C h e m i c e ] S o c i e t y ' 9 7, 7 0 2 3 ( 1 9 7 5 ) ' l
[Reprinted from the Journal of the American
by permission of the copvright owner'
reprinted
ch"*i.ut"il;lt;;d
Am;;i;;n
th;
copyright 19?5by
Studyof
A DynamicNuclearMagneticResonance
in Liquid SulfurTetrafluorider
FluorineExchange
Walter G. Klempererr*2"JeanneK' Krieger, Michael D' McCreary'
E. L. Muettertie5.x,2b'p"nielD. Traficante, and GeorgeM. Whitesides*2"
Instituteof Technology,
of Chemistry,Massachus.etts
Contributionfromthe Departments
02t 39,and CornellIlniuersity,Ithaca,
Massachusetts
Cambridge,
N ew York I 4850. ReceiuedApril 7, I 975
and the observedline shapesin
of .theNMR spectrumof SF+has beenreexamined,
Abstract:The temperaturedependence
exchangecomparedwith theoreticalline shapescalculatedfiora numberof differentmethodsof
the regionof intermediate
spectrain goodagreementwith
permu-ting
axial and equatorialflriorineuto*r. CarefullypurifiedSFa yieldsexperimental
theseexperimental
of Berry pseudorotation;
ihosecalJulatedassumingthe intramolecularfluorineexchangecharacteristic
spectrado not closelyresemblethosecalculatedon the basisof uny intermolecularpermutationwe haveexamined'The exfor unpurihigherthan in carefuilypurifiedmaterial.The line shapesobserved
.^hung"rate in unpu.ifi.d SF+is substantially
fied material can be matched to those calculatedassumingpermutationscharacteristicof severalplausiblebimolecular
exchange.
of this impurity-catalyzed
availabledatado not uniquelydefinethe mechanism
mechanisms;
liquid SFa displaysan AzBzNMR
At low temperatures,
spectrumcharacteristicof a Czv molecule;3as the temperature is raised,fluorine site exchangeleadsto line broadento a singlesharp resonance.3
ing and eventualcoalescence
has beenextensively
This spectraltemperaturedependence
examined,but a unique mechanisticinterpretationof this
has provedelusive.In 1958,Cotton, George,
dependence
and Waughasurmisedthat fluoride impuritiesinducedfluorine exchangein their substantiallycontaminatedsamples.
Muetterties and Phillipss subsequentlypublished similar
of fluorine exchangerate
spectra,and, noting a dependence
on sampleconcentration,advocatedintermolecularmechanisms involvingdimeric or ionic intermediates.In a later
publication,6however,they emphasizedthe possibilitythat
traces of HF might be catalyzing fluorine exchangeand
also expressedthe belief that intramolecularexchangedoes
occur. but at a rate lower than the observedhigher-order
processes.
The hypothesisof impurity catalysiswas supported by Bacon,Gillespie,and Quail,Tand more recentlyby
who retardedthe rate of fluoGibson,Abbott, and Janzen,8
rine exchangeby careful samplepurification.The latter authors,however,were unableto establishthat all impurities
had beenremoved.
Other physicalstudiesof sulfur tetrafluoridehavefailed
to clarify the relativeimportanceof intra- and intermolecular paths for the fluorine exchange.Redingtonand coworkitrongly favoredbimolecularmechanismson the basisof
"rr
and variations in
matrix-isoiationinfrared spectra,e'10
NMR couplingconstantsand chemicalshifts with medium
have beeninterpretedas indicatingintermolecularassociation of liquid SFa.rrGas phasestudies,employingboth far2 and electrondiffraction,l3implicatinfraredspectroscopyl
ed intramolecular exchange processes.Theoretical studiesl4'ls also proposeintramolecularexchangein the gas
phase,thus lending credenceto Muettertiesand Phillips'
hypothesisthat intramolecularexchangemight be observed
could be supin the liquid phaseif higher-orderprocesses
pressed.
The presentdynamicNMR studywas undertakento defor fluorineexlineatethe site exchangeschemeresponsible
dechangein sulfur tetrafluoride,and thus unambiguously
termine which, if any,.of the proposedexchangemechanismsare consistentwith experiments.The resultsof this
investigationare reportedin three parts: (i) generationof
all possiblesite exchangeschemesimplied by intramolecular, impurity catalyzed, and bimolecular mechanisms,
Whitesideset al. / NMR Study of F Exchangein Liquid SFa
1024
Table I. A Complete Set of NMR Differentiable Exchange
Reactions for Intramolecular and Impurity Catalyzed
Exchane Exchange in SFod
.A5
*hrww
hr*
ho*
*hrww
' nrW
l\ x I
3/ 8
(Az
\s/e
F i g u r e l . L a b e l i n go f t h e f l u o r i n e n u c l e i a n d s i t e si n S F r a n d a f l u o r i d e
r n r p u r i t r a r e d e l i n e d b y t h e r e f e r e n c ec o n f i g u r a t i o ns h o w ni n ( a ) . F l u o a n d s i t e sa r e l a b e l c d i n ( b ) f o r b i m o l e c u l a re x c h a n g ep r o :.1:.:r.'.'
u h i c h m ight im ply d i ffe re n td e p e n d e n c i eosf N MR l i ne
'hape on rate, (ii) simulationof rate dependentspectra
and (iii) comparison
besedon thesesite exchangeschemes,
spectraof highly
oi the simulatedspectrawith experimental
purifiedSFasamplesas well as samplescontainingtracesof
HF. Interpretationof resultsindicatesthat both intramoare operativein
lccular and impurity catalyzedprocesses
S F.r.
