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MICROWAVE AND INFRARED SPECTROSCOPIC STUDIES OF WEAKLY BOUND COMPLEXES (VAN DER WAALS, INTERMOLECULAR POTENTIALS, PREDISSOCIATION, AMMONIA)

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8520198
F raser, Gerald T.
MICROWAVE AND INFRARED SPECTROSCOPIC STUDIES OF WEAKLY
BOUND COMPLEXES
Ph.D.
Harvard University
University
Microfilms
international
1985
300 N. Z eeb Road, Ann Arbor, Ml 48106
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HARVARD UNIVERSITY
T H E GRADUATE SCHOOL OF ARTS AND SCIENCES
THESIS ACCEPTANCE CERTIFICATE
(T o be placed in Original C o p y )
The undersigned, appointed by the
Division
Department
C hem istry
Committee
have examined a thesis entitled
"Microwave and I n fr a r e d S p e c tr o s c o p ic S tu d ie s o f
S e v e r a l Weakly Bound Complexes"
presented by G erald T. F r a se r
candidate for the degree of Doctor of Philosophy and hereby
certify that it is w orthy of acceptance.
/ *
« * * » , ....
„
T yped name
W illiam A. Kleitperer
Signature ....
_
,
T yped name
RowG. Gordon
.......
Typed name
...............................
D ate . . ^ i 1 , 1 9 ' J 9 85 .
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MICROWAVE AND INFRARED SPECTROSCOPIC STUDIES
OF WEAKLY BOUND COMPLEXES
A thesis presented
by
Gerald T. Fraser
to
the Department of Chemistry
in partial fulfillm ent of the requirements
for the degree of
Doctor of Philiosophy
in the subject of
Chemistry
Harvard University
Cambridge, MA 02138
April, 1985
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MICROWAVE AND INFRARED SPECTROSCOPIC STUDIES
OF WEAKLY BOUND COMPLEXES
Research D ir e c to r
Gerald T. Fraser
W illiam Klemperer
A p r il, 1985
ABSTRACT
R o ta tio n a l and v ib r a t io n a l s p e c tr a o f
s e v e r a l weakly
bound com­
p le x e s have been ob tain ed u sin g th e m olecu lar beam e l e c t r i c resonance
te c h n iq u e .
The com plexes which were examined
HCCH, NH -C02 , H C N-C O j,
in c lu d e :
NH^-HCN,
NHg-
<S02 ) 2 . Ar-HCN, BFg-NCCN, Ar-NHg, and (NH3 >3 .
3
The two com plexes NH^-HCN and NHg-HCCH are hydrogen bonded, sym m etrical
com plexes i n which th e a c e t y le n ic hydrogen bonds to th e n itr o g e n . The
hydrogen bond le n g th s and weak bond s tr e c h in g fo r c e c o n s ta n ts fo r NH^HCN are 2 .1 6 A and 0 .1 2 2 mdyn/A w h ile f o r NHg-HCCH th e y are 2 .3 3 A and
0 .0 7 0 mdyn/A.
The s p e c tr o s c o p ic c o n s ta n ts
su ggest
th a t
th e
hydrogen
bond i n NH^-HCN i s str o n g e r and more d ir e c te d than th a t i n NHg-HCCH.
NH -CO
3
2
and HCN-C0
2
a r e both shown to
be T-shaped
com plexes in
which th e n itr o g e n o f th e NHg or HCN i s bonded to th e carbon o f C02 «
The N-C weak bonds le n g th fo r NHg-C0
2
2 .9 9 A and 3 .0 0 A r e s p e c t iv e l y .
and HCN-C0
2
a re n e a r ly th e same,
The r o t a t io n a l spectrum o f NHg-C0
2
is
com p licated by th e e f f e c t i v e l y f r e e in t e r n a l r o t a t io n o f th e NHg a g a in s t
th e C02 .
The pa typ e r o t a t io n a l spectrum o f (S0
2
) 2
has been m easured.
The
spectrum i s perturbed due t o th e p re sse n c e o f a 70 kHz tu n n e lin g m otion
which in te r c h a n g e s th e two S
0 2
u n its.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The spectrum o f both Ar—HCN and Ar—NHg a re
r ig id ity .
com p licated
by non­
For Ar-HCN, th e c e n t r i f i g u l d i s t o r t io n i s la r g e and extrem ely
s e n s i t i v e to i s o t o p i c s u b s t it u t io n . A model i s p resen ted t o account fo r
th e observed d i s t o r t io n e f f e c t s .
spectrum i s
observed which
is
For Ar-NH^, a ra th er unique r o t a t io n a l
c o n s is t e n t
w ith
an Ar-NHg in t e r a c t io n
which i s n e a r ly I s o t r o p ic .
For <NH ) » th e r o t a t io n a l spectrum appears s u r p r is in g ly sim p le and
3
2
i s in c o n s is t e n t w ith th e c l a s s i c a l hydrogen bonded p ic tu r e o f t h i s com­
p le x .
The
d ip o le moment components fo r
(ND
3
)
2
are sm a ll
(0 .7 4 (2 ) and 0 .5 7 (2 ) D r e s p e c t iv e ly ) w h ile th e d is ta n c e s between th e two
NH /ND
3
3
u n it s are la r g e (3 .4 1 A and 3 .4 7 A r e s p e c t i v e l y ) .
In fra r e d microwave double reson ance s t u d ie s a re a ls o rep orted on
NH -HCCH, NH -C02 . NH -A r, and (N H ^ j.
3
3
3
m otion was e x c it e d by a C0
2
determ ined fo r NH - c o
3
2
la s e r .
In each c a se th e
NHj um brella
In fra red t r a n s i t io n lin e w id th s were
(0 .4 5 (2 0 ) cm- 1 ) and NHg-HCCH (150 MHz).
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ACKNOWLEDGEMENTS
There are many p eop le whose c o n tr ib u tio n s have h elped make t h i s
t h e s i s p o s s ib le .
Foremost o f th e se peop le i s B i l l Klemperer.
B i l l has
been both an in s p ir a t io n and an e n d le s s source o f knowledge to me.
Most
im p o r ta n tly , B i l l ’ s approach to resea rch has made my s i x y e a r s in h i s
group e n jo y a b le and seem in gly s h o r t.
I have a ls o had th e p r iv ile g e to
work i n P r o fesso r E.B. W ilso n 's la b o r a to r y in my f i r s t year a t Harvard.
I have had many i n t e r e s t i n g d is c u s s io n s w ith P ro fesso r W ilson on v a r io u s
a s p e c ts - o f my work and h i s I n t e r e s t i n my work h a s been v a lu a b le and
en cou ragin g.
I would a ls o l i k e
to thank P r o fe sso r W ilson a s w e ll a s
P r o fe sso r R. G. Gordon f o r s e r v in g on my t h e s i s d efen se com m itte.
Two
p eo p le who have been e s s e n t i a l to th e c o m p le tetio n o f t h i s t h e s i s are
Ken Leopold and Dave N elson .
Ken Leopold and I c o lla b o r a te d on approxi­
m ately 50 % o f the r e se a r c h i n t h i s t h e s i s .
Ken i s an e x c e lle n t e x p e r i­
m e n ta lis t and w ith K it Bowen i s most r e s p o n s ib le fo r g e t t in g th e van der
Waals beam to
coworker
th e s is .
fo r
run l i k e
a V arian sp ectro m eter.
approxim ately
th e
oth er
50 % o f
Dave N elson
th e
rese a r c h
was
in
my
th is
Though Dave h a s o n ly been i n th e group fo r two y e a r s he seems
to a lrea d y have com pleted enough work to f i l l a t h e s i s .
Dave have been r e s p o n s ib le fo r making l i f e
Both Ken and
in th e subbasement e x c it in g .
I have a ls o had th e p r iv ile g e to work w ith Karen P eterso n , S tev e Coy,
and Art Charo.
Karen P eterson was r e s p o n s ib le fo r making th e OH r a d ic a l
study a s u c c e s s ,
Art Charo fo r ex ten d in g our spectrom eter toward th e
v i s i b l e , and S te v e Coy fo r p ro v id in g e n d le s s a d v ic e on microwave te c h ­
nology and fo r i n i t i a t i n g th e stu dy on NgO r o ta t io n a l r e la x a t io n .
would l i k e
e n lig h te n in g
to
thank both Mark M arshall
d is s c u s s io n s
about
and K evin Lehmann
sp ectroscop y
and George
fo r
P is ie llo
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I
many
fo r
a s s is t a n c e in apparatus m o d ific a tio n s .
I a ls o owe a g r e a t debt to the
p a st
Altman,
and
p r e sen t
group
members:
Bob
Frank B a io c c h i,
K elly
Chance, Tom D ixon, Tom F is h e r , Gary G erfen, Chuck Joyner, H elen Leung,
F loren ce L in, A lic e Sm ith, George S ch erer, Ian S u n i, David Yaron and Dr.
K. Zhao.
F in a lly , I would l i k e to acknowledge th e c o n tr ib u tio n s o f my
p aren ts whose lo v e and support have made a l l o f t h i s p o s s ib le .
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TABLE OF CONTENTS
INTRODUCTION
1
CHAPTER 1
WEAKLY BOUND COMPLEXES OF NH3
21
CHAPTER 2
WEAKLY BOUND COMPLEXES OF HCN
51
CHAPTER 3
ROTATIONAL SPECTROSCOPY OF MOLECULAR
70
COLTLEXES OF BF$ WITH 1ICC1:, C02> AND NjO
CHAPTER 4
ELECTRIC DIPOLE MOMENTS OF KF-C jII .
h f - c 2 h4
CHAPTER 5
,
74
and h f - c 3 h 6
IHCROWAVE AND RADIOFREQUENCY ROTATION-
88
INVERSION SPECTRUM OF (S02 >2
CHAPTER
6
ELECTRIC DIPOLE MOMENT OF X2!! OH and OD
113
IN SEVERAL VIBRATIONAL STATES
CHAPTER 7
ABSORBER SPEED DEPENDENCE OF THE COHERENCE
RELAXTION RATE OF THE J=0-1 TRANSITION OF
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120
i ;t t r o d u c t i o : i
I n v e s t ig a t io n s o f ga s phase a g g r e g a te s o f a to n s and m o le c u les i s an
a c t iv e area o f r e se a r c h .
The primary go a l o f th e s e s tu d ie s i s to d e te r ­
mine th e in te r m o le c u la r p o t e n t ia l between two weakly in t e r a c t in g a to n s
or m o le c u le s.
O b viou sly, t h i s i s a form id ab le c h a lla n g e .
to
c h a r a c te r iz e
co m p letely
th e
in t e r a c t in g asym m etrical to p s ,
in te r m o le c u la r
For in s ta n c e ,
p o t e n t ia l
between
two
th e quantum m echanical c a lc u la t io n s must
search over the s i x d e g r e es o f freedom which are a s s o c ia te d w ith the van
der U aals modes.
T his im p lie s th a t c a lc u la t io n s done a t even moderate
r e s o lu t io n
sample
must
R esearch ers th e r e fo r e
over
1 0 6
P°i n t s
of
have c o n cen tra ted t h e ir
p o r tio n o f the p o t e n t ia l energy s u r fa c e .
c o n fig u r a tio n
sp a ce.
e f f o r t s on on ly a sm all
The most im portant area o f
t h i s su r fa c e i s th e r e g io n near the a b so lu te mimimum s in c e t h i s d e fin e s
th e
s tr u c tu r e
of
the
com plex.
R o ta tio n a l
sp ectro sco p y
of
com plexes
formed in a d ia b a tic ex p a n sio n s probes th e in te r m o le c u la r p o t e n tia l near
its
a b s o lu te minimum.
in s i g h t in to
Knowledge o f th e se minima a llo w s us to
o b ta in
th e nature o f van der U aals and hydrogen bonded in t e r a c ­
t io n s .
Of th e s e , the hydrogen bond i s o fte n co n sid ered th e most impor­
ta n t.
Its
im portance
in
b i o lo g i c a l
chem istry has been noted numerous tim e .
tan ce o f C-H
X in t e r a c t io n s in
sy stem s,
biopolym ers and and a ls o
on weakly bound com plexes o f
3
due to the
o f hydrocarbons in
p olar
X hydrogen bond h as r e c e iv e d s u b s t a n t ia l a t t e n t io n .
In Chapter 1 o f t h i s t h e s i s ,
w ith Ar [ 1 ] , NH
and s o lu t io n
Furtherm ore, due to th e impor­
im portance o f und erstanding th e s o l u b i l i t i e s
s o lv e n t s th e C-H
c r y s ta ls ,
th e r e s u l t s o f s p e c tr o s c o p ic s t u d ie s
are p r e se n te d .
[ ] , HCCH [ 2 ] , HCB [ 3 ] , and CC
1
>2
The com plexes o f
[4] w i l l be d is c u s s e d .
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2.
The r o ta t io n a l
spectrum
of
each
complex has been ob tain ed u sin g th e
tech n iq u e o f m olecular beam e l e c t r i c resonance s p e c tr o s c o p y .
The r e s u l­
ta n t s tr u c tu r e s show a r ic h ste r o c h e m isty and a r e , in some c a s e s , some­
what s u r p r is in g .
Most im p o r ta n tly , th e r e s u lt s show th a t KH^ e x h ib it s
no p ro p en sity fo r proton d o n a tio n .
b it in g
sim p le
hydrogen
bonding
T his u n iq u en ess o f KK^ in not e x h i­
is
e x e m p lifie d
by
th e
s tr u c tu r e
of
T h is complex has been stu d ie d e x t e n s iv ly t h e o r e t ic a l ly [5] with
each c a lc u la t io n s u g g e s tin g or assum ing a hydrogen bonded s tr u c tu r e fo r
t h i s com plex.
The N-H
N arrangement i s ex p ected to be n e a r ly lin e a r .
I t has been shown r e c e n t ly
s tr u c tu r e .
[ 1 ] , though, th a t
d oes not have t h i s
In F igure 1 , the J = 0 -1 , K=0 t r a n s it io n o f (NH
3
) 2
i s shown.
The s p l i t t i n g p a tte r n d isp la y e d by t h i s tr a n s t io n i s th e o v erla p o f two
14K n u clear quadrupole h y p erfin e p a tte r n s f o r two v ib r a tio n a l s t a t e s o f
th e com plex.
The two v ib r a tio n a l s t a t e s are p o s s ib ly th e A and E i n t e r ­
n al r o to r s t a t e s fo r the in t e r n a l r o ta t io n o f one the the TIH^ s u b u n its .
At l e a s t
m otion
in
th e se
exchanging
sta te s,
th e
two
(NH3 >2 ,
s u b u n its .
u n lik e
shows no in v e r s io n
The
uSi d ip o le moment component
measured by the Stark e f f e c t o f the J = 0 -1 , K=0 t r a n s it io n i s
T h is d ip o le moment component i s
moment
component
bonded (UHg)
exp ected
fo r
e n t ir e ly
the
0 .7 4 (2 ) D.
in c o n s is t e n t w ith the d ip o le
t h e o r e t ic a l ly
The Fa d ip o le moment component o f
p r e d ic te d
hydrogen
(0 .5 5 (1 ) D) i s
i n agreement w ith th e measured na d ip o le moment component o f
(KH3 ) 2 .
The r e l a t i v e i n s e n s i t i v i t y o f the dimer d ip o le moment to i s o t o p i c sub­
s t i t u t i o n a s w e ll a s the o b se r v a tio n o f a pure r o t a t io n a l spectrum for
th is
complex in d ic a t e s
v a lu e to th e eq u ilib riu m
th a t
th e
measured d ip o le moments are near in
d ip o le moment.
It
should be noted th a t
t h e o r e t ic a l ly p r e d icte d hydrogen bonded s tr u c tu r e fo r OiK
3
)
2
the
g iv e s a na
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3
d ip o le moment component g r e a te r
exp ected to
bonding.
be the t r i v i a l
than 2 D.
I n t e r e s t in g ly ,
(NKg)
was
case fo r which MII^ would e x h ib it hydrogen
The la ck o f a hydrogen bond shows th a t
poor hydrogen bond form er.
is
an extrem ely
V-'e p r e se n tly do not know the s tr u c tu r e of
B + C
The r o t a t io n a l c o n sta n t — 2— y i e l d s a cen ter o f mass separa­
(H H g^.
t io n o f 3.411 A between th e two
the n e a r e st neighbor
str u c tu r e
of
d is ta n c e
c r y s t a l li n e
hydrogen bond.
s u b u n its .
observed
NH^ i s
in
T his i s c o n s is t e n t w ith
c r y s t a l li n e
s u r p r is in g ly la r g e compared to th o se found i n
8
(HF
observed
(H 0
2
in
(
2
fu r th e r in d ic a t e s th e u n iq u en ess o f th e (NK
3
> 2
is
(2 .9 8 A )[ 7 ] , HHg-
) 2
(2 .7 5 8 A )[ 9 ] , and HF-K20 (2 .6 8 0 A) [ 1 0 ].
) 2
The
6
complex and does not show a lin e a r
The c e n te r o f mass se p a r a tio n
H20 (3 .0 6 A) [ ] ,
NK^ [ ] ,
in t e r a c t io n .
This
The d is s o ­
c ia t i o n en ergy, Dq o f t h i s complex has been shown to be l e s s
than
2 . 8
K cal/m ole by m icrow ave-infrared double resonance s t u d ie s i n a m olecular
beam e l e c t r i c resonance spectrom eter u sin g a l in e tu n a b le C
0
2
la s e r a s
th e in fr a r e d source
[ 1 ] . The HH^ um brella m otion V was e x c it e d in the
com plex.
2
shown to
2
S ev era l C0
la s e r
p h o to d is s o c ia te
l i n e s between 975 to 985
(NH3 >2 .
cm
1
have
been
The in fr a r e d t r a n s it io n s where moni­
to re d by record in g th e s ig n a l str e n g th o f th e J=0-1,K=0 t r a n s it io n a s a
fu n c tio n o f C
0 2
la s e r l i n e .
