e d a t a d e s c r i b e di n t h i s p a p e r
e s t a b l i s ht h a t t h e o b s e r v e d n m r l i n e s h a p e o f I i s
p r i m a r i l y d e t e r m i n e d b y t h e m e g n i t u d eo f l t v . T h e
di fferencei n the temperaturedependenceof th e spect r a
o f 1 i n t o l u e n e a n d n - p e n t a n e( F i g u r e l ) i l l u s t r a t e sa
point of practical importattce: when varying the
temperature of an nmr sample to determine ii
anomal ousspectrall i ne broaderti ngi s due to the ef f ect s
o f c h e m i c a l e x c h a n g eo r q u a d r u p o i e r e i a x a t i o n ,i t i s
useful to keep i n mi nd the fact that temper at ur e
v a r i a t i o n sw i l t p r o d u c el a r g e c h a n g e si n t h e s p i n - l a t t i c e
r e l i r x a t i o nt i m e o f a q u a d r u p o l a rn u c l e u so n i y i f t h e y '
r e s u l t i n l a r g e c h a n g e si n s a m p i ev i s c o s i t y . T h e e f f e c t
oi prac' ti ca.l l .vrttai nabl e changes i n tempe r at ur e at
c o n s t a n t v t s c o s i t yo n T L p r c d i c t e d b y e q 7 i s s m a l l .
T h u s , i n t l - ^ ep r e s e n t s t u d y , t h e s p e c t r u m o f I i n t t '
p e n t a r . es o l u t i o n a t l 0 o w i t s o b t a i n e da t t h e e f f e c t i v e
l o w ' e rl i m i r o f s o l u t i o n v i s c o s i t y . A l t h o u g h a f u r t h e r
d e ' o r e x Si n
€ n : T w o u l d i n p r i n c i p l eh a v e b e e nd e s i r a b i c
i n c l r c l e rt o i n c r e a s e1 1 i ' l n d t h t r s r e s o l v ed i r e c t l ! t h c '
spectri rlfi ne structLl reexpcctedto occur i or l og Tt t u i
- 0.5 (Figure :), such i,t decre se could have been
a c h i e v e di n p r a c t i c eo n i y -b v t a k i n g s p e c t r ao f t i n t h c
v a p o rp h a s e .
E xperi mentalS ecti on
Gcncral. Nmr spectra were takcn on Varian HA-60 or HA-100
s p e c t r o r n c t e r se u u i p p e d . ' v i t h a v ' - r t ) l ( ) I ' a r i a b l e - t e m p c r a t u r ep r o b c
a n ( i c o l l t r o l i c r . C a i i b r a t r o r r o f t h c t e m p e r . l . t u r ec o n t r o l L t n i t r ' , a s
a c c o m o i i s f i e db y n t e a s u r i n gp e a k s e i l a r i t t i o n si p m e t h a n o l o r e t h y ' l '
e n e g l y . c o l s a m p i e s . V i s c c s r r i c s w 3 : - em e a s L r r e dw i t I a B r o o k f i e i d
v i s c o m e t e rc e i t l t r a l c d a g l i n s t l i t e r l t u r : v a i L t c sl b r t h e v i S C O s i t i eosl '
c P a t 3 0 . 0 r . r ) \ u j o l ( p : i 9 . t )c P a t 4 5 ' 0 ' ) , " '
c y ' c l o o c t a n(ep : 1 . 0 - <
rt Litetaturevaluesfor the
a n d t o l u e n e ( n : 1 . 5 - i 8c P a t - J ( ) )
{ ere used
. i i s C O S i t r eOsf l - p e n t a n e . r : n e t ) p c l l t a n e . r ra n d t O l U e n e s W
w h e n a p p i i c a b l e . A C d i t r o n a i r a i u e s o t ' t h e v i s c o s i t yo i t o i u e n c
were lnersured at temperatures belorv -J0'. usittg samples prot e c t e d l i o m a t r n o s p h e r t cc o n d e n s a t r c . nu n d e r a n i t r o g e n a t m o s p h c r e
( i e r n p e r a t u r ev.i s c o s i t yc, P ) : - J 2 . : . l . 5 l ; - 6 3 . 6 5 . 0 ; - 7 8 . ' l ' .