Site ExchangeSchemes
Three classesof fluorine exchangemechanismswill be
cra m inedher e:int r a m o l e c u l aer x c h a n g ee, x c h a n g einvol vi n g fluor ideim pur it ie sa, n d b i m o l e c u l aer x c h a n g eT.he general procedurefor enumeratingNMR differentiablereacrions u'ithin each classhas been presentedin detail elseu h e r e: r 6only r es ultsw i l l b e re p o rte dh e re .[n b ri e f , the n!
possiblepermutationsof the n atomsinvolvedin eachmechenistic class are divided into sets of permutations(reacrrons).usingsymmetryarguments,suchthat reactionswithreactions,imply identirn eachset,NMR nondifferentiable
e NMR l i n e s h a p eo n ra te .T h e n a si ngl e
ca l d e pendencof
reectionis chosenfrom each set, thus forming a complete
sc't of NMR differentiablereactions.The site exchange
schemeimpliedby any mechanismwithin a givenclassmay
then be expressedin terms of combinationsof reactions
differenchosenfrom the appropriatecompletesetof NMR
'
t i a b l er e a c t i o n s .
Thereis an importantsymmetryargumentthat simplifies
s .t th e s l o w e x c h a n g el i m i t, the
rh e analy s isof pr oc e s s e A
.\:B: NM R s pec t r u mo f S F + i s a s y mme tri cs p e c t rumi n
that the half of the spectrumdue to axial fluorine resonancesis the mirror imageof the other half of the spectrum
When exwhich is due to equatorialfluorine resonances.
changebroadeningsetsin, the spectramay retainthis symmetry or becomeasymmetric,i.e., lose mirror symmetry.
Therefore,a site exchangeschememay be classifiedas either symmetric or asymmetric,dependingon whether it
impliessymmetricor asymmetricspectra.tlA completeset
of NMR differentiablereactionsmay accordinglybe dividone containingsymmetricreactionsand
ed into two subsets,
the other containingasymmetricreactions.Asymmetricreactionswill occur in conjugatepairs such that the entire
spectrumimplied by one member of a pair is the mirror
imageof the spectrumimpliedby the other memberof the
p a i r (seebelow) .
IntramolecularExchange.Since SF+ containsfour fluorine atoms,thereexist4! or 24 possiblefluorinesite permu. b e l i n ga to m sAr-A + a s i n F i g ure l a,
ta ti o n s( r eac t ions )La
it can be shownthat the threereactionsh2**-h4** listedin
Table I form a completeset of NMR differentiablereactions.One of these,h2**, impliesno changeof NMR line
shapewith rate. The remainingtwo are symmetricreacany intramolecularexchangescheme
tions. Consequently,
must imply a symmetricNMR spectrumthroughoutthe exch a n g er egion.
hu*
hr*
h,,*:
:
:
:
:
:
:
(2{)ww
(12)ww
(12X34)w*
(1J)ww
(15X34)!vw
(3+S;**
(12)(l{J)ww
xhrww : (2J)ww
: (25x34)ww
h.*
(354)ww= hn-'ww
h,o*:
(12)(354)ww- h,,-rww
h,r*:
aConjugate pairs of asymmetric reactions have been written on
the same line, and reactions which imply more than one resonance
in the fast exchange limit have been starred.
Table II. A Complete Set of NMR Differentiable Reactions
Which Involve Bimolecular Exchange of Only One Fluorine Atom
from Each SFoMoleculea
h , r , : (47)zz
*hrz' : (Jl)zz
hou : (12)(47)zz
hun : (L2)(fl)zz
hrzz : (12)(47)(56)22
hn"' : (r2)(Jl)(Jg)zz
f h , , , ,=: ( 3 4 1 ) z z
(374)zz .
Lh,rt'
f h , , , ,:= ( 1 2 ) ( 3 4 7 ) z z
Lh,," -- ( l 2 ) ( f l { ) z z
(12)(478\zz
f h,rtt
Lh,,,,: ( 1 2 ) ( 4 8 7 ) z z
fh,," :: ( 1 2 ) G 4 7 ) ( 5 6 ) 2 2
( I 2 ) (3 74 ) ( 5 6 ) 2 z
Lhrot'
: (3478)7'z
fh,,"
Lh,"" : ( 3 B l d ) z z
h"ozz = (3487)zz
f n'"t' =: (( t122))((J3{8l g7)4z)zz z
Lhr,"'
: (12)(3487)22
f hr.,tt
lhr." : ( 1 2 ) ( J l g / , ' 1 z z
hro"' : ( r 2 ) ( 3 4 ' t 8 ) ( 5 6 ) z z
f
- ( 1 2 ) ( 3 8 74 ) ( 5 6 ) z z
Lhtrt'
hr"r, : ( 1 2 ) ( 3 4 8 7 ) ( g g ) z z
*h3zz - (49)zz
hrzz - (12)(39)zz
hrr. : (I2)1+t7zz
hro"
: (t2)(48)(59)zz
(38{)zz
(348)zz
(12)(J84)zz
(12)(34$)zz
(12)(38'1)zz
(12)(378)zz
(12)(384)(56)zt
(12)(348)(56)zz
f h,o" =
Lh,,r" :
=
f h,o"
Lhrn" :
:
fhr,t'
Lhrrtt:
:
f hrutt
Lh.,,,, =
a C o n j u g a t ep a i r s o f a s y m m e t r i c r e a c t i o n sh a v e b L ' c nr r r i t l c n r , n
t h e s a m el i n e , p a i r s o f r e a c t i o n sr e l a t e d a s r c ' a c t i o na n d r c r t r . c
r e a c t i o n a r e e n c l o s e db y b r a c k e t s ,a n d r e a c t i o n sr i h i c h i n r n l l t t t o r c t h a n o n e r e s o n a n c ei n t h e f a s t e x c h a n g el i m i t h a v c t r t - . ' nr t l r r c ' d .
ExchangeInvolvingFluorideImpurities.\\'hen fluorine
five fluorine
impuritiesare involvedin an exchangeprocess.
atoms,l abel edA r-A s i n Fi gure l a, must be takeni n t o account. Species,A.5ma! be the fluorineatom in HF, an Fion from self-ionizationof SFa, or any other fluoride impurity. The set of 5! = 120 possiblesite permutationscontains I I NMR differentiablereactions,eight of which involveparticipationof As in the exchangeprocess'Theserein Table I. Eachof them
actions,hs**-hr 2**, arepresented
is an asymmetricreaction,but membersof two of the conjugate pairs are related as reactionand reversereactionand
must therefore occur with equal probability (microscopic
a sinreversibility).Thus eachof thesetwo pairsrepresents
gle processwhich impliessymmetricspectra.