Another rath er in tr ig u in g complex o f NH
3
i s Ar-KH
3
[1 ].
T his com­
p le x has an extrem ely dense spectrum in th e r e g io n between 13-21 GHz as
shown i n Figure 2 .
S in ce NH
3
has an in v e r s io n spectrum a t 23 GHz, the
clump o f t r a n s it io n s a t 19-20 GHz i s
in v e r s io n spectrum fo r th e com plex.
h ig h ly s u g g e s tiv e o f a Q-branch
T h is r e q u ir e s th e p
d ip o le moment
component o f the complex to be antisym m etric w ith r e s p e c t to the in v e r ­
s io n .
One model p r e s e n tly bein g examined c o n s id e r s th e NH
3
su b u n it a s
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v i r t u a l ly f r e e ,s in c e i t i s s i t t i n g in a n early is o t r o p ic p o t e n t ia l due
to the argon.
[I]
The o b se r v a tio n o f an in fr a r e d tr a n s t io n a t 9 3 8 .6 9 cm
- 1
fo r Ar-NHg su p p orts t h i s m odel.
The frequency o f t h i s tr a n s tio n
shows th a t the MH^ was not a f f e c t e d s u f f i c e n t l y
by com plexation to per­
turb th e um brella motion o f the HHg.
The s tr u c tu r e s o f th e com plexes o f KH^ w ith HCN [ 3 ] , HCCH [ 2 ] , HF
[ I I ] , CC
>2
[ 4 ] , and H20 [ ] are more t y p ic a l fo r the binding o f IIHg.
8
In
each o f th e se com plexes NH^ behaves a s a Lewis base w ith the bond form­
in g alon g th e
a x is o f
For the com plexes NCH-NEj, HCCH-HH^, and
FH-NHg t h i s le a d s to sym m etrical top s tr u c tu r e s w ith a hydrogen bond to
th e NHg s u b u n it.
The com plexes HCK-NHg and HF-KH^ are the g a s phase
s p e c ie s which condense to
ammonium f lo u r id e .
phase.
T h is i s
quadrupole
form th e i o n ic s o l i d s ammonium cyanide and
Ammonium cyanide shous no i o n ic ch aracter in th e gas
most c le a r ly
co u p lin g
approaches NH^+-X
c o n s ta n ts
shown by exam ination o f the
of
14
the NH^ in th e com plex.
the e l e c t r i c f i e l d g ra d ien t
As HHg-HX
(and thus th e quadrupole
co u p lin g c o n sta n t) a t th e n itr o g e n nucleus approaches z e r o .
observed i n HCM-NH^.
HC1I
N nuclear
T h is i s not
Both the la r g e s tr e t c h in g fo r c e c o n sta n ts (kg
= 0 .1 2 mydn/A) and la r g e induced e l e c t r i c d ip o le moments (
= 1 .3
D [11]
and ^ NH3"HCI' = 0 .9 4
s tr e n g th s o f HF-MH^ and
D )
in d ic a t e
th a t
the
NH —
3
IJH —KF
‘3
binding
are g r e a te r than th a t observed i n the
other van der VJaals com plexes o f KH which have been s tu d ie d .
3
The com plexes IJCH-NH^ and HCCH-KHj form
part o f
an in t e r e s t in g
c l a s s o f m o le c u les which have an a c e t y le n ic hydrogen form ing a bond.
The sym m etrical str u c tu r e o f HCCH-HHg was a t f i r s t p u z z lin g s in c e i t had
been p r e v io u sly determ ined th a t th e complex Ar-HCCH [12] has a T-shaped
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5*
s tr u c tu r e .
Both the sym m etrical KCCK-MH^ and T-shaped Ar-IICCH s tr u c ­
t u r e s , though, can be e a s i l y ex p la in ed by the fr e q u e n tly used HOMO-LUIIO
bonding p ic tu r e [ 2 ] ,
h ig h e s t unocuppied
Due to symmetry, in th e T shaped c o n fig u r a tio n the
*
it
o r b i t a l s o f HCCH have z e ro o v erla p w ith the lone
©
p air o r b it a l o f M L.
*
With Ar th e n o r b it a l i s o f th e c o r r e c t symmetry
fo r o v erla p w ith th e px and py o r b i t a l s o f Ar.
The next h ig h e s t unocup-
pied o r b it a l o f HCCH, the a* o r b i t a l , i s cen tered on th e hydrogens and
i s o f th e c o r r e c t symmetry to a c h ie v e o v erla p w ith the lo n e pa-r o r b it a l
o f NHg. A q u a n tita t iv e t h e o r i t i c a l study o f th e b in d in g o f KH^-HCCK was
undertaken by F r is c h ,
P op le,
and Del Bene [ 1 3 ] ,
Using SCF p lu s t h e ir
M o lle r -P le s s e t p e tu rb a tio n Cl t h e o r ie s a t th e HP4SDS/6-31G** l e v e l they
p r e d icte d a sym m etrical complex w ith an e q u ilib r iu m N
bond le n g th o f 2 .3 2 9 A.
These r e s u l t s appear to be i n e x c e lle n t ag ree­
ment w ith th e v ib r a t io n a lly
from th e microwave s t u d ie s .
d is s o c ia t io n en e r g y , Do ,
c a te d ,
though,
th a t
H van der VJaals
averaged bond le n g th
o f 2.333
These authors a ls o have c a lc u la t e d th e bond
o f NHg-HCCH to be 3 .6 K ca l/m o le.
la r g e r
A ob tain ed
b a s is
energy c lo s e r to 3 K ca l/m o le.
set
c a lc u la t io n s
They in d i­
su g g e st
a b inding
As w i l l be d isc u sse d below , th e observed
in fr a r e d p h o to d is s o c ia tio n o f NHg-HCCK a t 9 8 4 .3 8 cm
- 1
p la c e s th e binding
en ergy, DQ, a t l e s s than 2 .8 K cal/m ole.
NH -C0
3
n itr o g e n .
2
[4] i s a T-shaped complex in which th e carbon bonds to the
Such a complex d is p la y s a s i x - f o l d b a r r ie r to in te r n a l r o ta ­
t io n o f th e NH^ su b u n it a g a in s t th e C02 .
For s t a b le m o le c u les s i x f o ld
b a r r ie r h e ig h ts are low (on th e order o f a few c a lo r i e s per m ole) and
th e sp e c tr a tend to be th a t o f a n ea rly fr e e in t e r n a l r o to r .
a ls o observed i n NHg-COj.
co n sta n t fo r NH,-C0„ i s
T h is i s
I n t e r e s t in g ly , th e weak bond s tr e t c h in g fo r c e
id e n tic a l
to
th a t o f NH.-HCCH (0 .0 7 0 mdyn/A)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i
s u g g e s tin g th a t th e b in ding str e n g th fo r th e se two system s m ight be very
s im ila r .
The average bending am p litu d es o f th e IJH^ su b u n its are a lso
n e a r ly th e same.
T his s i m i l a r i t y , though, i s most l i k e l y th e r e s u lt o f
th e bending a m p litu d e 's in v e r s e
fo r c e c o n s ta n t.
fo u rth r o o t dependence on th e
bending
The measured asymmetry o f th e quadrupole c o u p lin g con­
s ta n t i n NHg-CC^ a llo w s th e d eterm in a tio n o f th e d iff e r e n c e in am plitude
o f the in plane and o u t-o f-p la n e bend o f the NH^ su b u n it.
T his d i f f e r ­
ence i s 1 .0 ( 4 ) ° w ith th e am plitude o f th e in -p la n e bend b ein g g r e a te r .
The measured quadrupole c o u p lin g c o n s ta n ts o f th e ground and th e f i r s t
e x c it e d in t e r n a l r o to r s t a t e s show th a t the average bending am plitude o f
th e
WHj su b u n it
is
in s e n s itiv e
to
th e in te r n a l r o ta t io n
(bending am plitude changes by l e s s than 0 .2 ° ) .
o f th e MHj.
Thus th e presen ce o f
6
cm * o f in te r n a l r o ta tio n energy d oes not le a d to a g y r o sc o p ic r e d u c tio n
o f th e bending am p litu d e.
We have r e c e n t ly
measured in fr a r e d
NHj-KCCH i n th e r e g io n o f th e ^
sp e c tr a
of
both
NH^-CC^ and
um brella m otion o f NH^ [1] (th e ^
o r ig in fo r n o n in v e r tin g f r e e NH^ i s a t 950.3 cm
).
band
T h is was done by
i n j e c t in g th e r a d ia tio n from a a l i n e tu n ab le CO^ la s e r in to th e m olecu­
la r beam e l e c t r i c reson ance sp e c tr o m ete r.
Due to th e sm all r o t a t io n a l
c o n s ta n ts o f van der Waals com plexes and t h e ir
1 0
K r o t a t io n a l tempera­
tu re i n th e m olecu lar beam [14] th e in fr a r e d bands o f such com plexes are
dense and exten d over 5 cm _ 1 .
sp a c in g s and 25 t o
With a l i n e
50 MHz lin e w id th ,
tu n a b le la s e r o f 1 cm~*
many com plexes o f
NH^ have
in fr a r e d spectrum which o v e r la p s a t l e a s t one CO^ la s e r l i n e .
3 we show a sim u la ted p a r a l le l band f o r NHj-HCCH.
an
In Figure
For NHg-HCCH in fr a r e d
s p e c t r a l se a r c h s were made by lin e tu n in g th e C0^ la s e r from 983.25 to
9 8 8 .6 5 cm * .
A reson ance was d e te c te d a t 984 .3 8 cm- 1 .
T his resonance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7
p h o to d is s o c ia te s th e complex and th u s p la c e th e d is s o c i a t i o n en ergy, Do ,
a t l e s s than 2 .8 K ca l/m o le.
id e n tifie d
th e i n i t i a l
9 8 4 .3 8 cm
Infrared-m icrow ave double resonance s tu d ie s
sta te
i n th e resonance a s J=4, K =l.
Thus the
in fr a r e d t r a n s i t io n i s e it h e r the P ( 4 ) , Q ( 4 ) , or P.(4) tra n ­
s i t i o n o f th e \)^ NHg p a r a l le l band o f t h i s com plex.
Because th e t r a n s i­
t io n i s observed to be p h o t o d is s o c ia tiv e an e s tim a te o f th e upper s t a t e
life tim e i s o f in te r e s t.
S in ce a t l e a s t 5 CO^ la s e r l i n e s should over­
la p th e in fr a r e d band, th e
o b se r v a tio n o f on ly one C
la s e r c o in cid e n c e
0 2
w ith one r o t a t io n a l s t a t e o f th e complex s u g g e s ts a narrow lin e w id th fo r
th e
in fr a r e d
tr a n s itio n s .
A sim p le
p r o b a b lis t ic
model
s u g g e s ts
a
lin e w id th o f 150 MHz which correspond s to an e x c it e d s t a t e l i f e t i m e o f 1
n s.
The assignm ent o f th e in fr a r e d t r a n s it io n a llo w s th e d eterm in ation
o f the band o r ig in a s 9 8 4 .4 (9 ) cm
fo r
- 1
NHg-HCCH.
\ ) 2
Thus com plexation
o f NHg w ith HCCH c a u se s a b lu e s h i f t o f the non- in v e r tin g NH^
^
2
fre ­
quency o f 34 cm * .
S im ila r ly , we have a ls o ob tain ed th e MH^
HH -C02 .
2
in fr a r e d spectrum o f
\>2
The spectrum should be c h a r a c t e r is t ic o f a p a r a l le l band o f an
asym m etrical top
e ffe c tiv e ly
( kappa = - 0 .7 2 ,
fr e e in t e r n a l r o to r .
B'- ~ -C = 3 7 5 6 .1 7 8 (3 )
MHz)
w ith
an
As in NHg-HCCH, the in fr a r e d t r a n s i­
t io n s are p h o t o d is s o c ia tiv e and th ey thus p la c e th e bond d is s o c ic a t io n
en erg y , Dq , a t l e s s than 2 .8 K ca l/m o le.
Infrared-m icrow ave double r e s o ­
nance s t u d ie s are summarized i n F igure 4 .
double
resonance
986.57 cm- * .
s t u d ie s
p la c e
R (l)
The J = 0 -1 , K=0 and J = l - 2 , K=0
near 9 8 7 .6 2
cm
- 1
and P (2)
near
In c o n tr a s t to HHj-HCCH, each la s e r l i n e o v e r la p s s e v e r a l
r o t a t io n a l s t a t e s o f th e
com p licated in fr a r e d
com plex.
band a s w e ll
The band o r ig in i s 9 8 7 .1 (2 ) cm
- 1
T his i s
th e
r e s u l t o f both a more
a s a sh o r te r
upper s t a t e l i f e t i m e .
and th e in fr a r e d t r a n s it io n lin e w id th
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8
i s 0 .4 5 (2 0 ) cm 1 .
20 p s .
T his corresponds to an upper s t a t e l i f e t i m e o f
In Table I
life tim e s
energy
fo r
fo r
we summarize in fr a r e d band o r ig in s , lin e w id th s , and
HHg-HCCH,
both
to
8
NHg-COj,
NHg-tJjO,
NH -K20 and NHj-OCS i s
3
and HHg-OCS.
le s s
The
binding
than 2 .8 K cal/m ole.
No
t r a n s it io n lin e w id th s or l i f e t i m e s were determ ined fo r th e se two com­
p le x e s .
In Chapter 2 o f t h i s t h e s i s I d is c u s s the r e s u lt s o f our r o ta t io n a l
s p e c tr o s c o p ic s t u d ie s on Ar-HCN and HCN-COj.
The str u c tu r e o f HCN-C
0
[14] i s com p letely analogous to th a t o f NH ~C02 .
3
I t i s a T-shaped com­
p le x in which the N— C van der Waals bond le n g th i s 3 .00 A.
der Waals bond len g th
is
id e n tic a l
induced d ip o le moment o f NH ~C
3
HCN-C0
2
NHj.
0
2
to
th a t
2
found in
This van
NH -C02 .
The
3
i s o n ly s l i g h t l y g r e a te r than th a t o f
even though the d ip o le moment o f HCN ( 3 .0 D) i s tw ic e th a t o f
A low
order
moments o f HCN-C0
2
e le c tr o s ta tic
and HH ~C0
3
2
c a lc u la t io n
of
the
induced
d ip o le
poorly accou n ts fo r the observed d ip o le
moment enhancements i n th e se com plexes.
The n o n - r ig id ity p resen t i n Ar-HCN g iv e s r i s e
microwave spectrum
fo r t h i s
complex
[1 5 ].
to a ra th er unique
The microwave spectrum i s
c h a r a c t e r is t ic o f a lin e a r m olecu le in which th e re i s anom olously la rg e
c e n tr ig u g a l d i s t o r t io n .
The c e n tr ifu g a l d is t o r t io n co n sta n t fo r Ar-HCN
i s 172 kHz and becomes 102 kHz in Ar-DCN.
th e
c e n tr ifu g a l
d is t o r t io n
co n sta n t
to
The extrem e s e n s i t i v i t y
is o t o p i c s u b s t it u t io n
is
of
con­
s i s t e n t w ith la r g e co u p lin g between th e angular and r a d ia l d eg rees o f
freedom s a s s o c ia te d w ith
th e van der Waals modes.
The o r ig in o f t h i s
unusual co u p lin g i s most l i k e l y due to the presen ce o f a double mimimum
i n th e in te r m o le c u la r p o t e n tia l w ith one mimimum lo c a te d a t th e lin e a r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
c o n fig u r a tio n and th e oth er minimum a t a T-shaped c o n fig u r a tio n o f the
complex.
As i n Ar-HH3 , a poorly d efin ed a b s o lu te mimimum in th e i n t e r ­
m olecular p o t e n tia l makes th e concept o f geom etric s tr u c tu r e
somewhat
nebulous.
In Chapter 3 , the r e s u lt s o f a s p e c tr o s c o p ic stu dy o f th e com plexes
o f BF
w ith HCCH, BF C02> and BF^N^O are p resen ted [ 1 6 ].
3
3
th a t the BFg-HCCN has a sym m etrical s tr u c tu r e w h ile BF ~C
3
have
asym m etrical
nature o f CC
>2
s tr u c t u r e s .
T h is
fu r th e r
0 2
It is
shown
and BF -N
3
2 0
dem onstrates th e complex
and II20 in t e r a c t io n s w ith Lewis a c id s .
In Chapter 4 , I r e p o r t measurements o f th e e l e c t r i c d ip o le moments
o f s e v e r a l hydrocarbon-HF com plexes [ 1 7 ].
C H j,
2
and CjHg
moments o f
(cyclop rop an e)
th e se
were
The d ip o le moments o f C H2 ,
determ ined.
2
The
induced
d ip o le
com plexes do n o t c o r r e la te w e ll w ith th e frequency
s h i f t s o f the HF subm olecule s tr e t c h in g v ib r a tio n measured i n
m atrix
i s o l a t i o n s t u d ie s .
In Chapter 5 , th e a -ty p e r o ta t io n -in v e r s io n spectrum o f (S02 )^ i s
rep orted [ 1 8 ] ,
^
0 2
> 2
i s shown to tu nnel between two e q u iv a le n t c o n f i­
g u r a tio n s a t a r a te o f 70 kHz.
The gas phase s tr u c tu r e o f th e dimer i s
not w e ll determ ined but i t i s shown to be in c o n s is t e n t w ith th e o r ie n ta ­
t io n o f th e in d iv id u a l
s in c e S
0 2
u n it s in th e c r y s t a l .
T his i s s ig n if ic a n t
i s know to form a "m olecular" c r y s t a l .