' . 1 9 . 6 . V i s c o s i t i e s ( c P ) a n d c o m p o" s i t i o n s ( ' ' v t T ,
9.2: -95.1
Nujol) at 30" lor ttre cyclooctane-iiu;oimirtures usedin Figure 4
a . " , l . - < 1 .l 0 % ; 4 . 0 1 . : 5 : 1 1 . 1 .: 0 : : i . 1 . 6 8 1 3 3 . 8 ' 7 5 ; 4 0 . 6 .
8 0 ; 6 4 . 1 . 8 6 : 8 9 . 1 . 9 0 ; 1 6 5 . l 0 ( ) . T h e v i s c o s i t . "o"i N u j o l a t l l .
w a s i 7 7 c P . T o l u e n e - c / e( D i a p . r e p t r v a s u s e d a s r e c e i v e d a f t e r
deoxygenatlon.
T r o p l ' l i u m v a n a t l i u m ( - i ) t r i c a r b o n r I r v a s p r e p a r e c ib y a m o d i t i c r t i o n o t ' t h e l i t e r a t u r e m e t h o d . { A l l o p e r a t i o n sw e r e c a r r i e d o u t r n
f l a m e - d r i e t i g l a s s r v e r eu n d e r n l t r o g e n : l i c l u i d s l v e r e t r a n s f e r r e c ib v
f o r c e d s i p h o n t h r o u g h s t a i n l e s ss l e e I c a n n u l a s u s i n g a p o s i t i t c
pr3ssure of nitrogen. To a 300-ml round-bottomed flask fittcu
w i r h a r e t l u x c o n d e n s e rw i i s a d d e c i - 3 . 2 8 I ( - 1 5 m m o l ) o f v a -
( 3 0 ) H . I ( i e t t r a n d T . G ' T r e l i e ' r r ,J . . 1 r n e r .C h e m . S o c ' , 8 9 , 6 6 6 7
(1e57).
(31) L. G. Bclirrskrl'r,Lich' Zur' \losk Obl' Ped' In;t'' 33' :ll
( 1 9 5 5:) C l t e m A
. ll (l9rB).
. b s t r . , 5 2S
( 1 2 ) . . s e l c c t e dv a l u c s o f P r o p e r r r eos i H y - d r o c r r r b o n sN, "B S C i r c u l r t r
c 4 6 1 , U . S . D e p a i l m c n ro f C o m m e r ; e .N a r i o n a lB u r e a uo f S t a n d a r r i s ,
WashingtonD
, . C . , 1 9 ' 1 7P, 1 0 9 .
( 3 3 ) E x t r l p o l i r t c df r o m d a t a o f J . L o f i r e n z ,P c t r o l .R e f i n e r . , 3 5 '1 6 9
(19)6).
( 3 . 1 ). . l r r t e r n a r i o n acl r i t i c a l T a b i e s , " v o l . v l I , M c C r a w - H i l l B o o k
C o . . I r t c . .N * v Y o r k , N . Y . ' 1 9 3 0 p, i l S .
lVltitesides,Mitcltell I Spin-Lttrtice,Relu.rurionin r-Trop.t'litncururdiun{-l) Tricrtrbonl/
n50
nadium(O)hexacarbonvl16
and 9.3 g (o.l mol) of freshiy distilled
cycloheptatrienein l0O ml of hexane.3t Air (l ml) was then injected imo the rEaction flask through a serum stopper by syringe,n
and the solution was heatedat reflux for I hr. The reactionmixture was cooled, transferred by cannula to a 250-ml centrifuge bottle. and centrifuged. Portionsof the resultingdark greensolution
(,-30 ml) were successivelytransfered into a 4o-ml centrifugetube
€ppd with a serum stopper, and he.raneand excesscycloheptatnene were removedat room temperatureunder vacuum until the
entire solution was concentratedto -5 ml. The residualoii was
diluted with l0 ml of penune and centrifugedand the supernatant
solution again transferredto another stopperedcentrifuge tube.