BimolecularExchange.Bimolecularmechanismsinvolve
eight atoms,labeledAr-As in Figure lb. Eighty-twoof the
8! = 40320 possiblesite permutationsmay be chosento
form a completeset of NMR differentiablereactions.If one
ignoresthose reactionswhich involveonly intramolecular
exchange,and further ignoresthosereactionswhich involve
transfer of more than one fluorine atom from one sulfur
atom to the other,only 36 NMR differentiablereactionsremain.Thesereactionsare listedin Table II.
Resultsand Discussion
observed
Figure 3 illustratesthe temperaturedependence
for purified liquid, SFa at 9.2 MHz Low valuesof the Ho
Journal of the American ChemicalSociety / 97:24 f Nouember26, 1975
7025
-67.30
\-J
--)V\--./
r--/
,---t
-)J--l
u-Jv.
-7
\-/!s
-7 3.6"
| .9o
I
i
-)
v \,.-,r'
!.-/
\-/
F i g u r e2 . S c h e m a t i cs l o w - e x c h a n gsep e c t r u mo f S F + .
I
+s
l , i '
- 79.9"
I
,,||
I
, t
, ,
t
-Je
Q
\-,/
"
g.).-----------j'.-..:'*"*
- 85.O"
F i g u r e 4 . T e m p e r a t u r e - d e p e n d e nr e
t F N M R s p e c t r ao i u n p u r i f i e d l i q u i d S F r ( 9 . 2 M H z ) . T h e d i r e c t i o no f s c a no f t h e s p e c t r u ma t - 8 0 o i s
r e v e r s e df r o m t h a t o f t h e o t h e r s p e c t r a( n o t e t h e p o s i t i o no f t h e S O F :
n e a k .m a r k e dw i t h a n a s t e r i s k ) .
*r
r,*",
*r;-*rr,r*r,;;r.
r.'
F i g u r e 3 . T e m p e r a t u r e - d e p e n d e nr e
t F N M R s p e c t r ao f p u r i f i e d l i q u i d
S F l ( 9 . 2 M H z ) . T h e p e a k i n d i c a t e db y a n a s t e r i s ki s S O F 2 p r e s e n ra s
an impurity. These spectrawere not taken with a frequency-locked
s p e c t r o m e t e ra, n d s m a l l a p p a r e n tv a r i a t i o n si n c h e m i c a l s h i f t a r e n o t
s i g n i l i c a n t .C c r t a i n d e t a i l s o f t h e a p p a r e n t i n t e n s i t i e so f l i n e s 6 a n d 7
c l o s ct o t h e s l o w - e x c h a n g e
l i m i t a r e a r t i f a c t s ;s e et h e t e x t f o r a d i s c u s sion.
field were usedin theseexperimentsto introduceas much
second-order
characterinto the spectrumas possible.The
line shapesof theselow-fieldspectraweremuch moresensitive to mechanismthan were thoseat higherfield, both becausethe relativelylarge value of J^.f 6v resultedin large
differencesin the broadeningof the individuallines in the
intermediateexchangeregion and becausethe increased
separations
betweenthe components
of the multipletsat low
field made thesedifferencesmore easilyobservable
experimentally.Carefulattentionto the amplitudeof the H1 field
was requiredto avoid saturatingthesespectra,particularly
closeto the slow exchangelimit. The form of the spectra
was not alteredwhen Ph3P:NCeHaF was includedin the
purifiedsampleas a fluoridescavenger.
To simplify discussionthe spectrallineswill be referencedas indicatedin Figure 2. Two spectralfeaturesare important in mechanistic
distinctions.First, the experimentalspectraare symmetrical with the broadeningof eachline in the multipletof lines
I -7 mirrored by the broadeningof the symmetricallydisp o sedline in t he mu l ti p l e to f l i n e s8 -1 4 . S e c o n dg, roupsof
linesare characterized
by well-defineddifferentialbroadenings:line 7 broadensmore rapidly than line 6, line 4 broadensmore rapidly than line 3, and line I broadensmore rapidly than line 2, as the sampletemperatureis raised.Note
th at t his r elat iv eli n e b ro a d e n i n gi s o n l y c l e a rl yvi si bl ei n
the spectraof Figure 3 at temperaturesabove-64". The
apparentrelativepeaksobservedin the spectraat -l I and
-64" (particularly,the apparentlygreaterheight of line 7
relative to line 6) are artifacts,reflectingsaturationand
transientinstrumentresponse.
The differentialbroadenings
of the lines in thesemultipletsform the basisfor the most
importantof the mechanistic
distinctionsthat follow.
Spectratakenof unpurifiedSFa undersimilar conditions
are qualitativelydifferentin severalrespects(Figure 4). In
the intermediateexchangeregionthe spectrashowa subtle
_, ,-t20
F i g u r e 5 . T e m p e r a t u r e - d e p e n d e nr e
t F N M R s p e c t r ao f p u r i f i e d S F + i n
l - b u t e n es o l u t i o n( l 2 o / ov ' . v )a t 6 . 5 M H z . T h e f e a t u r e si n d i c a t e db y a r r o w s a r e a r t i f a c t s ,r e s u l t i n gf r o m f o l d - o v e ri n t h e F o u r i e r t r a n s f o r m .
but real asymmetry.
Especially notable are the differences
in the peak-to-valley
ratio for the 6,7 and 8,9 transitions,
a n d i n t h e s h a p e os f 3 , 4 , 5a n d l 0 , l l , l 2 m u l t i p l e t a
s t -67o.
A criticaldistinctionis the absence
of oneof the differential
line broadenings,
characteristicof the spectraof pure SFa,
i n the i mpuresampl e;the 3 and 4 transi ti onsi n the im pur e
sampleseemto broadenapproximatelyequallyas the sample temperatureis increased.Finally,there is a differential
in absoluteexchangerate sincea corresponding
degreeof
line broadeningfor the unpurifiedsampleoccursat significantly lower temperaturethan for the purifiedsample.The
l i ne broadeni ng
j udgedby t he
of the 6,7 and 8,9 mul ti pl ets,
peak-to-valley
ratio, correspondfor spectraof the purified
sampl eat -50o and the unpuri fi edsampl eat -720.