In Chapter
6
,
I r e p o r t our measurements o f
moments o f % OH and
th e
e le c tr ic
d ip o le
0D in s e v e r a l v ib r a tio n a l s t a t e s [ 1 9 ] .
These
measurements w i l l se r v e a s a t e s t o f t h e o r e t ic a l d ip o le moment fu n c tio n s
o f ^ OH.
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L a s tly , In Chapter 7 , I re p o r t some measurements on th e absorber
speed dependence o f the
r e la x a t io n r a te o f th e J=
0 - 1
t r a n s it io n o f
1SU20 [2 0 ].
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REFERENCES
1.
G.T. F r a se r, D.D. N elson , J r . , A.C. Charo and VJ. Klemperer,
J . Chem. Phys. ( t o be p u b lish ed March, 1 9 8 5 ).
2.
G.T. F r a se r, K.R. Leopold and W. Klemperer, J . Chem. Phys. 80
1423 (1 9 8 4 ).
3.
G. T. F r a se r, K.R. Leopold, D.D. N elson , J r . , A. Tung and
W. Klemperer, J . Chem. Phys. 8 0 , 3073 (1 9 8 4 ).
4.
G.T. F r a se r, K.R. Leopold and W. Klemperer, J . Chem. Phys. 81
2577 (1 9 8 4 ).
5.
Z. Latajka and S . S c h e in e r , J.Chem. Phys. 8 1 , 407 (1984) and
r e fe r e n c e s t h e r e in .
6
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I . Olousson and D.H. Tem pleton, Acta C r y s t ., 1 2 , 832 (1 9 5 9 );
J.W. Reed and P.M. H a rris, J.C hem .P hys., 3 5 , 1730 (1 9 6 1 ).
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12-
7.
T.R. Dyke, K.K. Hack, and J .S . Muenter, J.Chem .Phys. 66,498
(1 9 7 7 ).
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T.R. Dyke, Top.Curr.Chem. 120, 85 (S p r in g er -V e r la g , N.Y. 1 9 8 4 ).
9.
T.R. Dyke, B .J . Howard, and V). Klemperer, J.Chem.Phys. 5 6 , 2442
8
(1 9 7 2 ).
10.
Z .K is ie l, A.C. Legon, and K .J. M ille n , J.Chem .Phys. 7 8 , 2910 (1983);
J.W. Bevan, Z .K i s i e l, A.C. Legon, D .J. M ille n , and S.C . Rogers,
Proc.R .Soc.L ondon S e r . A 372, 441 (1 9 8 0 ).
11.
B .J . Howard (p r iv a te com m unication).
12.
R.L. DeLeon and J .S . IJeunter, J . Chem. Phys. 7 2 , 6020 (1 9 8 0 ).
13.
M.J. F r is c h , J .A . Pople and J .E . Del Bene, J.Chem .Phys. 7 8 ,
4063 (1 9 8 3 ).
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14.
K.R. Leopold, G.T. Fraser and U. Klemperer, J.Chem .Phys. 80,
1039 (1 9 8 4 ).
15.
K.R. Leopold, G.T. F r a se r,
W. Klemperer, J.Chem .Phys.
16.
K.R. Leopold, G.T. F r a se r,
F .J . L in , D.D. N elson , J r . , and
81, 4922 (1 9 8 4 ).
and W. Klemperer, J.Ara.Chem.Soc.
106, 897 (1 9 8 4 ).
17.
D.D. N elson, J r . , G.T. F r a se r, and 17. Klemperer, J.Chem.Phys.
( to be p u b lis h e d ).
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D.D. N elson, J r . , G.T. F ra ser, and VI. Klemperer, J.Chem .Phys.
(su b m itte d ).
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K .I. P eterso n , G.T. F r a se r, and U. Klemperer, C an .J.P hys. 62,
1502 (1 9 8 4 ).
20.
G.T. Fraser and S .L . Coy (m anuscript in p r e p a r a tio n ).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table I
Infrared band origins, linewidths, and lifetimes
ve
r
NHg-HCCH
9B4.4(9) c m ’ ^
150 MHz
n h 3- c o 2
987.1(2) cm "1
0.45(20) cm"1
NHg-OCS
981.5(15) cm"1
-
n h 3- n 2 o
980.(2) cm"1
-
t
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FIGURE CAPTIOUS
F igure 1 .
High r e s o lu t io n spectrum o f th e J=0-1 t r a n s it io n o f
The s p o t t i n g p a tte r n d isp la y e d by
t h i s t r a n s i t io n i s due to th e o v erla p o f two h yp erfin e
p a tte r n s fo r two v ib r a tio n a l s t a t e s o f th e com plex.
F igure 2 .
Observed microwave spectrum o f Ar-NH^ from 13 GHz to
21 GHz. The s p e c tr a l r e g io n s from 65 kHz - 91 11Hz and from
3 .7 5 GHz - 1 3 .0 GHz were a lso searched but no reson an ces
were found in th e se r e g io n s .
Also shown are two h yp efin e
components o f th e only microwave t r a n s it io n which was
observed in m icrow ave-in frared double reson an ce.
F igu re 3 .
In fra red spectrum o f NHg-HCCH assuming
AA= -3 GHz and AB = - 5 IIHz. The i n t e n s i t i e s
are d eriv ed from Boltzman f a c t o r s a t 10 K. The r e l a t i v e
i n t e n s i t i e s o f th e K=0 and K=1 s t a t e s are assumed e q u a l.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.
M icrow ave-infrared double resonance study o f NKgC02 . The microwave t r a n s it io n s which were m onitored
are in d ic a t e d .
The th r ee t ic k marks alon g the y - a x is in
each f ig u r e in d ic a t e
1 0 0
ft, O ft, and
microwave s ig n a l s tr e n g th .
th e
6
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“
6 4 3
ft change in the
- 1 0 0
For exam ple, a t 985.49 cm
t r a n s it io n i s detuned by
- 1
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1
( ) ft.
6
A ll th e t r a n s it io n s are in th e ground in te r n a l r o to r
s t a t e ex cep t where o th erw ise n oted .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10220.5
MHz
10221.5
n
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14091.9
140923
MHz
i |i
i
I ---------------1-------------| — n ------- p
13
15
---------- p . --------- . -------------- J U U f l l , --------------
17
GHz
19
Reproduced with permission o f the copyright owner. Further reproduction prohibited wi;
without permission.
21
zn
U
O
zn
i
C*5
oa
CM
cn
o
ll
O
q
a
z
<
oa
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(S lIN fl A d V d lia d V ) A 1ISN 31N I
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
FREQUENCY SHIFT FROM BAND ORIGIN (cm
n
I
*0 2 " 303
«
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1
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1
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FREQUENCY (cm
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)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o
CHAPTER 1
WEAKLY BOUND COMPLEXES OF NHg
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
22.
The rotational spectrum, internal rotation, and structure of NH3-C02a)
G. T. Fraser, K. R. Leopold,1” and W. Klemperer
D epartm ent o f Chemistry, H arvard University, Cambridge, Massachusetts 02138
(Received 30 April 1984; accepted 24 May 1984)
The radio frequency and microwave spectra of NH -C 0 have been measured using the
molecular beam electric resonance technique. The spectrum is characteristic of an asymmetric
top in which the NH subunit exhibits effectively free internal rotation. The spectroscopic
constants obtained for the ground internal rotor state are presented below:
3
2
3
iL t£(M H z)
3756.178(3),
2
B~ C (MHz) 597.4(2),
2
A ~ B + C (MHz) 8035.(8), Aj (MHz) 0.0240(4),
SK (MHz) 0.20(2), Ajk (MHz) 0.23(5),
Sj (MHz) 0.007(1), eQqm(MHz) -3.175(4),
eQlbb (MHz) 1.557(9), eQqcc (MHz) 1.617(11), /r(D) 1.7684(14).
The N-C0 framework of the complex has C2„ symmetry with a N-C weak bond length of
2.9875(4) A. The average bending angle of the NH subunit is 22.71(5)° with a difference in
amplitude of 1.0(4)° between the in plane and out of plane excursions. The weak bond stretching
force constant is0.070( I)mdyn/A and the induced dipole moment is 0.411( )D. ( ?+ C )/2 for the
first excited internal rotor state (|m| = 1) is 3753.008(4) MHz and the quadrupole coupling
constant eQq
= —3.176(9) MHz is identical with that measured for the ground internal
rotor state.
2
3
2
1™ 1 "
1
INTRODUCTION
High resolution spectroscopic studies of van der Waals
complexes of first row hydrides have provided numerous
opportunities to study weakbonding interactions in a variety
of systems The early investigations have involved HF (as
well as the heavier hydrogen halides), while more recent
work has been concerned with complexes of HzO, NH3, and
HCN. These molecules are convenient binding partners
since they are small (and therefore theoretically tractable),
and have diverse, but presumably well understood, elec­
tronic structures. Thus, the study of their behavior with
common binding partners enables in some sense a study of
the influence of electronic structure (and physical-chemical
properties) of one binding partner on the structure and prop­
erties of the complex.
C0 is one of the more interesting of these common
binding partners. The structure of its complex with HF is
linear and this result has been pronounced as difficult to
understand Surprisingly, knowledge of the structure of
HF-C0 has not aided in the prediction of the stereoche­
mistry of other weakly bound complexes of C0 with Lewis
acids. For. instance, the complex C0 -BF is not a symmet­
ric top though an examination of the structure of HF-C0
would lead to this prediction. Thus it seems that, at least
with Lewis acids, there is no simple picture of C0 interac­
tions.
With simple Lewis bases, however, the situation has
been much clearer. The complexes Ar-C0 HCN-C02,s
and H 0-C 0 have all been structurally characterized by
.1
2
.2
2
2
2
3
3
2
2
2 ,4
2
2
26
*'Supported by the National Science Foundation.
b| Present address: National Bureau of Standards, Boulder, Colorado 80302.
J. Chem. Phys. 81 (6), 15 September 1984
rotational spectroscopy and exhibit a T-shaped geometry
which has been rationalized in terms of a simple HOMOLUMO picture. In this picture, the lowest unoccupied it*
orbital(s) of the C0 “acccept” electron density from the
lone pair orbital(s) of the basic donor. The high barrier to
internal rotation of HzO with respect to C0 in H 0-C 0
has been discussed in terms ofthe formation ofa w-type bond
in which the filled lone pair orbitals of the H20 interact with
the two empty it* orbitals of the C02. Though this simple
kind of picture has been able to provide a pleasing and che­
mically intuitive qualitative description of these, as well as a
wide variety of other complexes, its lack of quantifiability
can easily be criticized. The complicated contributions from
electrostatic, polarization, dispersion, and exchange forces
casts serious doubt on almost any simple-minded view of van
der Waals interactions in general. Thus, in light of the lack of
complete understanding of the van der Waals bonding of
C02, its complexes with simple first row hydrides are worthy
of examination. We report here the structural characteriza­
tion of the complex NH -C 02. The structural result of this
work agrees with that obtained for the similar complexes
HCN-C0 and H 0 - € 0 which were studied simulta­
neously with NH -C 02. NH -C 0 is shown to have a Tshaped geometry in which the nitrogen of ammonia bonds to
the carbon of COz. Although this is precisely the structure
which would be predicted on chemical grounds, and is also
suggested in matrix isolation studies a few interesting com­
parisons can be made with the other similar complexes.
The T-shaped structure of NH -C 0 also offers the
possibility of observing nearly free internal rotation in a van
der Walls complex. The barrier anticipated for NH -C 0 is
sixfold, and such barriers in stable molecules are low, less
2
2
2
2
3
2
0021 -9606/84/182577-08502.10
2
3
2
3
2
7
3
2
3
© 1984 American Institute of Physics
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2
2577
2578
Fraser, Leopold, and Klemperer: Spectrum and structure of NH,-CO,
than 14 cal/mol in the molecules CH N 0 and CH BF
(which are both isoelectronic to NH -C 02). As shown be­
low, the part of the spectrum which is accessible to our ex­
periment is quite insensitive to the height of this barrier, but
the study of the complex will, nonetheless, permit the deter­
mination of some structural and dynamical properties of the
first excited internal rotor state.
3
28
3
29
3
RESULTS
The microwave spectrum of NH -C 0 is consistent
with the expected T-shaped structure for this complex in
which the nitrogen of NH is bonded to the carbon of C02.
Such a structure gives rise to a sixfold barrier to internal
rotation of the NH subunit against the C02. The two stable
molecules CH N 0 and CH BF have previously been
studied and are spectroscopically similar to the NH -C 0
system. Accordingly, the spectral analysis will parallel that
of CH BF and CH N 02.n The distortionless rotational
Hamiltonian for these types of molecules can be written as
3
2
3
3
3
28
3
29
3
EXPERIMENTAL
3
A NH -C0 beam was formed by a supersonic expan­
sion of a mixture of 1% NH and %C0 in argon through a
25 fi nozzle at room temperature. The stagnation pressure
was 3 atm. Spectra were taken using the molecular beam
electric resonance technique. Since NH -C 0 was expected
to be similar in structure to H 0 -C 0 2, which is a prolate
asymmetric top the original spectral searches were begun
in the radio frequency region for AT= 4 asymmetry doublets.
Two transitions were observed at 4.7 and 23.5 MHz and
were assigned to the/ = 5, K —4 and / = , K = 4 asymme­
try doublets. Next a search was made for the J = 4, K = 2
doublet which was found at 1886 MHz. Microwave searches
near 7,15, and 22 GHzallowed the observation of t h e /= 01, 1-2, and 2-3 transitions of the ground (m = 0) internal
rotor state and the J = 1-2 and 2-3 transitions of the excited
internal rotor states (|m | = ).
All the reported measurements were made while moni­
toring the NH3+ ion fragment of the complex since the signal
to noise ratio is greatest on this ion peak. The relative signal
strength of the — transition was measured on various
mass peaks and these results are presented in Table I. It is
seen that the resonance intensity is greatest on the NH3+ ion
peak, and that no transition could be observed on the parent
ion peak NH C02+. Similar observations were made in the
NH3-acetylene mass spectrum Although no transitions
could be observed on the parent ion peak, the observation of
the resonances on both the NH3+ and HC02+ /NH CO+ ion
peaks, as well as the unique rotational spectrum and the
characteristic I4N hyerpfine structure of each transition, al­
lows the positive identification of the species as the NH3COz complex.
3
2
3
8
2
2
3
2
3
2
+ »»,
in
2
,6
where
^
6
1
1 01
2 02
3
. 10
3
TABLE I. Signal intensity of the 10i-2 o2transition of N H ,-C 0 2on various
ion peaks.
(m/e)
Probable
ionic aperies
Signal strength
(arbitrary units)
12
14
IS
16
17
28
29
44
45
61
C+
N+
NH+
NHj+
NH +
CO+
HCO+
c o ,+
H C O r, NHjCO+
NH3COj+
a
a
1
4
9
a
a
1
1
a
‘ No signal was observed on these mass peaks.
^
^
~ 8^ ( 4 , - 4 ) ’
“
877*4 ’
^=
”
^
877*4 ’
.and
In the rigid molecule limit, Ia is the moment of inertia of the
internal top about its C axis and 4 > 4 > and I„ are the
moments of inertia ofthe entire complex about the a, b, and c
principal axis. J is the total angular momentum and j is the
angular momentum of the internal rotor along the a axis of
the complex. Matrix elements of Hm are calculated in the
free internal rotor basis |JKM )dma, where \JKM) are the
usual prolate symmetric top wave functions and a is the
angle specifying the orientation of the internal top with re­
spect to the N-C0 framework. The barrier V(a)
= (fV2)(l —cos a) is sixfold and is diagonal in J, K, M
and off diagonal by six in m. For the case of small asymme­
tries and low barriers both mand K are nearly good quantum
numbers and the selection rules are AK = 0, Am = 0. The
transition frequencies of the ground internal rotor state
(m = ) are insensitive to both the barrier height and the
internal rotation and thus the spectrum for this case is treat­
ed by the usual semirigid rotor treatment of asymmetrical
tops. Any effects of the small barrier to internal rotation will
be small and indistinguishable from centrifugal distortion
contributions. For the excited internal rotor states (|m | > 0)
an analysis must be made via Eq. ( ).
3
2
6
0
1
Ground internal ro to r state
The measured transitions of the ground internal rotor
state are listed in Table II. These transitions were fit to a
semirigid rotor Hamiltonian with an additional term being
necessary due to the effect of the nuclear quadrupole mo­
ment of the 14N nucleus. The Hamiltonian can be written as
(3)
H = H M + Hai + H quld ,
where HM is the Hamiltonian of Eq. (1), i 4 *s the centrifu­
gal distortion Hamiltonian, and ffqiud is the expression for
the nuclear quadrupole interaction. Since the transition fre­
quencies of the ground internal rotor state (m— ) are insen0
J. Chem. Phys., Vol. 81, No. 6,15 September 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fraser, Leopold, and Klemperer: Spectrum and structure ot NH,-CO,
2 .M
TABLE II. Observed m = 0 zero-field transitions for NH3-C 0 2.
F'
F■
5«
64,
7*4
22,
2ji
22,
54i
642
743
220
^20
220
^20
2m
220
220
^21
*22
*22
*22
*22
*22
*22
*22
*01
*01
^02
2o2
2o2
2o2
303
hx
2
2
1
2
3
3
1
2ji
22i
^21
322
*23
*23
4*
*23
*23
3
5
4
3
5
4
4
1
1
2
0
2
1
*23
Qoo
*01
*01
*01
*01
2o2
2m
Observed-calculated
(kHz)
vfMHz)
4.739(2)
23.509(1)
85.099(2)
130.741(2)
131.304(5)
1
3
I)
2 (
3 *
2
2
4
4
4
;i
5
3
2
0
0
0
0
0
132.324(2)”
133.337(4)
133.904(2)
651.089(3)
1 885.184(1)
1 885.296(2)
1 885.730(2)
- 1
-1
1
- 1
0
3
1 885.758(3)”
1 886.188(1)
. 1 886.304(1)
7 512.421(5)
7 513.845(5)
14 890.670(13)
14 890.826(7)
14 891.690(7)
14 893.200(8)
22015.3(6)
23 047.1(13)
0
2
1
3
1
2579
1
-1
2
-2
-5
3
2
-4
-4 0 0
-5 0 0
• F = I + J.