Cooling this solution to -78" for 8-36 hr resultedin crystallization
of I as green-black plates. The mother liquor was removed by
cannula from thesecrystalsat -78o and the resultingr dried in i
slow stream of nitrogen at room temperature. Final purification
of I before preparing nmr samples was effecred by iublimation
(.12', 0.05 Torr). The total yield of I is -157". Solid 1 reacrs
slowlywith air; solutionsof 1 oxidizeveryrapidly.
sample Preparation. The preparationof samplesin solventsof
low viscositywas carried out with carefurexcrusionof oxygenand
water, using unexceptionalprocedures. The preparationof solutions of I in solvents more viscous than cyclooctanerequired a
(35) R. Ercoli, F. Calderazzo,and A. Alberola,J. Amer. Chem. Soc.,
8 2 , 2 9 6 6 ( 1 9 6 0 ) ; R . P . M . W e r n e r a n d H . E . p o < l a l l ,C h e m .I n d . ( L o n d o n t , l . l 4 ( 1 9 6 1 ) : R . , B . K i n g , " O r g a n o m e r a l l i cS y n t h e s e s , ,V
' ol. I,
A c a d e m i cP r e s s N
, e w Y o r k , N . Y . , 1 9 6 5 ,p 8 2 .
(36) oxvgen and olcfins were carcfully removed from the hexane
before use by stirring with 96 f, Hrsor, folrowed by distillation from a susp e n s i o no f s o d i u m b c n z o p h c n o n ek e t y i u n d e r n i t r o g c n .
(37) rf this reaction is carried our wirh stricr exclusion of
oxygen, no
I i s f o r m e d . P r e s u m a b l y ,r r a c e so f v a n a d i u m i n h i g h c r o x i d a r i o ns t a t e s
than v(0) or V( i) are rcquired as catalystsfor thc rbrmation of l.
special procedure. since the rate of solution in these solvents wa-s
very slow. ca. 4o mg. of freshly sublimed I was transferred in a
nitrogen-filled glove bag to a 5-ml round-bottomed ffask. l0
irt of
deoxygenated benzene was added, and the mixture_wasground into
an oil. Then 0.25 ml of the desired solvent. previously degas.sed
under vacuum by three freeze-thaw c),cles (liquid nitrogen), wirs
added with further stirring, a serum sropper praced on the rla.sk.
a n d t h e s o l u t i o n f o r c e d i n t o a s y n n g e u s i n g a p o s i t i v e p r c s s u r eo r '
nitrogen. The solution was transfcrred into an oxygen-irec nmr
t u b e t h r o u g h a s e r u m s t o p p e r a n d t h e t u b e s a a l e du n d e r n r r r o g c n .
T h e p r e s e n c eo f t h e s e s m a l l a m o u n t s o f b e n z e n ei n t h e s a m p l c h a r i
no significant effect on the spectral line shapes. samples in rolucnc
and cyclooctane were -2.5-3.5 mol ft l; samplesin Nujol rverc
. - 1 . 5 - 3 . 0 w t / " l . T h e v i s c o s i t i e so f a l l s o l u r i o n s o f I \ \ e r c a s sumed to be the same as the viscosities of the solvents then:selvts.
considering the low concentration of I in these samples. thrs assumption seems reasonable.
values of i"rv were obtained by comparison of the shapesand halfheight line widths of calculated (Figure 2) and observed specrra.
The peak widths of I were corrected lbr viscous broadening unrelared to the vanadium quadrupole relaxation by the use of benzene as an internal line width standard in the hydrocarbon solvenrs
and TMS in the toluene-r/ssample. All of t[.redata in Figure 4 have
been so corrected.
A cknow l edgments. W e are i ndebted to pr of essor
E . W . M e r r i l l o f t h e D e p a r r m e n ro f C h e m i c a E
l nginceri ng for the use of the B rookfi el d vi scomet erused in
thesestudi es,to P rofessorA l an D avi sonof t his depar t ment for hel pful suggcsti ons
concerni ngthe pr epar i. r r i( ) n
of l , and to John Li sl e l br extensi veassi st ance
wit h t hc
c o m p u t e rc a l c u l l t i o n s .