D i l uti onof the sampl ehasno si gnfi canti nfl uen ceon t he
temperaturedependence
of the spectraof the purifiedSFa.
Figure5 showsseveralspectratakenof a solutionof SF+in
1-butene(l 2o/ov:v S Fa:butene).
A l though these spect r a
w eretakenat 6.5 MH z, and are thusnot di rectl ycom par abl e to thoseshow n i n Fi gure 3, i t i s cl ear that t he line
Whitesides
et al. I N M R Studv of F Exchangein Liquid SFa
7026
coool
TO'
\ ooo2
ooo2
'- 90.
o.o oa
..-oT'
o.o0a
.
9:016
oo?
o.o4
o.oa
.
i:o7
o.o5
o.l
o.l
qra
o?2
. 4 ,
DI
@oo2
o.oo2
zt'HqttB*
o.oo4
------'/
o.?:"
,rt
/\
, // \
\..
--=-
rH
o'1"
o.oot
o.oo4
o.oo8
o.oool
o.o4
o.ool
o.oo4
oooS
o.02
o.04
o.06
o.o7
o.l
o.2
-_
l
o.lo
o.l4
._J--
o.zz
ll
o.02
o.o4
-/'J [r!,[-
rr I
,*_/t-fl,_
i t'
rI
Ju-
ll
_iv\
ill
II
o.oool
o.o6
o.lo
o.t4
o.22
5.OO
, Figure 6. Spectra calculated for the permutations hrrw! h4s*, h6q*, hs". h$", and (h{** + 2h6**) as a function of the preexchangc lifctime. t
(sec). As a result of changes in the program ? is defined differently for the series hn** and h-"; r for the latter group should be divided by two to be
consistent with the definition used for rhe former. The line in the center ofthe spectra for h5"" + 2h6'* is fluoride. For mechanisms hn"" and 2he*"
+ h6"", t refers to 7sr_a.
broadeningscharacterizingthe two setsof spectra at -55o
are comparable.Thesespectraand those shown in Figure 3
were taken in different laboratoriesusing samplespurified
by different procedures;the good agreement between the
differential line broadeningscharacterizing these two sets
of spectraindicatesthe reproducibilityof thesefeatures.
Theseexperimentalspectrawere comparedwith theoretical simulations derived from the NMR-differentiable per-
mutations listed in Tables I and II (Figurcs 6 and 7). The
proceduresusedto carry out thesesimulationsare described
in a following section.Only sevenpermutations (or combinations of permutations)correspondingto mechanismsthat
seemedparticularly plausible, or that had previously been
explicitlypostulatedin the literature,werecalculatedovera
full range of preexchangelifetimes; the remainder were examined only at two representativeexchangerates in the in-
Journal of the American Chemical Society / 97:24 / Nouember26, 1975
7027
;r-
tJ''
^l-1.-ilJ.-
M
.l
,il
lr
lr.
tl h
r[
,u.
l- 1,,
,,{-/ U\------,,--,r -/ .-,'q.-- ff
-"4-U_,1I , q,
,JL_-,Li,-_ - / lrr[
u,'
tLr_,r
-rL,q- t-,[- -,t r 1,,1./i I
_rl^
I
tr{h
-,tt
.f.r,
rI
lf
ilh
I
ll
*/ l
I
li\ r
ii
fI
ili\
lt]''-A
iifl
l,\
-{,,t]i._
-- _',',
,s,h8
ir
''il,rii
I
l|ih
u
I
il i',
ll
n
d
^l
,.J.-,,,.J-[-, -,.,,1,
l.
i
1l,r'\
i-',\a"
u\
Il\
I
I
I
I
l/
I
\i"lt"
I
Figure ?. Spectra calculated for a variety of permutations in the intermediate exchange region. For each p€rmurarion two values of i were used: the
lefthand spectrum for each was calculated for rsFa = O.l sec: for th€ right-hand spectrum. rsF. = O.O5sec. The line in the cenrer of the specrra for
. h s r ' - h r 2 * * i s f l u o r i d e .F o . t h € s es p e c t r a ,I F - ] / [ S F r ] = O . O S .
termediateexchangeregion. The two intramolecularexchanges,h3** and h4**, are the permutationsthat characterize non-Berry and Berry pseudorotations,respectively.
PlausiblebimolecularmechanismsinvolvingSFa and fluoride ion (ho**) or two SFa molecules(he'. and h36'.)and a
dissociative
mechanism(h-5*** 2h6**) werealsocalculated (SchemeI). Many other possiblepermutationscould,of
course,also be rationalizedin terms of plausiblemechan i sms .
Remarkablyand fortunately,only one of the possible
permutationsgeneratesspectrain satisfactoryagreement
with the experimentalspectraof purified SFc, viz., h4**,
the permutationcorresponding
to the intramolecularBerry
pseudorotation.
A number of featuresof the experimentar
and calculatedline shapescan be usedto identify h4** as
the permutationcharacterizing
the experimentalipectrum.
The mostdistinctiveis the differentialbroadeningof lines3
a n d 4 ( or , s y m m et r ic a l l yo,f l i n e s l l a n d l 2 ). O n l y in the
experimentalspectraand in the calculatedspectrabasedon
ha** does line 4 broadenmore rapidly than line 3; in all
other permutations,either line 3 broadensmore rapidly
than line 4 or they broadenat comparablerates.We conclude that the processresponsible
for averagingthe chemical shiftsof carefullypurifiedSFa (pure liquid or in butene
solution)is an intramolecularrearrangementthat has the
ligandatom permutationalcharacterexpectedfor the intramolecular Berry pseudorotation.
This conclusionreceives
independentsupport from the observationthat this ex-
S c h e m eI .
A x i a l - E q u a t o r i a l I n t e r c h a n g eM e c h a n i s m s
P ' F
ht'
3
zo -,.>Q,
N o N - B E R R YP s E U D o R o r a r r o N
F .