” These lines could not be unambiguously assigned and were excluded from the fit.
sitive to both the barrier height and the internal rotation, no
hindering potential is included in Hm . Thus H rol + H as
takes the form of Watson’s semirigid rotor Hamiltonian12
and becomes
+ Hcd = ^ ± £ y (/ +
1) +
(a - 1 ± £ ) K 2
- A j J 2( J + 1)2 - A jkJ ( J + 1)K 2 - A k K a
+
(31 -
J 2) - 2 S j J ( J + 1)(J| - J 2)
[J2( J ? - J 2) + ( J ^ - J 2)J2]-
-SK
(4)
The nuclear quadrupole interaction is treated to first order13
and is
^quid
“
/(/+ )
+ ^ < J? )]F (W ).
shown in Fig. 1. The hyperfine free line centers were then fit
to Watson’s Hamiltonian by an iterative nonlinear weighted
least squares procedure. (B + C ) / 2, (B — C ) / 2,
A —(B + C)/2,A j , A JK,8j,BJid8K were sensitive enough to
the observed transitions to be determined. Since only
A K = 0 transitions were observed A K cannot be determined
independently from A and was thus set to zero in the fit. A
further result of this is that all the rotational and centrifugal
distortion constants are highly correlated except for
(B + C)/2 and A j which are only correlated to each other
(correlation of 0.93). The resulting spectroscopic constants
are given in Table III.
The dipole moment was determined from the measure­
ment of the Stark effect of th e / = 3, K = 2 asymmetry doub-
1
(5)
Y (JJJF)is Casmir’s function and eQq^ are the diagonal ele­
ments of the nuclear quadrupole coupling tensor which is, in
this case, diagonal in the inertial frame.
Only fl-type A K = 0 transitions were observed. Fur­
thermore, only even K levels are observed when m = 0 due
to the indistinguishable spinless oxygen nuclei. The hyperfine structure of each line was first fit to determine eQq^,
eQqbb, and the hyperfine free line centers of the rotational
transitions. The asymmetry of the quadrupole coupling ten­
sor (e0 ?w> —eQqcc)was determined primarily from the mea­
sured hyperfine splitting pattern of the J = 4, K = 2 asym­
metry doublet. The AF = 0 components for this doublet are
FIG. 1. The A F = 0 hyperfine components of the
423-4^ asymmetry doublet transition of NH3CQj. This is the average of four scans using a 4 s
time constant.
I
.
1885.7 1885.8
MHz
1
J. Chem. Phys., Vol. 81, No. 6,15 September 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2580
Fraser, Leopold, and Klemperer: Spectrum and structure of NH,-CO,
TABLE III. Spectroscopic constants of the m = 0 internal rotor state of
J = 0 to J = 3 and diagonalized. The dipole moment was
N H j-C O j.
then found iteratively to be 1.7684(14) D. The ratio of the
dipole moment determined from the Oqo-Ioi 1° that deter­
mined from the 3 asymmetry doublet is 1.00079(21). No
attempt was made to establish the origin of this descrepancy.
It should be noted that the dipole moments are reported with
an absolute uncertainty while their ratio is reported with a
relative uncertainty. The limitation on the absolute accuracy
of our dipole moment determinations is due primarily to the
uncertainty in separation of the electric field plates.
^ (M H z )
3756.178(3)
-^ f^ (M H z )
597.4(2)
A - - * C (MHz)
2
8035.(8)
0.0240(4)
0.20(2)
0.23(5)
0.007(1)
- 3.175(4)
1.557(9)
1.617(11)
1.7684(14)
1.7669(12)
d.,(MHz)
* jc( M H z )
4„(M H z)
5 ,(MHz)
<fi?„(MHz)
<0?*(MHz)
e ftJ M H z )
MW
M(D)b
E xcited interna l ro to r states
Uncertainties are two standard errors as determined from the least squares
fit.
‘ from 7 = 0-1 transition.
’’from J = 3, K = 2 asymmetry doublet.
let and the J — 0-1, K = 0 rotational transition. The 7 = 3,
K — 2 doublet was chosen since this transition has no hyper­
fine structure at the experimental resolution. The frequency
of the M j = 3, AM j = 0 component of this doublet was
measured at three values of the electric field. These data are
presented in Table IV. The dipole moment was calculated by
treating the asymmetry doublet as a two-level system with a
coupling matrix element <32 „M , = 3|p,*E|322, M j — 3).
Due to the large asymmetry of this molecule this matrix
element cannot be approximated by the symmetric top val­
ue. The effect on the calculated dipole moment of other near­
by levels is only about 0.003% and this is included in the
reported value. The dipole moment is calculated to be
1.7669(12) D.
As a check on this value of the dipole moment the Stark
effect of the Ow- I q, transition was measured. Due to the
molecular beam selection rules this transition has only two
resolvable hyperfine components at both zero and nonzero
electric fields. The Hamiltonian used to analyze these data is
H , = H m + H a l - V : Q -ix -E ,
(6 )
where V is the electric field gradient tensor and Q is the
nuclear quadrupole moment tensor. The matrix elements of
Hs were calculated in the uncoupled basis \Jk M j IM ,), and
the Stark matrix was set up in MF = M j + M , blocks from
The observed transitions of the excited internal rotor
states are listed in Table V. Only |m| = 1, K = 1 excited
state transitions were seen. This is a direct result of the iden­
tical spin zero oxygen nuclei requiring [K —m) to be even
and the —10 K rotational temperature of the supersonic
expansion enabling only |m| = 1 , excited internal rotor
states to have sufficient population to be observed. Hyper­
fine structure was resolved for the J = 1-2, K = 1 transi­
tions verifying their assignments. The quadrupole coupling
constant cQq]™{~ 1 was determined from the observed hyper­
fine splitting pattern. The observed splitting pattern is that of
a symmetric top since the principal axis of the quadrupole
tensor does not change with internal rotation. Due to the
Coriolis type term —2Aj J„ the contribution to the observed
transition frequency of an asymmetry in the quadrupole cou­
pling constant eQqbb —eQq„ of 100 kHz is less than 1 kHz.
Thus the observed transitions are insensitive to this asymme­
try and only eQq1™
1 is obtained and shown in Table VI.
The value of the quadrupole coupling constant determined
for the \m\ = 1 states agrees with the ground state constant.
As will be seen later this implies that the bending amplitude
of the NH3 subunit in the excited internal rotor state is near­
ly the same as in the ground state.
From the hyperfine free line centers determined above
and the Hamiltonian Hm of Eq. (1) (with V6= 0), the effec­
tive rotational constants for the excited internal rotor state
were determined. An examination of H„, shows that both
{B+ C)/2
and [(B-C)2/A ]H ” ' are well deter­
mined and uncorrelated since 2(2? + C )|m| is the average
of the frequencies of the two J —1-2, |/n| = 1,AT= 1 transi­
tions and to second order [(2? —Cf/A ]|m| is their fre­
quency separation. An inspection of the perturbative expres­
sions for the J =2-3, |m | = 1, K = 1 transitions shows that
[(B+ C){B—Cf/A 2] |m| should likewise be determin”
|m |-
1
1
“
“
“
1
TABLEIV. Observed nonzero field transitions o f the m = 0 internal rotor states of N H j - C 0 2.
Transition
%■(«(,- 3 ) 4 b W r - 3)
< W 1, M r = 0, ± I ,M j = 0(-lol(F = 0 ,M r = 0,M J ’=0)
( W F = 1. M , = 0, ± 1, M j m 0>-lol(F = 2,M r <= ± \ , M j = 0)
1
E [S /a a f
Frequency (MHz)
0.00
99.82
199.90
299.69
998.2
998.1
651.089(3)
656.996(2)
674.470(3)
702.565(2)
7568.632(5) .
7567.694(10)
‘ Electric field known to better than 0.1%.
J. Chem. Phys., Vol. 81, No. 6 ,1 5 September 1684
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
Fraser, Leopold, and Klemperer: Spectrum and structure of NH.-CO,
24
TABLE V. Observed |m| = 1, K = 1, Am = 0 rotational transitions NH}-C 0 2.
m
J
F‘
J'
F'
+ 1
+ 1
+ 1
+ 1
+ 1
+ 1
-1
-1
- 1
-1
-1
+ 1
-1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
0
1
2
2
2
0
2
2
2
2
2
2
2
2
2
2
2
3
3
2
2
1
3
1
1
2
2
3
1
1
2581
Observed-calculated
(kHz)
Frequency
(MHz)
-2
2
1
-1
-8
3
0
2
-2
1
-2
-6
6300
14 957.142(3)
14957.622(2)
14957.939(2)
14 958.130(2)
14 958.406(3)
14959.132(2)
15 065.333(3)
15065.811(2)
15066.318(3)
15 066.604(2)
15067.316(2)
22 026.6(3)
22 663.0(15)
•F = I * + J .
able as well as uncorrelated from (B + C )/2|m| “ 1 and
[(B — C f / A ]|m| ” In Table VI we list these combinations
of rotational constants for both the ground and excited inter­
nal rotor states as well as the percentage change of the excit­
ed state constants from that of the ground state. The large
changes in the rotational constants as well as a 6 MHz resid­
ual from the fit for the one of the transitions indicate that this
model Hamiltonian H mt poorly describes the internal rota­
tion in this system. An inclusion of a nonzero barrier does
not improve the fit since the observed transitions are insensi­
tive to the barrier height. We note that the predicted frequen­
cy, of the transition most sensitive to the barrier height
(J = 2-3, K — 1, m = 1), shifts by less than 1 kHz/cal/mol
for a barrier height which is expected to be less than 2 0 cal/
mol. It should be further noted that a simple internal rotor
Hamiltonian similar to that used here poorly fit the spec­
trum for the weakly bound complex HF-CH 3CCH. ' 4 We
might assume that the failure of this simple Hamiltonian to
adequately describe the data is the result of the neglect of the
interactions between the low frequency van der Waals vibra­
tions and the internal rotation. An examination of the spec­
tral data for the two stable models CH3BF2 and CH3N 0 2
should allow us to see if these poor fits are symptomatic of
van der Waals complexes or are also seen in stable molecules.
In both of these molecules [B + C )/2 changes by only 200
kHz with the addition of one unit of internal rotation while
the same change is 3 MHz for NH3-C 02. Furthermore, for
CH3BF2 the rotational constants for the ground internal ro­
tor state adequately reproduced the data for the excited in­
ternal rotor states (all the residues are less than 5 MHz for
\m | = 0—
3)®while for NH3-C 0 2 the residuals are as large as
30 MHz when only considering internal rotor states up to
|m| = 1. Inspection of the larger amount of data available
for CH2N 0 215 though, indicates that this simple Hamilton­
ian is not able to reproduce the data very well unless centrifu­
gal distortion coefficients are included (two coefficients be­
ing as large as 22 MHz) and the A rotational constant is
allowed to differ from the A constant in the —2A J„ j term.
Furthermore, by examining the same transitions in CH3N 0 2
that were observed in NH3-C 0 2, it is seen that the ground
state constants poorly reproduce the excited state transitions
with one residual as large as 58 MHz. It thus appears that
this model Hamiltonian poorly describes the free internal
rotation of both CH3-N 0 2 and NH3-C 0 2 implying that the
lower vibrational frequencies of the van der Waals modes are
not necesarily responsible.
S tructural analysis
The observed spectrum of NH3-C 0 2 demonstrates that
this complex has a T-shaped structure. The.4 rotational con­
stant of 11791(8) MHz is similar in value to
TABLE VI. Spectroscopic constants of the |m | = 1internal rotor state of NH3- C 0 2and a comparison with the
corresponding m = 0 constants.
m= 0
|m | = l
% difference
3756.178(3)
3753.008(4)
0.08%
121.061(12)
108.356(30)
10%
■ ^ C . H f r £ £ (MH z)
77.130(42)
74.37(30)
4%
«Gg.,(MHz)
-3.175(4)
-3.176(9)
A
-
Uncertainties ate two standard errors as determined from the least squares fit.
J. Chem. Phys., Vol. 81, No. 6 ,1 5 September 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2582
FIG. 2. Coordinate system used to describe the structure and dynamics of
NH j-CO j .
11 698.2(12) of free C0 216 and is consistent with a Tshaped structure for this complex. In addition, the spectrum
is characteristic of a cold CH3N 0 2 type molecule as shown
by the observation of the excited internal rotor states
(|m | = 1) and by the absence of (AT—m) odd levels. This last
result shows that the two spinless oxygen nuclei are equiva­
lent and supports an average C2l> structure for the C02-N
framework. The complexes HCN-C0 2,5 Ar-C0 2,4 and
H20 -C 0 26 have been studied and all have been shown to
have this T-shaped geometry in which the basic atom bonds
to the carbon of C02. Comparison of NH3-C 0 2 with these
complexes indicates that it is unlikely that the hydrogens in
NH3 point toward the C0 2 and thus the chemically reason­
able N-C bonded structure is assumed.
To obtain quantitative information on the average
structure of this complex we proceed in the usual manner
and treat the large amplitude bending and stretching modes
of the complex as small displacements from an assumed
equilibrium geometry. Simplicity dictates the assumption
that NH3-C 0 2 has a T-shaped equilibrium structure in
which the heavy atom framework has C2„ symmetry. The
two subunits are assumed to be unchanged upon complexation with each having their vibrationally averaged r0 struc­
ture. The NH 3 inversion motion is quenched by complexation since the potential associated with the umbrella motion
is no longer symmetric. The coordinates necessary to de­
scribe the orientation of the two subunits in the complex are
shown in Fig. 2. y is the COzbending angle while* and are
the two angles necessary to describe the in and out of plane
bending of the NH3 subunit, y and * arc referenced to the
equilibrium configuration,
is the distance between the
centers of mass of the two subunits. The instantaneous iner­
tial tensor and quadrupole tensor of the complex are para-
B0 =
metrized in terms of these coordinates and the moments of
inertia and quadrupole coupling constants of the free mole­
cules. Neither the inertial tensor nor the quadrupole tensor
will be diagonal but after averaging over the zero point oscil­
lations both will become diagonal and the principal axis of
each will coincide. (This situation arises due to the symmetry
of the assumed equilibrium structure.) Furthermore, rc m
will coincide with the a axis on the average and a will corre­
spond to the angle which describes the internal rotation and
is associated with the quantum number m. The results for
the three vibrationally averaged moments of inertia and the
three vibrationally aveaged components of the quadrupole
tensor are
<4 ,) =/i<sin2*> + / 3 <cos2* ) + / 0 <cos2*> .
eQgaa = eQgm i (P2[cm x >.
<4 > = /i< l —sin2 x sin2 <p) + / 3 <sin2 x sin2 <p)
+ 70 <sin2 y) + Ms<r£m. >»
</„) = / 2<l - s i n 2 * c o s V ) + / 3 <sin2 *cosV >
+ 10-f M, (r m.) ,
2
eQgcc = e NH3</>2(sin^cos <p) ) ,
where/x and / 3 are the b and c moments of inertia of NH3,/„
is the moment of inertia of C02, and Ms is the reduced mass
of the complex. In order to analyze the difference between
the in and out of plane bending amplitudes of the NH3 sub­
unit it is convenient to define two new angles £out and
£out is the angle which describes the out of plane bending of
the NH 3 subunit and is the corresponding angle for the in
plane motion. The relationships between the coordinates in
Fig. 2 and f to and £„« are
2 9
«:n (•
sin sin*
. 2
, • 2
• 2 \l/2 9
(cos x + sm X sm <P)
. *
cosfl?siny
^^
SUl £ out
2
. 2
2 vI/2 *
(cos * -1- sin * cos <p)
Due to the nearly free internal rotation, the measured A rota­
tional constant only has contributions from the C0 subunit.
Therefore the rotational constants are related to the vibra­
tionally average moments of inertia as follows:
" “ •bin
2
87T2/ O< c o s 2 y ) ’
TABLE VII. Structural and dynamical constants of NH3-C 0 2*
£oot
Y
fcAC.
rH-C
k.
v,
ftidiigd
0.8508(7)
0.915(2)
0.924(2)
0.9921(8)
22.71(5)*
17.0(2r
16.0(2r
5.1(3r
3.0538(4) A
2.9875(4) A
0.070(1) mdyn/A
98.(l)cm -‘
0.411(2)D
‘ Derived for m = 0 internal rotor state.
(7)
eQgt,, = eQqNHi(P2{sin x sin <p)),
A _____^_____
(cos2* )
(cos’ fto)
(cos’ fo a )
(COS2)')
X
27
Fraser, Leopold, and Klemperer: Spectrum and structure of NH,-CO,
n
C —___ —
___
h
’
877^ < T „ )
(9)
From the quadrupole coupling constants of the com­
plex and the expressions given above the three expectation
values <cos2* ), <cos2 4 >, and <cos2
are determined
and shown in Table VII. Operationally defining *
= cos_ ,«cos2* ) ' /2), etc. it is seen that * = 22.72(7)°,
f = 17.0(2)°, and
= 16.0(2)°. The measurement of the
asymmetry in the quadrupole coupling constant
eQgbb — eQgcc fro™ the observed hyperfine pattern of the
/ = 4 , K = 2 doublet allowed the determination of this dif­
ference between the in and out of plane bending amplitudes
of the NH3 subunit. The bending amplitude of the C0 sub­
unit is calculated from the^ rotational constant. This results
in :<cos2 *) =0.9921(8)°-corresponding to a value of
2
..........
J. Chem. Phys.. Vol. 81, No. 6,15 September.1084
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fraser, Leopold, and Klemperer: Spectrum and structure of NH,-CO,
y = 5.1(3)°. Finally, from (7^,) + </„) the distance between
the centers of mass of the two subunits rc m = (r£ m > 1/2 is
determined to be 3.0538(4) A corresponding to an N-C weak
bond length of2.9875(4) A. The structural parameters deter­
mined above are summarized in Table VII.
From the centrifugal distortion constant A Jt the weak
bond stretching force constant is determined. If the domi­
nant contribution to A j is assumed to be the stretching of the
van der Waals bond then5
k
2563
TABLE VIII. Comparison of several NH} van der Waals complexes.
/^induced|B |
k, (mdyn/A)
rN-B (A)
X
0.41
0.63
0.94
1.3
0.070
0.070
0.122
2.99
2.33
2.16
1.78
22.7
23.2
20.4
H jN -C O /
HjN-HCCH‘
HjH-HCN‘
H ,N -H Fa
...
‘ This work.
‘ Reference 10.
‘ Reference 17.
d Reference 18.
32ir*(Kr, m.)2lB4+ c 4]
hAj
Use of this expression results in a stretching force constant of
0.070{ 1 )mdyn/A corresponding to a stretching frequency of
98(1) cm- The induced dipole moment for the complex is
calculated by
/^induced “ / f complex
A n H 3 (C O S
X)
is chosen as the N-C bond distance the induced dipole mo­
ments are then calculated to be 0.50 (NH3-C 02) and 0.70 D
(HCN-C02). Thus, setting the interaction distance between
rc.m. and rN^ does not give an induced dipole moment which
agrees with experiment. It should be noted that electrostatic
calculations of induced dipole moments can be criticized for
several reasons, one of which is the lack of a reasonable crite­
ria for choosing the interaction distance.
Besides that with C02, the interaction of NH3 with
HCN, 17 HF, 18 and HCCH10 has been studied and these re­
sults are summarized in Table VIII. The two binary com­
plexes HF-NH 3 and HCN-NH3 are the most strongly
bound while NH 3-C 0 2 and HCCH-NH3 appear nearly
equal in binding strength when measured by the stretching
force constant. The two bond lengths though are quite differ­
ent due to the differences in size of carbon and hydrogen. It is
also seen in Table VIII that the average bending angles of the
NH 3 subunit are nearly equal. This consistency in bending
angle has also been noted in the case of both hydrogen19 and
antihydrogen5,19 bonded HCN subunits and most likely re­
sults from its weak inverse fourth root dependence on the
bendng force constant. The wider amplitude motion of the
NH3 subunit compared with that of the N-bonded HCN (23°
vs 18°) is undoubtedly a combined effect of the difference in
force constants and bending reduced masses. Approximat­
ing the bending reduced mass for HCN and NH3 by / HCN
and 7X, respectively, the observed angles show the bending
force constant for the NH3 systems to be 2.5 times greater
than that for HCN.
The trend in binding strength seen for the NH3 com­
plexes in Table VIII is also observed for the corresponding
H20 complexes. In Table IX we compare the weak bond
force constants and bond lengths for complexes of NH3 and
H20 with COz, HCCH, HCN, and HF. The complexes with
,
where (cos j ) i s approximated by (cos2 x ) U2-The resultant
induced dipole moment is 0.411(2) D.
DISCUSSION
The structure of the NH3-C 0 2 complex is clearly quite
consistent with the structure of other complexes of C0 2 with
Lewis bases which have been examined, i.e., Ar-C0 2,4 H20 C 0 2,6 and HCN-C0 2.5 The stereochemistry of each of these
binary interactions can be rationalized in terms of the inter­
action between the lone pair(s) of electrons of the base with
the lowest unoccupied tt® orbital of the C02. A comparison
of the properties of these four complexes has been previously
made3 and has shown, as expected, that Ar-COz is the most
weakly bound complex in the series while H 20 -C 0 2 and
H 3N-C0 2 appear nearly equal in binding strength. It was
also noted that the N-C bond lengths for HCN-C0 2 and
NH 3-C 0 2 are the same (both 3.0 A), while the force con­
stants are somewhat different (0.049 and 0.070 mdyn/A for
HCN-C0 2 and NH3-C 0 2, respectively). The induced di­
pole moment of NH3-C 0 2 is greater than that of HCN-C0 2
(0.41 vs 0.36 D) though the dipole moment of HCN is twice
that of NH3. A low order electrostatic calculation of the
induced dipole moment, considered as the sum of the mo­
ment induced on the C0 2 subunit by the dipolar base and
moment induced on the base by the C0 2 quadrupole mo­
ment, gives 0.46 and 0.38 D for the dipole moments of NH3C0 2 and HCN-C02, respectively when the interaction dis­
tance is arbitrarily chosen as
. If the interaction distance
TABLE IX. Comparison of several NH3 and HjO van der Waals complexes.
H j N-CO j *
HjN-HCCtf1
H 3N-HCN c
HjN-HF1
•This work.
‘ Reference 10.
‘ Reference 17.
'Reference 18.
k, (mdyn/A)
rN-B (A)
0.070
0.070
0.122
-•
2.99
2.33
2.16
1.78
H j O-CO j*
HjO-HCCir
HjO-HCN*
HjO-HF*
k , (mdyn/A)
rO-B (A)
0.064
0.065
0.111
0.15
2.84
2.23
2.08
1.74
‘Reference 6.
'Reference 20.
'Reference 21.
‘ Reference 22.
J. Chem. Phys., Vol. 81, No. 6,15 September 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2584
Fraser, Leopold, and Klemperer: Spectrum and structure of NHj-C O j
CO; and HCCH are apparently the weakest while those with
HF and HCN are stronger. With the same Lewis acid bind­
ing partner, the force constants and bond lengths are similar,
though for the HzO complexes they are both somewhat
smaller. A closer examination of the structure of these com­
plexes show that there are in fact large differences in HzO
and NH 3 interactions. For instance, H 20 -C 0 2, unlike NH3C 02, has a high torsional barrier. This barrier height has
been determined to be approximately 1 kcal/mol and ap­
pears to come about due to the two lone pair oribtals on the
oxygen interacting with the it* orbitals of the C 02. This re­
sults in a double bond for the complex which inhibits the free
internal rotation of the H20 subunit.
It was noted earlier in the text that the bending ampli­
tudes of the NH3 subunit in the ground and excited internal
rotor states are the same, differing at most by 0.2*. This im­
plies that the ~ 6 cm- 1 of internal rotation energy does not
lead to appreciable gyroscopic alignment of the NH3 axis
with the a axis. It was further seen that the amount of hinder­
ing of this internal rotation by the presence of a sixfold bar­
rier could not be determined from the observed transitions.
Measurement of this V6 barrier would require that |m| = 3,
internal rotor states be observed since these states are split by
the barrier." Such states, though, are anticipated to be ap­
proximately 50 cm- 1 above the ground state in energy and
are thus not expected to be populated at the temperature of
the beam.
In conclusion, internal rotation in van der Waals mole­
cules has only begun to be studied. Such studies should allow
the testing of simple models about the origin of potential
barriers hindering internal rotation. We are currently inves­
tigating the weakly bound complex NH 3-N 20 which is isoelectronic to NH3-COz. Assuming the same structure for
these two complexes the internal rotational symmetry is re­
duced in NH 3-N 20 and thus a threefold barrier term is pres­
ent. It would thus be interesting to see if the barrier height in
this case is small giving rise to nearly free internal rotation of
the NH3 subunit or large as are most threefold barriers in
stable molecules arising from adjacent interactions.
'T. R. Dyke, in Hydrogen Bonds, Topics in Current Chemistry, edited by F.
L. Boschke (Springer, New York, 1984), Vol. 120.
JF. A. Baiocchi and W. Klemperer, J. Chem. Phys. 78,3509 (1983).
3K. R. Leopold, G. T. Fraser, and W. Klemperer, J. Am. Chem. Soc. 106,
897 (1984).
4J. M. Steed, T. A. Dixon, and W. Klemperer, J. Chem. Phys. 70,4095
(1979).
5K. R. Leopold, G. T. Fraser, and W. Klemperer, J. Chem. Phys. 80,1039
(1984).
*K. I. Peterson and W. Klemperer, J. Chem. Phys. 80,2439 (1984).
7L. Fredin and B. Nelander, Chem. Phys. 15,473 (1976).
SE. Tannenbaum, R. J. Myers, and W. D.Gwinn, J. Chem. Phys. 25, 42
(1956).
E. Naylor, Jr. and E. B. Wilson, Jr., J. Chem. Phys. 26,1057 (1957).
I0G. T. Fraser, K. R. Leopold, and W. Klemperer, J. Chem. Phys. 80,1423
(1984).
"E . B. Wilson, Jr., C. C. Lin, and D. R. Lide, Jr., J. Chem. Phys. 23,136
(1955).
1JJ. K. G. Watson, J. Chem. Phys. 46,1935 (1967).
,3C. H. Townes and A. L. Schawlow, Microwave Spectroscopy (Dover, New
York, 1975).
I4J. A. Shea, R. E. Bumgarner, and G. Henderson, J. Chem. Phys. 80,4605
(1984).
,SF. Rohart, J. Mol. Spectrosc. 57,301 (1975).
,6C. P. Courtoy, Can. J. Phys. 35,608 (1957).
,7G. T. Fraser, K. R. Leopold, D. D. Nelson, Jr., A. Tung, and W. Klem­
perer, J. Chem. Phys. 80,3073 (1984).
laB. J. Howard (private communication).
I9P. D. Aldrich, S. G. Kukolich, and E. J. Campbell, J. Chem. Phys. 78,
3521 (1983).
“ K. I. Peterson and W. Klemperer, J. Chem. Phys. (to be published).
2IA. J. Fillery-Travis, A. C. Legon, and L. C. Willoughby, Chem. Phys.
Lett. 98.369 (1963).
“ J. W. Bevan, Z. Kisiel, A. C. Legon, D. J. Millen, and S. C. Rogers, Proc.
R. Soc. London Scr. A 372,441 (1980).
nt.
J. Chem. Phys., Vol. 81, No. 6,15 Septem ber 1884
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3o
The stru ctu re of NH3-acety len ea)
G. T. Fraser, K. R. Leopold, and W. Klemperer
Department o f Chemistry. Harvard University. Cambridge, Massachusetts 02138
(Received 25 August 1983; accepted 9 November 1983)
The microwave spectrum of the weakly bound complex NH3-acetyIene has been measured by molecular beam
electric resonance spectroscopy. A spectrum characteristic of a symmetric top is observed and the following
spectroscopic constants are determined;
B0 (MHz)
D j (kHz)
D jk (kHz)
eQ q ^ (MHz)
(D)
2724.567(5)
7,14(70)
894(3)
-3 .1 3 7 (1 8 )
1.9871(16)
The observed spectrum is consistent with an axially symmetric complex in which the acetylene hydrogen
bonds to the ammonia with a hydrogen bond length of 2.33 A.
Recently, a number of high resolution microwave
spectroscopic studies of weakly bound complexes of
HCN and acetylene have been reported. The structures
of these com plexes reflect the differences between the
isoelectronic m olecules, HCN and acetylene, in their van
der Waals interactions. While the van der Waals bonds
of HCN complexes form along the HCN axis, the bonds
in acetylene complexes form between the n cloud of
acetylene and the other moiety. These trends are
clearly illustrated by the linear complexes H C N -H F,1
KCN-HC1.2 and HCN-H Br,3 and the T-shaped complexes
A r-a cety len e,4 H C l-acetylene,s COjHCN,8 and HCNa cety len e.7 The structures of the homogeneous dim ers
of HCN and acetylene further demonstrate this differ­
ence. The rotational spectrum of (HCN)2 shows this
complex to be linear8 while the limited information on
acetylene dimer does not support a hydrogen bonded
structure. Instead, it appears from both calculations9
and infrared spectroscopic studies10 that acetylene dimer
has a staggered configuration in which the two axes of
the acetylene m olecules are parallel. Thus, in the
weakly bound com plexes which have been studied by
microwave spectroscopy, HCN exhibits hydrogen bond­
ing while acetylene does not.
Examination of som e of the earlier, classical studies
of hydrogen bonding, however, indicates that such a gen­
eralization may only be of limited validity. A number of
papers have suggested, for example, that acetylene does,
in fact, form hydrogen bonds,11 though these are ex­
pected to be much weaker than those formed by HCN.12
In order to more fully understand the hydrogen bonding
of acetylene and to see how acetylene and HCN are dif­
ferent in their hydrogen bonded interactions it is im por­
tant to study hydrogen bonded complexes of acetylene
and compare these com plexes to sim ilar com plexes of
HCN. Recent structural calculations by F risch, Pople,
and Del Bene13 indicate that NH3-acetylene should be one
such system in which acetylene exhibits hydrogen bond­
ing. The calculated equilibrium structure is a sym ­
m etric top in which one of the acetylenic hydrogens is
bonded to the nitrogen of NH3. Further stimulating the
in terest in the structure of NHs-acetylene is an earlier
infrared study of NH3-HCN by Jones e t a l . u in which
they conclude that this molecule is also a sym metric
top in which the HCN is hydrogen bonded to NH3. A
■’T his w ork w as supported by the National Science Foundation.
J. Chem. Phys. 80(4), 15 Feb. 1984
structural study of NH3-acetylene, which is the topic of
this paper, thus allows comparisons to be made between
the hydrogen bonding of HCN and of acetylene to the
sam e species, NH3.
EXPERIMENTAL
Rotational spectra were obtained using the molecular
beam electric resonance technique. A molecular beam
of NHs-acetylene was formed by expanding a mixture of
3% acetylene and 1% NH3 in argon at room temperature
through a 25 p nozzle. Stagnation p ressures were be­
tween 2 .5 and 3 .5 atm. A m ass spectroscopic study of
the beam showed very little of the NH3-acetylene parent
and thus the complex was studied by monitoring the NHJ
peak (m /e = 17) though resonances could also be ob­
served on the HCCH*(m/e= 26). Interestingly, the r e s ­
onances could be observed on the (HCCH)H*(m/e = 27)
peak though NH3 is not hydrogen bonded to acetylene.
This indicates that considerable migration of hydrogens
can occur on electron impact ionization of van der
Waals m olecules.15 The microwave spectrum was
that of a sym metric top with the J = 0 -1 and J = l~ 2 ,
K = 0 ,1 rotational transitions being resolved. The iden­
tification of the resonances on both the NH3 and HCCH*
peaks, along with the characteristic 14N hyperfine struc­
ture of each transition, positively identifies the m icro­
wave resonances a s due to NH3-acetylene.
RESULTS
The observed zero-field transitions for the NHsacetylene complex are listed in Table I. The spectrum
w as fit to the sym m etric top Hamiltonian,
H o = B aJ ( j + 1 ) - D j J 2( J +
+
l)2- D
]KJ ( J + 1)K2
s 2 s iL _ _ r _ 3 K L .il
2 /(2 /-l)(2 J -l)(2 J + 3 )U (J+ l)
J
x [3(i - j ) 2+ | ( i - j ) - i (j + i )j (j + i ) ] ,
where eQqJa is the nuclear quadrupole coupling constant
for the 1 = 1 , 14N nucleus.** The spectroscopic constants
determined from this fit a re presented in Table n .
The dipole moment was determined by measuring the
Stark effect of the J = 0 - 1 transition. These data are
presented in Table in and a typical transition at 998
V /cm is shown in Fig. 1. Due to the m olecular beam
selection rules the J = 0 -1 transition has only two hy­
perfine components at both zero and nonzero electric
0021-9606/84/041423 04S02.10
© 1984 American Institute of Physics
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1423
1424
F raser, L eo p o ld , an d K lem perer: S tr u c tu r e o f N H r a ce ty le n e
TABLE I. O bserved z e ro -field tran sitio n s of N H j-acetylene.
J
K
F*
J'
K'
1
0
F '»
2
v(MHz)
0
0
1
0
0
1
1
0
0
5 450.670(8)
1
1
1
2
1
2
10 893.682(12)
1
1
2
2
1
3
10894.654(10)
1
1
2
2
1
1
10894.928(6)
1
1
0
2
I
1
10 895.650(10)
1
0
2
2
0
2
10 897.096(10)
1
0
0
2
0
1
10 897.258(8)
a
0
2
2
0
3
10898.104(10)
i
0
1
2
0
1
10 899.610(8)
5449.264(5)
fields. The electric field induced hyperfine splitting of
the J - 0 level was not observed though this splitting is
calculated to be 18 kHz at 1000 V /cm . Thus the experi­
mental uncertainty in the dipole moment reflects our un­
certainty as to which of the two MF components of the
J = 0 level were actually observed. The Hamiltonian
for this case may be expressed as
E,
where p is the molecular dipole moment and E is the
electric field. Matrix elem ents of H were calculated in
the uncoupled basis \ J K M j IMj > and the energy matrix
was set up in Mr —M j + M , blocks including lev els from
J = 0 to J = 3 and diagonalized to yield the energy levels
and thus the frequencies. The dipole moment was then
found iteratively to be 1.9871(16) D.
FIG. 1. Microwave tran sitio n ,
J * 0 , A = 0, F = l , M r = 0, ±1 —J
= 1, K = 0, F = 2, M f =±1, at
997,99(62) V /cm ,
MHz
We first assume, as is standard, that no distortion
of either NH3 or acetylene occurs upon complex forma­
tion. The NH3 inversion motion is quenched due to the
asym metry in the potential associated with the umbrella
motion. To describe the relative orientation of a sym ­
m etric top and a linear molecule five coordinates are
n ecessary and are illustrated in Fig. 2. In this coor­
dinate system , r c.m< specifies the distance between the
centers of m ass of the two submolecules. When van der
Waals vibrations are considered, the a axis will coin­
cide with r c-m> on the average and the motions of the C3
a x is of NH3 and the C„ axis of acetylene are described,
on the average, by cones of constant x and y, resp ec­
tively. The a coordinate will specify an overall rota­
tion and is associated with the quantum number K , while
cp, y, and x specify the van der Waals bending modes.