I
c-r
^tt
"4
BERRy
pSEU0oROTATtoN
I
\_t.a
r'1|
b
t \ 1
z2
h
9
h
36
>p
W h i t e s i d e se t a l . I
! l
w w
h, + 2ta
NMR Study,of F Erchange in Liquid SFa
7028
changereactionis sensiblyindependent
of the concentration
of SFa, and to a changein medium from pure SFa to butene-SFa.
The mechanismresponsible
for the averagingof the axial
and equatorialfluorinechemicalshiftsof SFain unpurified
samplesappearsto be differentthan that in purified samples. Exchangeoccursmore rapidly in unpurifiedthan in
purified samplesand is characterized
by line shapesin the
intermediateexchangeregionthat are appreciablydifferent
than thoseof the purified samples.The presentlyavailable
data are not sufficientto permit clear delineationof the
dominantmechanism(or mechanisms)
for exchangein the
unpurified samples.The asymmetrybetweenthe upfield
and downfieldmultipletsof the experimentalspectra(Figure 2) is compatiblewith any of severaltypesof associative
and dissociative
mechanisms.
The chemicalspeciesSFI*,'8
SFs-,le and HFz- 2o are all well-knownand could provide
plausibleintermediates
in suchreactions.Without more informationon the influenceof solutionvariableson this (presumably impurity-catalyzed)exchange,it is not profitable
to speculate
furtheraboutits mechanism.
In summary,the data in this paper establishthat pure
SFainterchanges
axial and equatorialfluorinesby an intramolecularprocesshavingthe permutationalcharacterof a
Berry pseudorotation.
Fluorineinterchangein impuresolutions appearsto proceedpredominantlythrough a rapid,
i mpurity-catalyzedreactionof unspecifi ed character.2I
ExperimentalSection
Preparation of SFa Samples. Two different sample preparation
p r o t o c o l s w e r e d e v e l o p e d .S a m p l e s u s e d a t M . l . T . f o r 6 . 5 - M H z
fluorine spectra were purified by the following procedure.Crude
S F a ( P e n i n s u l a r C h e m r e s e a r c h ,I n c . ) w a s d i s t i l l e d i n t o o n e b u l b o f
a dry Pyrex high-vacuum line equipped with unlubricated Teflon
s t o p c o c k s .T h i s b u l b c o n t a i n e d a s m a l l q u a n t i t y o f s o d i u m f l u o r i d e
that had been dried on the line at ca.250o and 0.001 Torr. The
SFr was distilled from this bulb through traps held at -83" and
-97o, and condensed into a second sodium fluoride-containing
t r a p , h e l d a t - 1 8 0 o . T h e s a m p l ei n t h i s t r a p w a s a l l o w e dt o w a r m
until it became liquid, let stand for 30 min, and distilled into a
dried, thick-walled, lO-mm Pyrex NMR tube. The tube was cooled
t o - l 8 0 o a n d w a s t h e n s e a l e du n d e r v a c u u m w i t h c a r e n o t t o p y r o lyze the sample during the sealing procedure. Certain samples
w e r e d i s t i l l e d i n t o N M R t u b e s c o n t a i n i n g p r e v i o u s l y d e g a s s e d1 butene in order to test the influence of SFa concentrationon fluor i n e e x c h a . n g er a t e s .
Samples usedat duPont for 9.2-MHz fluorine spectrawere prepared following a different procedure.Crude SFa, prepared from
SCI2 and NaF (acetonitrile), was purified by distillation at I atm
a n d w a s t h e n s t o r e d i n a s t a i n l e s ss t e e l c y l i n d e r . T h e s t e e l c y l i n d e r
was then attached to an all-quartz vacuum line. NMR samples
were prepared by first distilling SFa from the cylinder into a flask
on the flamed out vacuum line which contained triphenylphosphine(p-fluorophenyl)imine as a fluoride scavenger and a Tefloncoated magnetic stirring bar.?) The SFa was stirred over this scave n g e r f o r 4 5 m i n a t D r y I c e * a c e t o n et e m p e r a t u r e a n d t h e n s u b j e c t ed to two bulb-to-bulb distillations before being transferred to a
q u a r t z N M R t u b e a n d t h e t u b e w a s s e a l e d .S o m e N M R s a m p l e s
were prepared that contained a crystal of triphenylphosphine(pfluorophenyl)imine in the NMR tube; others did not contain this
scavenger.
N M R S p e c t r a l M e a s u r e m e n t s .l e F s p e c t r a a t M . l . T . w e r c t a k e n
with a Bruker HFX-90 spectrometer, modified to operate at
6.5000 MHz. Spectra were taken in Fourier transform mode using
Digilab Models FTS/NMR-3 data system and a Perkin-Elmer
Model 209 A RF ampliiier modified for pulsed N MR applications.
A B r u c k e r v a r i a b l e t e m p e r a t u r e a c c e s s o r yw a s u s e d w i t h a t h e r m o c o u p l e p o s i t i o n e d0 . 5 c m b e l o w t h e b o t t o m o f t h e N M R t u b e . T h e
thermocouplewas calibrated in place against a pentanethermometer.
Spectra at duPont were taken on a Varian HR-60 spectrometer,
w i t h a V a r i a n v a r i a b l e t e m p e r a t u r e a c c e s s o r y ,m o d i f i e d t o o p e r a t e
at 9.2MHz.
Computational Procedures
Site Exchange Schemes.Complete sets of NMR differentiable reactions for the intramolecular case and the case involving a fluoride impurity were generated using combinatorial aids reviewed elsewhere.r6The complexity of the bimolecular case necessitatedthe use of a computer. Generation of a complete set of NMR differentiable reactions for
the bimolecular case, i.e., generation of a complete set of
double coset representativesl6 in Ss with respect to the
subgroup Sz [Su + Sz] was accomplished by computer generating each double coset, printing out one member of each,
but storing all the members of each double coset in coded
form using Marshall Hall's Method of Derangements.23
The completenessof the set of coset representativeswas assured when all 40320 permutations in Sn had been stored
(in coded form). This approach proved to be reasonably efficient, the program requiring less than 150 K bytes of the
CPU and under 2 min time on an IBM 360165.
Spectral Simulations. Spectra corresponding to intramolecular exchange schemeswere obtained in the representation of eigenfunctions of the slow-exchange Hamiltonian
using standard density matrix procedures,2427 and solving
eq l.