Using the above vibrational picture the experimentally
determined moment of inertia Ibb for the complex is r e ­
lated to the internal degrees of freedom by
2
STRUCTURE AND DYNAMICS
»C2H2
Without spectroscopic information on excited vibra­
tional states only information about the average struc­
ture of a complex in the ground vibrational state can be
obtained. In certain ca ses where sufficient symmetry
ex ists, reasonable inferences may also be made about
the equilibrium structure. Given the sym m etric top
spectrum observed for N H ,-acetylene, sim plicity dic­
tates the assumption that the equilibrium structure of
this complex is a sym m etric top of C3„ sym metry. Un­
der th is assumption a more detailed analysis of zero
point oscillations can be made.
TABLE IL Spectroscopic constants of
N H j-a ce ty le n e .1
f i0<MHz)
2724.567(5)
D j (kHz)
7.14(70)
D jx (kHz)
894(3)
eQ<& (MHz)
-3 .1 3 7 (1 8 )
Mt (P>
(l + (cos2x»
(sin2x> +
(1 + (cos2y » ,
where M s is the reduced m ass of the two submolecules
and /JJJ*3, /« Hs, and l bba2 are the effective moments of
inertia of the subm olecules which are assumed to be
unchanged from the free molecule values. The averag­
ing i s taken over the ground vibrational state. To com ­
pletely specify the structure of the ground vibrational
state of the complex knowledge of (rc.m>), (x), and (y) is
n ecessary.
Information about x may be obtained from the m ea­
sured value of the quadrupole coupling constant eQqba
of the complex. With the usual assumption that the elec­
tr ic field gradient at the nitrogen in the complex is un­
changed from that at the nitrogen in free NH3 then
1.9871(16)
*Reported un certain ties a r e sta tistic a l so
a s to give 95% confidence lim its.
FIG. 2. Definition of coordinates used to d e sc rib e the stru c ­
tu r e of NH3-a c e ty len e .
J. Chem. Phys., Vo). 80, No. 4 ,1 5 February 1984
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
2-2.
Fraser, L eo p o ld , an d K lem perer: S tru c tu re o f N H 3-a c e ty le n e
142
TABLE m . N onzero field tran sitio n s of N H j-acetylene.
J
K
F
Mr
J'
K'
F'
£(V /cm )
v(MHz)
0
0
1
0, ±1
1
0
0
0
998.02(62)
5546.274(10)
0
0
1
0, ±1
1
0
2
±1
997.99(62)
5545.360(10)
eQeica = e Q q m ^ ic o s x)> ,
where eQg^„3 is the component of the quadrupole cou­
pling constant along the C3 axis of free NH3. This r e ­
sults in (cos2x) = 0 . 845(3) and consequently a value of
23.2(4)° for x- The choice of the acute angle for x
assu m es that the acetylene is hydrogen bonded to the
nitrogen of ammonia. We feel that the other structural
choice in which the NH3 is inverted is not chemically
reasonable.
Thus having measured x. r c.m.« 311(1 f remain to be
determined and only the moment of inertia of the com ­
plex is available to determine them. Fortunately
i s not very sensitive to y since the moment of inertia
of acetylene is sm all compared with that of the complex.
A s y is varied from 0° to 45°, the value of re.m. n eces­
sary to reproduce the observed rotational constant
changes from 4.057 to 4.100 Aand the hydrogen bond
length changes equally from 2.327 to 2.370 A. Without
any further knowledge about the zero point vibrations of
acetylene no additional information can be obtained about
rc.m. and y. An estim ate though can be made of y . In
the approximation in which the bending motion is treated
as harmonic, y sca les roughly with the fourth root of the
rotational constant of the submolecule. Since HCN has
a rotational constant sim ilar to that of acetylene and
since for those complexes measured most HCN average
bending angles are between 10° and 20° a value of y = 15°
w ill be chosen. This results in a r c.m. of 4.063 A and
a hydrogen bond length of 2.333 A.
If the van der Waals stretching and bending modes
can be treated as uncoupled oscillators then a value of
the stretching force constant may be determined from
the measured value of D j . Treating the distortion con­
stant D j as only arising from the stretching of the weak
bond then
2 hDj
where k, is the stretching force constant. The stretch­
ing force constant for NH3-acetylene is thus determined
TABLE IV. D erived constants of NH3acetylene.
<cos2x)
X
»N—H
v,
0.845(3)
23.2(3)°
4.063(4) A*
2.333(4) A*
0.634 D
0.070(7) mdyn/A
107 cm*1
‘ Using 7 = 15(5)° a s discussed in the text.
to be 0.070(7) mdyn/A, corresponding to a vibrational
frequency of 107 cm'1 for the van der Waals bond.
The induced dipole moment of the complex defined as
MInduced= Pcomplax ~
was calculated by approximating (cosx) by (cos2 x)1/2.
Taking the literature value16 of the dipole moment of
NH3(1.472 D) gives an induced dipole moment of 0.634
D for the complex. The structural and dynamical r e ­
sults are summarized in Table IV.
DISCUSSION
The present results are in excellent agreement with
the electronic structure calculation of F risch, Pople,
and Del Bene13 wmch predicts that the NH3-acetylene
complex should be axially sym m etric. In their most
complete calculation these authors found an equilibrium
N -H weak bond length of 2.329 Awhich appears to be in
excellent agreement with the observed vibrationally
averaged bond length of 2.333 A reported in the present
paper. This is noteworthy since other calculations on
this system predict equilibrium bond lengths which difter
by a s much as 0 .4 A from the observed vibrationally
averaged v a lu e.17,18
The structure of the van der Waals complexes of
acetylene with the sim ple Lewis bases Ar and NH3 are
quite different. The previously successful HOMOLUMO bonding picture can be applied to these complexes
to explain this difference. In this picture the T-shaped
structure of A r-acetylene a rises from the overlap of the
p x and py atomic orbitals of Ar with the jiJ molecular
orbitals of acetylene to form a x-type bond. No a bond
is formed between the Ar and the acetylene since the p t
orbital of Ar has zero overlap with the r\ orbitals of
acetylene. For NH3-acetylene the T-shaped structure
i s not predicted since the nonbonding orbital of NH3, like
the p , orbital of Ar, is of the incorrect symmetry to
overlap with the 7iJ orbitals of acetylene. Rather the
a* orbital of acetylene which is the next highest in en­
ergy unoccupied molecular orbital19 can have significant
overlap with the nonbonding orbital of NH3 if the struc­
ture is axially sym m etric. Thus we see that the
HOMO-LUMO picture can successfully explain the di­
verse structures of acetylene-L ew is base complexes.
The axially sym metric NH3-acetylene structure is also
predicted by consideration of the dipole-quadrupole
electrostatic interaction.
Besides structural information, electrostatic and dy­
namical information has been obtained for this complex.
In Table V hydrogen bond lengths, stretching force con­
stants, and induced dipole moments are tabulated for
various hydrogen bonded complexes in which the hydro­
gen of the acid bonds to the nitrogen of the base. For
J. Chem. Phys., Vol. 80, No. 4 ,1 5 February 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
1426
F raser, L eo p o ld , a n d K lem perer: S tru c tu re o f N H 3-a c e ty le n e
TABLE V. E stim ated hydrogen bond lengths, stretch in g force
constants, and Induced dipole m om ents of v a rio u s com plexes.*
r X-H <A)
k , (mdyn/A) ■
♦‘tad CD)
H jN -acetylene*
2.33
0.070
H3N—HFb
1.78
...
1 .3
HCN-HF*
1.87
...
1 .1
HCN-HCN11
2.23
0.082
0.77
HCN-HBr*
2.16
0.073
•••
HCN-HCl*
2.09
0.094
0 .9 4
‘ T his paper.
•’R eference 23.
•R eference 1.
‘'R eferences 8 and 24.
•R eference 3.
0.63
'R e fe re n c e s 2 and 24.
*Force constants w ere calculated
fro m the o riginal data using the
equation in the text.
the three complexes in which both the stretching force
constant and dipole moment are known the magnitude of
the induced dipole moment parallels that of the stretch­
ing force constant. Of the complexes listed, it appears
that the NHj-acetylene complex has the weakest bond.
This is as expected since hydrocarbons are not known
to form strong hydrogen bonds. The two com plexes in
which an acetylenic-like hydrogen bonds to a nitrogen
of a base, HCN-HCN and NHj-acetylene, have sim ilar
bond lengths, stretching force constants, and induced
moments. In order to further compare the hydrogen
bonding of HCN and acetylene, information on the hydro­
gen bonded complexes NCH-NH3 and acetylene-NCH
would also be valuable. A s previously mentioned how­
ever, acetylene-NCH is not linear but T-shaped, thus
making this comparison inappropriate. Some lim ited
information is available on NCH-NH3 from an earlier
low resolution infrared study by Jones et a l . u From
an analysis of the parallel band contour of the C=N
stretch, these authors suggested that NCH-NH3 was a
sym m etric top with a rotational constant of 3390(120)
MHz. Assuming the NCH-NH3 complex has an average
structure sim ilar to acetylene-NH3 results in a hydrogen
bond length of 1.92(8) A for NCH-NH3. In this sam e
work, Jones e t al. studied, by sim ilar methods, the
complex (HCN)2 and obtained a rotational constant which
has since been shown to be correct within their experi­
mental uncertainty. Thus assuming that these resu lts
for NCH-NH3 are also correct it would appear that
NCH-NH3 has a hydrogen bond length which is - 0 . 3 A
shorter than that of (HCN)2 or NH j-acetylene. This
,,2 0
seem ed rather surprising since the complex HjO-HCN2'
and the complex H20-acetylene21 have O -H bond lengths
which differ by only 0 .15 A. For this reason we have
examined NCH-NH3 by molecular beam electric re so ­
nance spectroscopy.22 The observed rotational constant
of NCH-NH3 is 3017(1) MHz providing a N -H van der
Waals bond length of 2 .1 6 A. This value is clearly quite
consistent with the N -H bond length of 2.33 A of NH3acetylene.
NHj-acetylene and NCH-NHj are two exam ples of
com plexes in which a “C -H ” group is hydrogen bonded
to a base. C lassical studies of C-H group hydrogen
bonding are abundant but further quantitative informa­
tion on this type of interaction is needed. It would be
valuable, for instance, to determine bond lengths and
force constants of C-H group hydrogen bonds with a
variety of carbon hybridizations and electron withdraw­
ing substituents. Such studies would give a more com ­
plete understanding of C -H group bonding and provide
valuable data to compare with the numerous calculations
on these system s.
' a . C. Legon, D. J . M illen, and S. C. R o g e rs, Chem. Phys.
L ett. 41, 137 (1976); P ro c . R . Soc. London S er. A 370, 213
(1980); A. C. Legon, E . J . Cam pbell, and W. H. F lygare, J .
Chem. P hys. (in p re ss).
2A . C. Legon, E . J . Cam pbell, and W. H. F lygare, J . Chem.
Phys. 76, 2267 (1982).
3E . J . C am bell, A. C. Legon, and W. H. F ly g are, J . Chem.
Phys. 78, 3494 (1983).
*R. L . Deleon and J . S. M uenter, J . Chem. Phys. 72, 6020
(1980).
SA . C . Legon, P . D. A ldrich, and W. H. F ly g are, J . Chem.
Phys. 75, 625 (1981).
6K . R . Leopold, G. T . F r a s e r , and W. K lem perer, J . Chem.
P h y s. (to be published).
TP . D. A ldrich, S. G. Kukolich, and E. J . Cam pbell, J . Chem.
Phys. 78, 3521 (1983).
8L . W. Buxton, E . J . Cam pbell, and W. H. F lygare, Chem.
Phys. 56, 399 (1981).
9N. Sakai, A. Koide, and T . K ihara, Chem. Phys. L ett. 47,
416 (1977).
10R. D. Pendley and G . E . Ewing, J . Chem. Phys. 78, 3531
(1983).
UG. C. Pim entel and A. D. M cClellan, The Hydrogen Bond
(F reem an, San F ra n c isco , 1960).
12A. A llerhand and P . von Rague Schleyer, J . Am. Chem. Soc.
85, 1715 (1963).
13M. J . F risc h , J . A . Pople, and J . E. Del B ene, J . Chem.
Phys. 78, 4063 (1983).
14W. J . Jo n e s, R. M. Seel, and N. Sheppard, Spectrochim .
A cta. P a rt A 25, 385 (1969).
15l t i s possible th at the observed (HCCH)H* ions w ere form ed
by lon-m olecule re ac tio n s Involving the NH3-a ce ty le n e parent.
In an effect to d e te ct such re ac tio n s, a ttem p ts w ere m ade to
observe the NH3, J = l , K =1 inversion doublet while m onitor­
ing the (NH3)H* peak. No tran sitio n w as observed.
leM. D. M arshall and J . S. M uenter, J . Mol. Spectrosc. 85,
322 (1981).
n D. Bonchev and P . C rem asch l, T heor. Chim . Acta 35, 69
(1974).
« A . Goel and C. N . R . R ao, T ra n s . F arad ay Soc. 67, 2828
(1971).
MW. L . Jorgensen and L . Salem , The Organic C h e m ist's Booh
o f O rbitals (Academ ic, New Y ork, 1973).
20A. J . F ille ry -T ra v is , A. C. Legon, and L . C. Willoughby,
Chem. P hys. L e tt. 98, 369 (1983).
21K. I. P eterson and W. K lem perer (in preparation).
« G . T . F r a s e r , K . R . Leopold, D. D. Nelson, J r . , A. Tung,
and W. K lem p erer, J . Chem . P h y s. (to be published).
^ B . J . Howard (private comm unication).
m E . J . Campbell and S. G . Kukolich, Chem . Phys. 76, 225
(1983).
3SNote that th is H am iltonian tr e a ts the quadrupole interaction
to f i r s t o rd e r in J . Second o rd e r contributions w ere not in­
cluded since th ese a re le s s than 1 kHz.
J. Chem. Phys., Vol. 80, No. 4 ,1 5 February 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3H
The rotational spectrum and structure of NH3-HCNa)
G.T. Fraser,K.R. Leopold,D.D. Nelson, Jr.,A. Tung,andW. Klemperer
Department o f Chemistry, Harvard University, Cambridge, Massachusetts 02138
(Received 7 November 1983; accepted 20 December 1983)
The microwave spectrum of H 3N-HCN has been measured using the molecular beam electric
resonance technique. A symmetric top spectrum is observed and the following spectroscopic
constants were obtained:
jB0(M H z )
3016.7561(24)
D,(kHz)
5.68(30)
Djk {MHz)
0.418 22(76)
eQgi+eQq2 (MHz}
(M H Z)
fi(D)
_ 3 9 2 9 4 (4 6 )
_ 0.584(16)
5.260 8(55)
eQq, and eQq2are the quadrupole coupling constants associated with the l4N nuclei of HCN and
NH3, respectively. The induced dipole moment is 0.939(12) D and the N-H weak bond length is
2.156(10) A. The average bending angle of the NH 3 subunit is 20.40(26)° while that of the HCN
subunit is 9.56(37)°. The force constant for the weak bond stretch is 0 . 1 2 2 (6 ) mdyn/A
corresponding to a stretching frequency of 141(3) cm-1.
INTRODUCTION
Recently, a new class of weakly bound binary complex­
es have been studied whose subunits, when condensed in
equal molar quantities, form crystalline solids. Included in
this list are NH 3-H F , 1 PH 3-H F ,2 PH 3-HCI,3 and PH3HBr4 which have all been characterized by high resolution
microwave spectroscopy and NH 3-HCN 5 which has been
studied at low resolution using infrared spectroscopy.
At room temperature, ammonium cyanide is an ionic
solid with a vapor presure of 500 Torr. The vapor consists
principally of free HCN and NH3. Jones, Seel, and Shep­
pard5 obtained a low resolution infrared spectrum of a mix­
ture of NH3 and HCN and observed a parallel band near the
C = N stretch of free HCN, which they assigned to the gas
phase complex of NH 3 and HCN. From the contour analysis
of this band, they concluded that NH3-HCN is a symmetric
top with a N -H weak bond length of 1.90 A. Though
NH4CN is a crystalline solid at room temperature, the hy­
drogen bond length for the vapor phase complex, as deter­
mined from the infrared band contour analysis, is essentially
the same as that found in other hydrogen bonded complexes.
Due to its simplicity, the NH3-HCN complex has served as a
convenient system for theoretical studies of the hydrogen
bonding of C-H groups to amines and these electronic struc­
ture calculations give a hydrogen bond length which is also
comparable to that observed in other van der Waals systems.
The exact values predicted, however, range from 1.8 to
2.1 A.6"9
Recently, high resolution microwave spectroscopy has'
been used to elucidate the structures of the hydrogen bond­
ed, weakly bound complexes HCN-H 20 ,'° HCCH-H 2Otu
and HCCH-NH 3 .12 With HCCH, the difference between
11Supported by the National Science Foundation.
J. Chem. Phys. 80 (7), 1 April 1984
the O-H and N-H weak bond lengths is —0.1A while with
HCN, this difference is 0 .1 8 A. Since the agreement between
these two numbers is expected to be considerably better
(within several hundredths of an angstrom) and suspecting
that the error lies in the infrared determined bond length of
NH 3-HCN, a more complete high resolution study of NH3HCN was undertaken.
EXPERIMENTAL
The microwave spectrum of the NH3-HCN complex
was measured using the molecular beam electric resonance
technique. A mixture of 1% NH 3 and 1% HCN in argon was
expanded through a 25 /r nozzle at room temperature. The
stagnation pressure was 2.3 atm which gives a partial pres­
sure of NH 3 and HCN well below the condensation pressure
for the formation of ammonium cyanide. As expected, a
symmetric top spectrum was observed with the .7 = 0 - 1,
K = Oand J = 1-2, K = 0,1 transitions being studied at high
resolution. The quadrupole hyperfine stnicture due to the
two/ = 1, l4N nuclei was resolved for each rotaitonal transi­
tion. A typical transition is shown in Fig. 1. The complex
was studied by monitoring the NH3+ ion arising from the
fragmentation of the NH3-HCN complex since the signal to
noise ratio of the observed resonances was greatest on this
peak. A summary of the measured signal strength of the
J = 1-2 transition on various ion peaks is given in Table I.
As shown in the table, the resonances could be observed on
NH3+, HCN+, and NH4+ but not on H(HCN)+ or the par­
ent ion peak, NH 3-HCN+. Interestingly, the transitions of
the complex HCCH-NH 312 could be observed on
H(HCCN)+ while those of HCN-NH 3 could not be ob­
served on H(HCN)+. This is an indication that the cracking
pattern upon electron impact ionization of structurally simi­
lar van der Waals complexes is not the same. The identifica-
0021 -9606/84/073073-05S02.10
© 1984 American Institute of Physics
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3073
3S3074
Fraser e f a/.:
nd structure ot NH,-HCN
Because the two quadrupole coupling constants are nearly
equal, their sum and difference were fit. 13 Furthermore,
since the sum enters in first order and the difference in sec­
ond order, only the sum is well determined. The spectro­
scopic constants obtained are presented in Table III. The
residuals from the fit were all less than 5 kHz.
The dipole moment was determined by measuring the
Stark effect of the highest frequency component of the
J = 0-1, K = 0 transition. These data are summarized in
Table IV. The Hamiltonian for this case is
4 6 0 3 6 .1 6
H = H0- \ l E,
MHz
FIG. 1. Microwave transition, / = 0, K = 0, F, = 1, F = 0,1,2-J = 1,
K = 0, F, = 0, F = 1, at 6036.108(5) MHz.
tion of the observed transitions with the NH3-HCN com­
plex was facilatated by the observation of the resonances on
both the NH3+ and HCN'1' mass peaks as well as by the
observed hyperfine structure which is characteristic of that
due to two I — 1 nuclei on the axis of a symmetric top.
where |i is the molecular dipole moment and E is the electric
field. Matrix elements ofH were calculated in the uncoupled
basis |JMj / ,
J2M,t ) and the energy matrix was set up
in
Mf =M j +M1i +Mh
blocks including levels from / = 0 to J = 3 and diagonalized
to yield the energy levels and thus the frequencies. The di­
pole moment was iteratively determined to be 3.2608(55) D.
RESULTS
The observed zero-field transitions for the NH3-HCN
complex are listed in Table II. The assignment of the hyper­
fine transitions for the / = 1 - 2 transition was complicated
by the complete overlap of the K = 1 hyperfine pattern with
that of K = 0 and by the similarity in value of the two qua­
drupole coupling constants of the i4N nuclei. The spectrum
was fit to the symmetric top Hamiltonian
H0 = B 0J ( J + l ) - D j J 2( J + l ) 2
- D jkJ(J+1]K2+ HQi +H&,
where
STRUCTURAL ANALYSIS
The spectroscopic constants of Table III allow the
quantitative determination of the average structure of the
complex. In the structural analysis, the individual submole­
cules will be assumed to be unchanged upon complexation.
The equilibrium structure is assumed to be
with the
HCN hydrogen bonded to the NH3. Due to the asymmetry
in the potential associated with the umbrella motion of NH3,
the inversion of NH3 is quenched in the complex. The co­
ordinates used in the structural analysis are illustrated in
Fig. 2. After averaging over the ground state vibrations, the
moment of inertia becomes
/N H ,
a
</w>=M,(rL) + -^ —(1 + <co?2*»
27,(27, — 1)(27— l)(2/+3)
X [3(1, • J )2 + j(I, • J) - / , ( / , + l ) / ( / + 1)],
eQqxand eQq2 are the quadrupole coupling constants for the
two/ = 1, UN nuclei. Matrix elements ofH0 were calculated
in the \JKFFXI xI2) basis where
Fj = J -f I , and F = F| +
12 -
The transitions in Table II were fit to the frequencies calcu­
lated from H0 by an iterative nonlinear least squares routine.
TABLE I. Signal intensity o f the 7 = 1-2 transition of NH3-H C N on var­
ious ion peaks.
(m/e)
Probable
km species
Signal strength
(arbitrary units)
16
17
18
26
27
28
44
NH,+
NHj+
n h 4+
CN+
HCN+
H(HCN)+
NHjHCN*
3
15
7
a
2
a
a
‘ No signal was observed on these ion peaks.
J. Chem. Phys., Vol.
rN H ,
rH C N
(1 + (cos2 y)),
*•
+•
where^- and y are the angles that the C3 axis of NH 3 and Ca
axis of HCN, respectively, make with the a axis of the com­
plex. M, is the pseudodiatomic reduced mass and /m*’,
1™ ', and I \ Jf®1 are the effective moments of inertia of the
free submolecules. rm is the distance between the centers of
mass of the two subunits.
Proceeding in the usual manner, the values of
+
(sin2* ) +
X = cos- , ((cos2^ ) l/2)
and
y = cos- '((cos2 y) ,/2)
can be determined from the measured quadrupole coupling
constants eQq2 and eQqy Before making use of eQqx and
eQq2in the structural analysis, it is necessary to determine
which of these two constants should be associated with
which of the l4N nuclei in the complex. The proper choice
may be made by examining the quadrupole coupling con­
stants of free HC14N and I4NH3. It should be noted that any
electronic distortion of the NH 3 due to the approach to an
I. No. 7,1 April 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fraser e /a /.: Spectrum and structure of NH,-HCN
3075
36>
TABLE II. Observed zero-field transitions for ,4NH3-H C I4N.
J
K
F,
F
J'
K'
F\
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
I
1
1
1
1
1
1
1
1
2
2
1
0
2
1
0
1
2
2
2
0
2
2
0
0
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0
0
0
0
0
0
0
1
1
1
2
2
2
2
0
0
0
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
2
0
I
2
2
0
2
1
1
2
1
3
1
1
1
3
3
1
1
1
3
1
1
3
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
frequency
(MHz)
F'
3
11
6033.886(6)
A
6034.442(6)
A
6036.108(5)
1J
1I
1)
12 063.612(5)
12063.683(10)
12 063.893(6)
12064.877(6)
I
3
1
1/
2)
12065.138(10)*
12065.232(10)*
A
1
1
1
2f
2I
0)
4
2
2
0
2
1
1
1
1
1
1
12067.004(12)*
12067.148(6)
12 067.778(8)
12 067.973(10)
12068.342(6)
12069.383(10)
12069.565(10)
12070.023(8)
l(
2
2
2
2
2
2
0
1
1
1
1
12 065.544(5)*
12 065.647(8)
12066.025(4)
12066.124(7)
12 066.185(4)
12066.308(7)
“These lines could not be unambiguously assigned and were excluded from the fit.
NH4+ CN~ structure will lessen the absolute value of the
respective MN quadrupole coupling constant from that in
free NH since NH4+ has no electric field gradient at the
nitrogen nucleus. Thus, since c2?hcn = —4.708 MHz
and
— —4.090
MHz
the
value
eQq, = —4.513(15) MHz must be the quadrupole coupling
constant of the HCN nitrogen and eQq2= —3.345(18)
MHz must be the quadrupole coupling constant of the NH
3
nitrogen. To determine y and x, the usual assumption is
made that the electric field gradient at the nitrogen does not
change upon complex formation. With this assumption,
eQq^ = eg^ncN <Jz(cos y)>
14
, 15
3
TABLE III. Spectroscopic constants of NH3-HCN.*’b
2?o(MHz)
4,1kHz)
2>,,(MHz)
*0?i +
3016.756 1(24)
5.68(30)
0.418 22(76)
(MHz)
-3.9294(46)
(MHz)
-0.584(16)
«0?,(MHz)
-4.513(15)
efiWMHz)
- 3.345(18)
aP )
and
eQq? = < ? 2 ? n h , <P2( cos X )>
so that (cos x > = 0.8785(36) and (cos y) = 0.9724(21) or
equivalently x —20.46(26)° and y = 9.56(37)°. With knowl­
edge of (cos x ) and (cos y), the moment of inertia expres­
sion is used to determine that
= 3.8466(3) A,
corresponding to a hydrogen bond length of 2.156(10) A.
The stretching force constant of the weak bond is deter­
mined from the measured centrifugal distortion constant
Dj. Approximating the van der Waals bending and stretch­
ing degrees of freedom as uncoupled oscillators and treating
2
2
2
2
TABLE IV. Observed nonzero field transitions of NH3-HCN.
J = 0 , K = 0, Mf = 0, ± 1 — J = l , K = 0, F = 1, F, = 0, Mf = 0
5.2608(55)
*Uncertainties are two standard errors as determined from the least squares
fit.
b 1 and 2 refer to the ,4N nuclei and HCN and NH3, respectively, as ex­
plained in the text.
E (V/cm)
frequency (MHz)
400.95(24)
500.01(31)
6133.763(33)
6187.754(50)
J. Chem. Phys., Vol. 80. No. 7,1 April 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3076
31
Fraser e la l. : Spectrum and structure of NH3-HCN
H
H
X
FIG. 2. Definition of the coordinates used to describe the structure of NH3HCN. The nitrogen atom on the ammonia subunit was omitted for purposes
of clarity.
the distortion constant D j as only arising from the stretching
of the weak bond
2hDj
where k, is the weak bond stretching force constant. This
expression gives a stretching force constant of 0 . 1 2 2 (6 )
mdyn/A or a stretching frequency of 141(3) cm " 1 for the
NH3-HCN weak bond.
Using the values of the dipole moment of free HCN
(2.985 D)u and NH 3 (1.471)15the induced dipole moment of
the complex is calculated by
P in d u cc d = /^com plex
<COS * ) ~ ^ H C N < « * f ) .
Approximating (cos x ) and (cos y) by (cos2^ ) ,/2 and
(cos2 y ) U2, the induced dipole moment for the complex is
determined to be 0.939(12) D. The structural results are sum­
marized in Table V.
DISCUSSIO N
The 2.156(10) A hydrogen bond length obtained for
NH3-HCN is clearly in disagreement with the 1.92(8) A val­
ue computed from the earlier infrared work of Jones et al.,5
though it is now consistent with the bond lengths observed in
the systems HCCH-NH 3(2.33 A), HCCH-OH2(2.23 A), and
NCH-OH2(2.08 A). It should be noted, however, that these
authors, who used a contour analysis of the infrared band
assigned to the C = N stretch to obtain rotational constants
for both NH3-HCN and (HCN)2, were considerably more
successful in their analysis of the latter complex. Their hy­
drogen bond length for (HCN)2 of 2.28(15) A agrees much
more closely with the microwave value of2.2295(3) A,16than
does that for NH 3-HCN. Unlike (HCN)2, which is a linear
molecule, NH3-HCN is a symmetric top and is thus expect­
ed to have a more complicated parallel band structure due to
AA contributions. Such additional complexity may account
for the difficulty in obtaining the correct B0 value from the
infrared measurements.
TABLE V. Derived constants of NHj-HCN.
<cosJ y>
<co«JT>
I
J
fem
rtm
0.9724(21)
0.8785(30)
9.56(37)*
20.40(26)*
3.8466(3) A
2.156(10) A
0.122(6) mdyn/A
141(3) cm- '
0.939(12) D
Summarized in Table VI are the results of four elec­
tronic structure calculations for the NH3-HCN complex. It
is seen from the table that the best agreement with the experi­
mental bond length has been obtained by Kollman et al.
using the 4-31G basis set, though the value obtained under­
estimates the experimental result by 0.07 A. Such a discrep­
ancy has similarly been found for the weakly bound com­
plexes (HF)2 and (H20)2, where use of the 4-31G basis set
underestimates the experimental bond lengths by 0.15 A.9
Thus, while the error is in the same direction, the calculated
bond length is seen to be more accurate for NH3-HCN than
for either (HF)2 or (H20)2.
The two complexes (HCN)216 and NH3-HCCH , 12
which both have an acetylenic hydrogen bonded to a nitro­
gen, may be compared with the NH3-HCN system studied
here. The bonding in both of the former complexes is weaker
than that of NH3-HCN as seen by examination of Table VII.
The induced dipole moment and force constant of NH3HCN are quite large, much larger than that of (HCN)2 or
NH 3-HCCH. In fact, the only other van der Waals complex­
es for which dipole moments have been measured and which
have a larger calculated induced moment are NH3H F ^ induccl = 1.3 D )1 and H C N -H FK d*a = 1.1 D ) .17
The induced dipole moments, force constants, and bond
lengths all suggest that the most strongly bound complex of
the three is NH3-HCN while NH3-HCCH is the most weak­
ly bound. The average bending angle f of the HCN subunit
of NH3HCN is less than that of the hydrogen bonded HCN
subunit in (HCN)2 and the NH3 bending angle in NH3-HCN
is similarly less than that in NH3-HCCH. The greater direc­
tionality of the NH3-HCN bond suggested by these results is
again indicative of the strong interaction of NH3 and HCN.
It is noteworthy that the absolute value of the quadrupole
coupling constant of the ,4N nucleus of NH 3 in NH3-HCCH
is less than that in NH 3-HCN. Since the approach to the gas
phase ion pair NH4+ CN“ would be accompanied by a de­
crease in absolute value of the UN quadrupole coupling con­
stant toward zero, the observed difference in this quantity
between NH3-HCCH and NH3-HCN is properly interpret­
ed in terms of the zero point oscillations.
Lastly, NH3-HCN is one of a class of complexes which
have recently been studied in which the corresponding solid
is an ionic crystal. Other complexes of this kind which have
TABLE VI. Summary o f the results of previous electronic structure calcu­
lations on NHj-HCN.
Method
rN-H (A)
A E (kcal/molf
P(D)
STO-3G*
CNDO/2b
C N D O /2'
4-31Gd
Experimental
1.873
1.9
1.802
2.09
2.16
7.9
2.1
3.64
9.7
5.366
4.18
5.03
. ..
S.Mf
‘ Reference 6.
‘ Reference 7.
‘ Reference 8.
dReference 9.
'A E is the binding energy.
'Equilibrium dipole moment estimated a s/i, = /iir,
. ..
. + /Thcn + P nh, •
J. Chem. Phys., Vol. 60, No. 7,1 April 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fraser et at, : Spectrum and structure of NH,-HCN
3077
TABLE VII. Comparison of NH ,-HCN with N H 3-HCCH and (HCN)2.
(HCN)S
NH3-HCCHd
NH3-H C N '
/^induced (^)
k, (mdyn/A)
rN-H (A)
*(deg)‘
rtdeg)"
0.77
0.63
0.94
0.082
0.070
0.122
2.23
2.33
2.16
...
11.0
23.2
20.4
9.56
•Average bending angle of the NH3 subunit.
6Average bending angle of the HCN subunit which is hydrogen bonding.
•Reference 16.
d Reference 12.
'T h is work.
been examined by high resolution microwave spectroscopy
include NH 3-H F,‘ PH 3-H F ,2 PH3-HCl3,and PH 3-HBr.4
As is the case for NH 3-HCN, the binding strength in each of
these complexes, as measured by bond length and force con­
stant, is comparable to other van der Waals complexes. No
evidence exists for a gas phase ion pair although as cluster
size increases, the species must begin to exhibit characteris­
tics of the solid phase. The spectroscopic study of these high­
er clusters, if possible, will contribute to an understanding of
such nucleation processes.
'B. I. Howard (private communication).
2A. C. Legon and L. C. Willoughby, Chem. Phys. 74,127 (1983).
3A. C. Legon, J. Phys. Chem. 87,2064 (1983).
4L. C. Willoughby and A. C. Legon, J. Phys. Chem. 87,2085 (1983).
SW. J. Jones, R. M. Seel, and N. Sheppard, Spectrochim. Acta Part A 25,
385(1969).
. ‘S. Vishveshwara, Chem. Phys. Lett. 59,26 (1978).
7A. Goel and C. N. R. Rao, Trans. Faraday Soc. 67,2828 (1971).
8D. Bonchev and P. Cremaschi, Theor. Chim. Acta 35,69 (1974).
9P. Kollman, J. McKelvey, A. Johansson, and S. Rothenberg, J. Am.
Chem. Soc. 97,955 (1975).
,0A. J. Fillery-Travis, A. C. Legon, and L. C. Willoughby, Chem. Phys.
. Lett. 98,369 (1983).
"K . I. Peterson and W. Klemperer (in preparation).
12G. T. Fraser, K. R. Leopold, and W. Klemperer, J. Chem. Phys. 80,1423
(1984).
,3R. S. Altman, M. D. Marshall, and W. Klemperer, J. Chem. Phys. 79,57
(1983).
I4A. G. Maki, J. Phys. Chem. Ref. Data 3,221 (1974).
,SM. D. Marshall and J. S. Muenter, J. Mol. Spectrosc. 85,322 (1981).
I6L. W. Buxton, E. J. Campbell, and W. H. Flygare, Chem. Phys. 56,399
(1981); E. J. Campbell and S. G. Kukolich, ibid. 76,225 (1983).
"A . C. Legon, D. J. Millen, and S. C. Rogers, Chem. Phys. Lett. 41,137
(1976); A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R. Soc. London
Scr. A 370,213 (1980); A. C. Legon, E. J. Campbell, and W. H. Flygare
(unpublished).