/ ( c o )- R e [ I + . A - r . l + / ]
(l )
Here, 1(<^r)
is the spectral intensity as a function of frequenc y , @ , A i s d e f i n e d a s p r e v i o u s l y , 2 sa n d I + = I + ' i s a v e c t o r
c o n s i s t i n go f m a t r i x e l e m e n t s o f t h e r a i s i n g o p e r a t o r b e tween eigenfunctions of the nuclear spin Hamiltonian giving rise to the lines involved in the exchange.28For problems involving intermoleculor exchange, in which the concentration of speciesA [A] is not equivalent to the concentration of speciesB IB], the elements of I+' contain correction terms for the relative concentration of the two species.
T h e e l e m e n t so f I + ' a n d I + a r e r e l a t e d b y t h e e x p r e s s i o n
I A * ' = I n + [ A ] / t B ] . I n t e r m o j e c u l a re x c h a n g es c h e m e sw e r e
simulated using related methods outlined by Kaplan and
Alexander.26
In this treatment the exchange process is envisioned to
occur within a collision complex that is sufficiently shortlived that its existencedoes not directly influence the spectra of the components,but simply servesas a vehicle to permit exchange of nuclei. This exchange processis treated by
a procedure analogousto that for intramolecular exchanges
by considering the influence of permuting nuclear spins on
the density matrices of the components. Since the collision
complex is assumed to be so short-lived that the detailed
forms of its nuclear spin Hamiltonian and wave functions
are not important, a wave function suitable for the problem
is assumed for convenienceto be that obtained simply bv
m u l t i p l y i n g t h e w a v e f u n c t i o n so f t h e t w o c o l l i d i n g c o m p o n e n t s .T h i s a s s u m p t i o ni s e q u i v a l e n tt o a p h y s i c a l p i c t u r e o f
the collision complex in which there is no interaction bet w e e n t h e c o l l i d i n g c o m p o n e n t so r , e q u i v a l e n t l y ,t o o n e i n
w h i c h t h e p e r t u r b a t i o no f t h e H a m i l t o n i a n s o f t h e c o l l i d i n g
components resulting for the collision is so short-lived that
the nuclear spin systemsdo not respond appreciably. Thus,
if the eigenfunctions ry'aand ry'sof the respective slow-exc h a n g e H a m i l t o n i a n s 3 C a a n d 3 C so f t h e r e a c t i n g m o l e c u l e s
A and B are expressedin matrix form in terms of suitable
basis sets of simple nuclear spin product functions @4 and
d s b y e q 2 , t h e c o r r e s p o n d i n gf u n c t i o n s f o r t h e c o l l i s i o n
complex are given by cross products of the matrices for A
a n d B , a n d t h e " d e n s i t y m a t r i x " o f t h e c o l l i s i o nc o m p l e x b y
t h e c r o s sp r o d u c t o f t h e d e n s i t y m a t r i c e so f A a n d B ( e q 5 ) .
Journal of the American ChemicalSociety / 97:24 f Nouember26, 1975
l n = 3f.n6x
{e = KeQs
(2a)
(2b)
7029
(3)
das=daXds
I
rl
JCnB=JCaXJCs
P A B= P x X p s
(4)
T ! lr
(s)
ill
i l i l\_rrvl'u
,/ [
The quantity requiredin this formalismfor the calculation
of the influenceof the exchangeprocess
on the line shapesis
the time derivativeof the densitymatrix, viz., for molecule
A, eq 6.
I
%)
0t
/ exchange
rA
1rnur,.,- robeforel
4orafter = f6orbefore
{,.B^frr, = JCea X SCns-l
yzorbefore:
02
6ppm
-lI,---}J.-..,
il t,tr.] -ilfur--o2
(6)
In this equationthe superscripts
"after" and "before" have
their usual meaningof "after exchange"and "before exchange",and zn is the meanpreexchange
lifetimeof species
A.
For the problemsin which the concentrationof speciesA
is not equal to the concentrationof speciesB, the ratio of
the meanpreexchange
lifetimesof speciesA and B is given
by raf rs = [A]/tB]. The permutationof nuclearspinsin
the collisioncomplexcan be summarizedby eq 7, and the
influenceof this permutationon the wave function pns for
the collisioncomplexby eq 8
Olscc
I
Figure 8. The influence of the chemical shift differencesbetweenfluoride ion and the fluorines of SFa on line shapesin the intermediateexchange region for hq** is small. Spectra were simulated assuming
I F - ] / [ S F . r l = 0 . 0 5( ' = r s r o ) .
(7)
ft/zorbeforc
(g)
[r-]r[sA]
o toosec
The term ,oarter in eq 6 is evaluated by separating pABuft.'
I
I
rlllr,
,. t, I
(eq 9) into the terms for the isolatedmoleculeof A by averaging corresponding
elementsof pas that containelements
diagonalin pr (eq l0);26in the latter equation,e.g.,Trps is
the traceof ps.
i
I
o.oo4 sec
,'
I
o250
,'
o.too
I
o o50
., d
I
pABuft"r = RpoBb"forep-l
= R(pob"fore y
Orbefore)R-l
t)
,oafter = Trs(Rpoubeforep/Tr ps
(9)
o.o25
I
(l0)
o.oto
Equation l0 can be combinedwith eq 6 and expandedto
yield the elementsof the kinetic exchangematrix K25(eq
I l). Four typesof elementsmake up this matrix: thosedescribingtransferof magnetization
betweenthe linesof moleculeA, Kn.,nithosedescribingtransfer from lines of A to
lines of B, K^,i those from B to A, Kun;and thoseamong
the lines of B, Ku,. ln theseequationsRoman indicesrefer
to moleculeA, and Greek indicesto moleculeB. The subscripts of the elementsof p and R refer to eigenfunctions;
thoseof K refer to lines.Thus, in eq I I b, K-, is the rate
constantfor transferof magnetizationbetweenline m (the
transitionbetween*; and {: of moleculeA) and line z (the
transition between{7 and {, of moleculeB). The term p"*
: (Qt lpl { ) is an ele me not f p s ; th e te rm
e = W'lplt ) @rl plL,)
eij,1
is an elementof pas. Na and Ns are normalizationconstantsderivedfrom Trpa and Trps, and numericallyequal
to the dimensions
of pa and ps, respectively.
(That is, to the
number of statesdefined by the respectiveslow-exchange
Hamiltonians,3C4and JCs.The ratio Nn/Ne is equivalent
to the total observedintensitiesof speciesA relative to
speciesB, if both speciesare presentin equal concentration.) The Kronekerdelta is 6.
K.n
-=
rA
l'
,i
o ool
F i g u r e 9 . S p e c t r ac a l c u l a t e da t t w o v a l u e so f 1 5 p . f o r h 6 * * , a t s e v e r a l
r e l a t i v ec o n c e n t r a t i o n o
sf F- and SFa.
K y n = a p . o . r r )= I
rB
-K=u,
dt
dP,rrJ."r,\
TB
t
f i y R i . , r , r _ 4 i o . r r ptu, , .l 1
/exch ,sL?
?
Na
I
=
/ crch
at
f I F R i . . . k r R i d , k- .-pdr",?- ^d o. r' P t ' fI
teLii
Nn
(lld)
EquationsI I a-d are specificfor problemsinvolvingmutual exchange,viz., nuclearpermutationschemesin which
the reverseprocessis indistinguishablefrom the forward
process(R = R-r; h+", hs.,).For problemsinvolvingnonmutual exchange(n.m. exch)-that is, for any elementary
processthat is not microscopically
reversible(e.g.,hs**)_-a
relatedequationthat explicitlyevaluatesboth forward and
reversereactionsmust be used(e.g.,eq l2)2e
apo)
E t / n . m. e x c n
dpii.tr\
=
t
dt /exch
'f T r s ( R p nX p s R - r *
f |-'Y Rio,rdR.io,rrrPu
- - d i t-d l^..
r o^..
r r^.J.-|
,aLtit
N,
2rL
(lla)
R-rpn X psR)
-
Ttpt
#)"_
Rio,r"v-4i.,.r.0p^v.l
2o^] (r2a)
=
. cxch
K^,=ry)
rA
at
= t f 'f f
/exch rnLTT
Ns
J
1rrul
*l
T r a ( R p aX p e R - r + R - ' p o X p s R )
Trpn
- ,o,f (r2b)
whitesideset al. / NMR study of F Exchangein Liquid sFa
7030
Use of the relationship between the transposeand inverseof
R , R t = R - 1 , p e r m i t s f a c i l e e v a l u a t i o no f e q l 2 b y s u m m a tion of diagonal elements of K and use of a symmetrical
form of K even for problems involving nonmutual exchange
(eq l3); these equations essentially avefagesymmetrical exchange paths that are not individually microscopically reversible.
( K - n ) n - e x c h= ( K n - ) n . - . e x c h= [ K , n n* K " ^ ] 1 2
( K r , ) n . . . e x c h= ( K , u ) n . ^ . e x c=h l K p , + K , r l l 2
(Krn)n
-. cxch
= (Knr)n.-.
exch
(l3a)
(l3b)
=
[ ( N s / N n ) K n u* ( N A I N B ) K u " ] 1 2
(l3c)
The K matrices assembled from these equations were
used in the programs describedpreviously for spectral simul a t i o n . : a ' 2 sT h e m a g n e t i c p a r a m e t e r s u s e d i n t h e c a l c u l a t i o n s w e r e : a t 9 . 2 M H z ( i n H z ) , 6 u = 4 7 8 . 8 ,J u , " = 7 6 . 3 : J " . "
= I 00.0; J ^., = 50.0. For simulations of mechanismsinvolving exchange between SF+ and fluoride ion, the chemical
shlft of the fluoride was routinely set equal to the averageof
r,, and u". At the concentrations used to stimulate these
spectra. tF-ll[SFal = 0'05, the chemical shift difference
between the fluoride and the fluorine of SF+ has no influence on the shape of the calculated spectra (Figure 8). The
relative signs of the fluorine-fluorine coupling constantsdid
not influence the spectra.
Several spectra were calculated for h6** to check whether the qualiiative features of the line shapesused to discard
this and related fluoride-catalyzed exchange processesdepended on the ratio tF-ll[SF+].30 Figure 9 sum-marizes
=
i h . r . s p e c t r a .E v e n a t t h e l o w e s t r a t i o t r i e d ( t F - ] / [ S F a ]
0 . 0 0 1 ) . t t r . s p e c t r ar e t a i n a p r o n o u n c e da s y m m e t r y a n d a r e
easily.distinguishable from those observed experimentally.
\\'e conclude from these calculations that the central conan intramolecular, Berry,
clusion from this work-that
pseudorotationis responsiblefor fluorine interchange in pu'-ili.a SF+-is independent of the particular F- concentration assumed in calculating fluoride-catalyzed exchange
path$'aYS.
Acknowledgments. Mr. Jim Simms provided invaluable
t e c h n i c a l a s s i s t a n c ei n s p e c t r o m e t e rm o d i f i c a t i o n sa t M . l . T .
Dr. Berrram Frenz of Texas A and M University provided
help with computer programming for the permutational
c a l c u l a t i o n s .D r . J . M . R e a d a n d M r . D . N i c k e r s o n o f d u reF spectral data at 9.2 Ml{z Dr' Paul
Pont obtained the
Meakin of duPont pointed out an error in our original treatment of the intermolecular SF+ + F- exchangecalculations.
Referencesand Notes
National Institutes of Health (GM
(1)
' ' supported in part by Grants from the
iObbO and HL 1502-9,to G.M.W.), and by the National Science Founda-
fellowshipto W.G.K.and Grantto E.L.M.).
tion,(predoctoral
(21(a) Departmentof Chemistry,ColumbiaUniversity,New_York, N.Y.
10027:(b) CornellUniversity;(c) MassachusettsInstituteof Technology'
(3) This structurehas been verifiedfor SFr in the gas phase by microwave
spectroscopyand electrondiffraction:(a) W. M. Tollesand W' D' Gwinn,
J . C h e m .P h y s . , 3 6 , 1 1 1 9( 1 9 6 2 ) ;( b ) K . K i m u r aa n d S . H . B a u e r ,i b i d . ,
39,3172 (1963).lt may be viewedas an idealizedtrigonalbipyramid'if
( 4 ) F. A. Cotton, J. W. George,and J. S. Waugh, J. Chem. Phys., 28,994
(1958).
'1084
( 5 ) E. L. Muettertiesand W. D. Phillips,J. Am. Chem. Soc., 81,
(1 9 5 9 ) .
( 6 ) E. L. Muetterties
and W. D. Phillips,J. Che1n.Phys.,46,2861 (1967).
( 7 1J. Bacon, R. J. Gillespie,and J. W. Quail, Can. J. Chem., 41, 1016
(1963).
( 8 ) J. A. Gibson,D. G. lbbott,and A. F. Janzen,Can. J. Chem.,51' 3203
(1973).
(s)R. L. Redingtonand C. V. Berney,J. Chem.Phys',43,2020 (1965);46'
2862 (1967).
( 1 0 ) R. A. Frey, R. L. Redington,and A. L. K. Aliibury,J. Chem. Phys.,54'
344 (1971).See also C. V. Berney,J. Mol.Struct.,12, 87 (1972\.
( 1 1 )W. Gomblerand F. Seel,J. FluorineChem.,4,333 (1974).
(12l, l. W. Levinand W. C. Harris,J. Chem.Phys.,55,3048 (1971).
( 1 3 )V. C. Ewingand L. E. Sutton, Trans.FaradaySoc.,59' 1241 (1963).
See ref 3b for criticismof this work.
( 1 4 )G. W. Chantryand V. C. Ewing,Mol.Phys.,5'209 (1962).
( 1 5 ) B. J. Dalton,Mol.Phys.,11, 265 (1966).
( 1 6 ) W. G. Klemperer in "Dynamic Nuclear MagneticResonanceSpectrosCotton and L. M. Jackman,Ed., Academic Press,New
copy", F. A.
'1975.
Y o r k ,N . Y . ,
( 1 7 )Intuitively,a reactionis symmetricif and only if transpositionof axial fluorine atoms and equatorialfluorine atoms is symmetric in a reaction
step. Formally,a reaction,h;, is symmetric if and only if there existb a
permutationp1, which permutesall the equatorialsites with axial sites,
are NMRnondifferentiable.
and hi and h, = p1-1.h;.p1
( 1 8 )D. D. Gibfer,C. J. Adams, M. Fischer,A. Zalkin, and N. Bartlelt, lnorg.
Cherfi.,11,2325 (19721,M. Azeem,M. Brownstein,and R. J. Gillespie,
Can.J. Chem..47, 4159(1969).
( 1 e ) C. W. Tullock,D. D. Coffman,and E. L. Muetterties,J. Am. Chem-Soc.,
86. 357 (1964);K. O. Christe,E. C. Curtis,C. J. Schack,and D. Pilipovich, lnorg.-Chem.,11, 1679(1972).
( 2 0 ) J. M. Williamsand L. F. Schneemeyer,J. Am. Chem. Soc., 95, 5780
(1973).
(21) Althoughthis study provides support for the contentionthat the Berry
rearrangementis the most common type of rearrangementobserved
for five-coordinatecomplexes, formally non-Berrytypes of rearrangement have been establishedfor HzPFgand Ph2PF3:C. G. Moreland,G'
J. Am. Chem.Soc., 95, 255 (1973);J. W.
O. Doak, and L. B. Littlefield,
Gilje,R. W. Braun, and A. H. Cowley, J. Chem. Soc., Chem. Commun.,
comof structurallycomplexfive-coordinate
15 (1974).Pseudorotation
poundsis complicated:G. M. Whitesides,M. Eisenhut,and W. M' Bunti
b
i
d
.
,
9
6
,
4143
(
1
9
7
4
)
;
R. R. Holmes,
i n g .J . A m . C h e m .S o c . , 9 6 , 5 3 9 8
( 1 9 74 ) .
(22) W A. Sheppardand D. W. Ovenall,Org.Magn.Reson, 4,695 (19721.
(231 b. H. lenmer, Amer. Math. Soc., Proc. Symp' Appl- Math" 10' 179
(1958).
(24\ M. Eisenhut,H. L. Mitchell,D. D. Traficante,R. J. Kaufman,J. M.
J. Amer. Chem.Soc.,95, 5385 (1974).
Deutch,and G. M. Whitesides,
(25) J. K. Krieger, J. M. Deutch, and G. M. Whitesides,lnorg. Chem-, 12,
1 5 3 5( 1 9 7 3 ) .
(261 S . A f e x a n d e rJ,. C h e m .P h y s . , 3 7 , 9 6 7 , 9 7 4( 1 9 6 2 ) J; ' K'la p l a n i, b i d . , 2 8 ,
278 (1958);C. S. JohnsonJr., Adv. Magn.Reson' 1' (1965),especiallypp 53-56; J. L Kaplanand G. Fraenkel,J. Am. Chem. Soc., 94,
2907n972\.
(27) p. Medkin,E. L. Muetterties,and J. P. Jesson, J. Am. Chem- Soc., 94,
F. N. Tebbe,andJ. P. Jesson'
P. Meakin,E. L. Muetterties,
5271(19721;
ibid.,93, 4701(1971).
o Beil'A-1'l], where I =
( 2 8 ) The simplifiedequationused previously,2s4c.r1
(l+)2 is a vector consistingof the intensitiesof the lines involvedin the
exchange, is clearly only useful when these lines have approximately
withineach exchangingblock.
equalintensities
( 2 e ) H. S. Gutowsky,R. L. Vold, and E. J' Wells,J. Chem.Phys.,43, 41O7
(1e65).
( 3 0 ) P . M e a k i na n d J . P . J e s s o n J, . A m . C h e m .S o c ' , 9 6 , 5 7 5 1 ( 1 9 7 4 ) J; . P .
J e s s o na n d P . M e a k i n i,b i d . , 9 6 , 5 7 6 0( 1 9 7 4 ) .
Journal of the American Chemical Society / 97:24 / Nouember26, 1975