J. Chem. Phys., Vol. 80. No. 7,1 April 1984
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
J
i
Microwave and infrared characterization of several weakly bound
NH3complexes”*
G. T. Fraser, D. D. Nelson, Jr.,1” A. Charo, and W. Klem perer
Department o f Chemistry, Harvard University, Cambridge, Massachusetts 02138
(Received 24 September 1984; accepted S December 1984)
We present the results or microwave and infrared spectroscopic studies of several
van der Waals complexes of NH3. These results were obtained with a molecular
beam electric resonance spectrometer. The microwave spectroscopy of the complexes
(NH3)2 and Ar-NH 3 show that both systems arc nonrigid. The observed dipole
moments for (NH3)3[0.74(2) D] and (ND3)2[0.57(1) D] arc not compatible with the
presently accepted theoretical structure. Ar-NH3, which has a complicated and
currently unassigned microwave spectrum, exhibits Q branch inversion transitions
near 19 GHz which indicate that the NH3 subunit is likely to be a near-free rotor.
Infrared studies of the complexes NH 3-HCCH, NH 3-CO}, (NH3)2, Ar-NH3,
NH 3-OCS, NH 3-N 20 , and NH3-HCN have been carried out with a line tunable
C 0 2 laser. Only for NH3-HCN were no infrared resonances discovered.
Photodissociative transitions are observed in all of the other systems. Band origins
for the photodissociative infrared transitions involving the v 2 umbrella motion of
NH 3 were determined for NH3-HCCH [984.4(9) c m '1], NH 3-COs [987.1(2) cm"'].
NHj-OCS [981.5(15) cm"1], and NH 3-N 20 [980(2) cm"']. The observation of an
infrared transition for Ar-NH 3 at 938.69 cm which is 40 cm ' ' lower than the
band origins in the other NH 3 complexes, lends support to the model of Ar-NH 3
mentioned above. NH 3-HCCH, NH 3-C 0 2, (NH3)2, and Ar-NH 3 were studied in
microwave-infrared double resonance experiments in order to eliminate much of the
inhomogeneous broadening present in their infrared spectra and to aid in the
rotational assignment of the infrared spectra. Linewidths were determined for
NH 3-HCCH (0.15 GHz) and for NH 3-C 0 2 [14(6) GHz]. An important result of this
study is that the dissociation energies of all the complexes studied, except for
NH 3-HCN, are established to be less than 990 c m '1, i.e., 2.8 kcal/moi.
INTRODUCTION
Since the pioneering infrared studies of Welsh,
McKellar, and co-workers1"8 and Ewing and co-workcrs,9" 13
the measurement and interpretation of vibrational prcdissociation lifetimes of van der Waals molecules has been
the subject of a lively debate. The current method for
determining the lifetimes, introduced by Gough, Miller,
and Scoles, 14 is to synthesize the complex in a supersonic
expansion and measure the molecular beam depletion
(via mass spectrometer or liquid He bolometer) as a
function of the frequency of an infrared laser beam which
intersects the molecular beam. The initial studies in this
area were done on the homogeneous dimers of N 20 , 14
C 0 2 , 15 SF6 , 16 and C2R t l7,18 while later studies, by Gen­
try, 19"22 Janda,23-25 Lee,26-28 and their co-workers, have
been undertaken on a large variety of both homogeneous
and heterogeneous dimers. The observed spectra tend to
be featureless and broad with linewidths from 1 - 2 0 cm"1.
This broadening has generally been interpreted to be
homogeneous with the corresponding lifetimes (5>0.25
ps) being determined by predissociation. Attempts to
understand the observed linewidths in terms of the energy
**Supported by the National Science Foundation.
w National Science Foundation Predoctoral Fellow.
J. Chem. Phys. 82 (6 ) 15 March 1985
gap law of Jortncr and Bcswick29 or the momentum gap
law of Ewing30 have not been successful and have led to
the suggestion that the observed broadening is not a
measure of the predissociation rate, but instead, is due to
intramolecular relaxation.22
In light of these results the recent determination of
the vibrational prcdissociation lifetime of (HF )2 by Pine
Laffcrty, and Howard,31 seems particularly surprising. In
a static gas cell Pine, Laffcrty, and Howard were able to
obtain the rotationally resolved infrared spectrum of this
complex near the HF stretch. From the pressure indepen­
dent linewidths (—200 MHz) observed upon excitation
of the hydrogen bonded HF subunit, they calculated a
prcdissociation lifetime of —0.8 ns. The linewidths ob­
tained upon excitation of the other HF subunit arc
Doppler limited and correspond to a lifetime > 10 ns.
DeLeon and Muenter32 have remeasured this latter lincwidth in a molecular beam and have obtained similar
results. These findings raise the concern that the broad
linewidths in the other molecular beam studies arc not
homogeneous but are predominantly the result of a
complicated band structure, as well as an overlap of
various clusters which cannot be separated by a mass
spectrometer or bolometer. We have noted in previously
published molecular beam electric resonance studies the
complicated cracking patterns of van der Waals complexes
0031-9606/85/062535-12$02.10
C
1985 American Institute of Physics
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2535
2536
Fraser et el.: Weakly bound NH3 complexes
upon electron impact ionization.33-35 Thus it might be
expected that any mass spectral peak in a mass spectrom­
eter will have contributions from various clusters which
can fragment to the mass peak which is monitored.
Among the results that we report in this work are
microwave-infrared double resonance spectra of the fol­
lowing weakly bound complexes of NH3: (NH3)2, NH3Ar, NH 3-HCCH, and NH3-C 0 2. In these studies the
signal strength of a single rotational transition of the
complex is monitored (using a molecular beam electric
resonance spectrometer) as a function of the infrared
frequency. The double resonance -technique eliminates
much of the inhomogcnous broadening which is present
in the other molecular beam experiments and in those
static gas cell studies where experimental resolution is not
sufficient to observe rotationally resolved structure. This
method is unique since it permits the observation of
homogeneously broadened lines with rotational resolution.
It should be noted that unlike the method described here,
high resolution static gas cell studies like those of Pine
and LafTcrty arc only sensitive to those complexes which
have both a reasonably long prcdissociative lifetime as
well as sufficient spectral simplicity to be resolved rota­
tionally.
In the present study a line tunable C 0 2 laser is used
to excite the v2 NH 3 vibration (the umbrella motion) in
several binary complexes of NH3. The complexes studied
include (NH3)2, NH 3-Ar, NH3-HCCH, NHj-OCS, NH3HCN, NH 3-N 20 and NH3-C 0 2. For some of these
complexes precise band origins arc obtained and upper
limits for the vibrational prcdissociation lifetimes arc
determined. Preliminary results on the microwave spec­
troscopy of Ar-NH 3 and (NH 3)2 are also reported.
EXPERIM ENTAL
A molecular beam electric resonance spectrometer36
was modified to allow the output of a carbon dioxide
laser to enter its resonance region, as shown schematically
in Fig. 1. The spectrometer is of conventional “flop-out”
design and utilizes electric quadrupole state selector and
analyzer fields and mass spectrometric detection. Briefly,
the quadrupole state selecting A field focuses those mol­
ecules through the C field resonance region whose energy
increases with electric field (i.e., molecules in states with
positive Stark coefficients). Molecules in rotational states
whose energy decreases with electric field are deflected
away from the resonance region. Nonpolar molecules arc
,1 c =7C"= A]
B
Q 'C
H G . I. Schematic o f the resonance region o f the molecular beam
(pectrometer. Pictured are the quadrupole Mate selecting field (A), the
quadrupole Mate analyzing field (B), the C field Stark plates (C), beam
Mop (S), and the approximate COj laser beam path (L). Microwave and
radio frequency couplings in the C field region are not shown.
HO
blocked by a beam stop (sec Fig. I). In the C-field
resonance region radiofrequency, microwave, or infrared
radiation (or combinations of these) arc applied to the
molecular beam. A static electric field can also be applied
in order to measure electric dipole moments. If a molecule
undergoes a transition to a rotational state with a negative
Stark coefficient it will be deflected from the beam by the
B-field state analyzer. Molecules which arc photodissociatcd will be ejected from the beam regardless of the
potential applied to the B-field state analyzer. Molecules
which do not undergo a transition arc focused by the Bficld stale analyzer into the detector. Thus a resonance is
typically observed as a decrease in the number of molecules
reaching the detector. In practice, the radiation is modu­
lated and phase sensitive detection is used.
Infrared radiation from 920 to 990 cm-1 and 1020
to 1092 cm -1 is provided by a 1.5 m grating tuned C 0 2
laser operating in the cw mode. Typical output power on
the strongest lines is 20 W. Although the C 0 2 laser
oscillates on a single longitudinal mode, the output in the
near field contains several higher order transverse modes.
The linewidth of the laser is estimated to be less than 50
MHz. The Doppler width of the molecular transitions,
which is due to the velocity dispersion of the molecular
beam, is estimated to be less than 2 MHz.
The C-field resonance region of the molecular beam
apparatus consists of two 15 cm diameter gold coated
quartz flats which arc separated by I cm precision quartz
spacers. Radiofrcqucncy radiation as well as a static
potential can be applied directly to one of the gold plates.
Microwave horns arc also available to introduce micro­
wave radiation into the gap between the plates. All
photodissociation spectra are obtained by directing the
unfocused output of the infrared laser into the C-field
resonance region at an angle of approximately 45 dcg.
The laser beam subsequently undergoes a series of reflec­
tions between the gold coated surfaces. The overlap of
the infrared beam with the molecular beam is unknown
and is dependent upon the transverse modal structure of
the laser line. The reported intensities, however, were
reproducible to within 20%. All the photodresociation
data reported here are normalized to the incident laser
power although saturation on a transition in ArNH3 was
observed with as little as 4 W of infrared power. An
extensive study of the saturation characteristics of each
absorption was considered inappropriate given the ge­
ometry of the present experiment and the multimode
nature of the C 0 2 laser.
Ammonia complexes were created in an argon beam
in a room temperature supersonic expansion through a
100 it nozzle. Typical stagnation pressures were 1.3 atm.
Previous observations have indicated that the binary
complexes found in the expansion are rotationally cold
( T ~ 10 K ) .37
U nfo cu se d m o le c u la r beam s tu d ie s
Searches for photodissociation of a nonstate selected
(“unfocused”) molecular beam were performed on the
straight through beam, i.e., with the beam stop out and
J. Chem. Phys., Vol. 82, No. 6 ,1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H
Fraser el al.: Weakly bound NH3 complexes
with no potential applied to the A and B quadrupole
fields. In this configuration our experiment resembled
those of Gentry17 and Janda . 18 While the output of the
mass spectrometer was monitored on a particular mass
peak by a phase sensitive detector, the C 0 2 laser was
amplitude modulated at 6 § Hz and tuned through its
discrete spectrum. A dedicated microcomputer averaged
the digitized output of the phase sensitive detector.
F ocused m o le c u la r beam s tu d ie s
Most of the photodissociation experiments were per­
formed with state selected (“focused”) molecular beams,
i.e., with the beam stop blocking the straight through
beam and the appropriate focusing potentials applied to
the A and B quadrupole fields. Several advantages are
gained by working with a focused molecular beam. First,
since only polar molecules (in rotational states with
positive Stark coefficients) reach the mass spectrometer,
background absorption by nonpolar species, e.g., (NH3)3,39
is eliminated. Furthermore, the focusing fields are state
selective, and, in favorable cases, one can focus different
rotational levels into the mass spectrometer by varying
the applied potentials. Finally, the quadrupole fields can
be used to select a particular molecule when two species
arc present at the same mass peak in the mass spectrom­
eter. The selectivity of the focusing patterns of a particular
species (by Stark effect and mass) enabled us, for example,
to separate Ar-NH 3 from NH 3 while monitoring the
NH3+ peak in the mass spectrometer. This increased the
signat to noise ratio in the Ar-NH 3 scans considerably.
Linewidths determined from experiments performed on
unfocused molecular beams have inhomogcncous contri­
butions from rotational band structure and the presence
of higher clusters in the beam. These broadening mech­
anisms are suppressed in the focused beam studies reported
here. Resonances on a focused molecular beam can be
due to cither photodissociation or pholoahsorplion. Photodissociating molecules are distinguished from photoab­
sorbing molecules since the former do not require the
presence of the state analyzing B quadrupole field to
remove them from the beam.
\
2537
that operated under computer control. Data were accu­
mulated during a 10 s portion of the 14 s interval to
allow for complete response of the phase sensitive detector.
The digitized output of this doubly modulated signal was
stored and averaged by the microcomputer.
The effect of infrared photodissociation on the signal
strength of a microwave transition was observed to be
either an increase or a decrease in measured signal
strength. There are two mechanisms which may be re­
sponsible for an enhancement of the microwave resonance.
Both mechanisms assume that the laser excites molecules
out of the rotational state involved in the microwave
transition which has a negative Stark coefficient. Suppose
a microwave transition occurs between states |n) and |/>)
where state <|n) has a negative Stark coefficient and state
|p) has a positive Stark coefficient. The first mechanism
assumes that the laser acts as a photodissociative state
selector by photodissociating molecules out of state |»).
An enhancement of the microwave resonance will occur
if the laser increases the efficiency of the B quadrupole
state analyzer. The second mechanism assumes that there
is significant overlap between the microwave field and
the laser field. In this model, the infrared laser perturbs
the equilibrium established by the microwave field (which
is assumed to saturate the transition). Since molecules in
state |n) are depleted by the infrared radiation the micro­
wave signal can drive population from state |p) to state
|w). This causes a further decrease in the number of
molecules in state |/>) and an enhancement of the micro­
wave signal occurs. If the infrared laser interacts only
with state |p) or with both sides |p) and |«) the double
resonance signal will decrease. In the case where there is
complete overlap of the microwave and infrared radiation
these results are qualitatively summarized by
/d rW
= / o [ 1 + />„(*>)][ 1 -
/ »
] ,
where / Dr(f) is the double resonance signal strength as a '
function of infrared frequency, /<>is the microwave signal
strength in the absence of infrared radiation, and PJiv)
and P^v) are the infrared transition probabilities for states
|p) and |«), respectively.
r
RESULTS AND DISCUSSION
M ic ro w a v e -In fra re d d o u b le re so n a n ce s tu d ie s
To further eliminate inhomogcncous broadening due
to rotational fine structure and to remove background
absorption due to the presence of other molecular com­
plexes, the experiment was also configured to examine
infrarcd-microwave double resonance signals. The micro­
wave and radio frequency spectra of the complexes had
already been investigated, and for some species these
spectra arc understood. The double resonance experiments
were performed with phase locked microwave oscillators
or radio frequency oscillators. The oscillators were am­
plitude modulated at 10 Hz and phase sensitive detection
(r = 2 s) was employed. The C 0 2 laser was adjusted to
maximize the output power and data were accumulated
for 12 min per laser line. The effects of molecular beam
and laser drifts were minimized by acquiring data while
alternately blocking the laser every 14 s with a shutter
Results for each NH 3 complex arc given below.
Preliminary microwave spectroscopy of Ar-NH 3 and
(NHsfe is also presented in order to aid in the interpretation
of the infrared spectrum. For complexes where both the
structure and microwave spectrum are well understood,
it is possible to report infrared band origins and estimates
of the linewidths of the infrared transitions. For the other
complexes only preliminary results can be presented. An
important result of these studies is that the dissociation
energies of alt of the complexes studied, except for NH3HCN, are established to be less than 990 cm-1, i.e., 2.8
kcal/mol.
When reporting the linewidths of the infrared tran­
sitions we also relate these linewidths to the lifetime of
the excited state. We use the expression,
1
f S '
.
2* IV
J . Chem. Phys., Vol. 62. No. 6 ,1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2536
Fresor of al.: Woakly bound NH3 comploxos
where r H is the full width of the line (in Hz) at half of
its maximum intensity. Recently, it has been suggested22
that t is not necessarily a direct measure of the vibrational
prcdissociation lifetime of the van der Waals complex. It
is, however, a rigorous lower limit for this lifetime.
In this study the v2 NHj vibration (the umbrella
motion) of the complex is excited. The frequency of the
inversion free v2 band origin of free Nll 3 is 950.3 c m '1.
The band origins measured in this experiment are blue
shifted by 30-40 cm-1 from this reference point. An FG
matrix calculation suggests that these frequency shifts arc
not due to kinetic coupling but instead are due to an
~5% change in the force constant associated with the
umbrella motion.
N H j-H C C H
The microwave spectrum of NHj-HCCH in its
ground vibrational state has been previously reported33
and shows that this complex is a symmetrical top with
the acetylene subunit hydrogen bonding to the NH3. The
rotational constant B0 is 2724.567(4) MHz while the
dipole moment is 1.9871(16) D. in the study reported
here, as well as in the previous microwave study, a
mixture of 1% NH 3 and 3% HCCH in argon was used as
the expansion gas. The rotational cooling of the complex
was efficient since we were unable to observe a microwave
transition involving a K = 2 rotational level. It should be
noted that the K = 1 rotational slates of this complex
cannot be relaxed further since this would require a
nuclear spin forbidden process.
An initial infrared spectral search was made with a
focused molecular beam while tuning the C 0 2 laser from
983.25 to 988.65 cm-1. The mass spectrometer was tuned
to the NH3+ (m/c’ = 17) mass spectral peak. A resonance
was detected at 984.38 cm-1 which could be observed on
both the NHj+ and H(HCCH)+ mass spectral peaks, in
PHOTODISSOCIATION OF NH.-HCCH AT 8 8 4 .3 8 ea
-1
FOCUSSING VOLTAGE KV)
FIG. 2. Infrared photodissociation intensity o f NHj-HCCH at 984.38
cm ' 1 as a function o f voltage applied to the A and B focusing fields.
This is the only COt laser line on which photodissadation is observed.
Fig. 2 we show the signal intensity of the 984.38 cm -1
transition as a function of the voltage applied to the
quadrupole fields. The extreme sensitivity of the signal
strength to this applied voltage is suggestive of an infrared
absorption from a single rotational level of the ground
vibrational, state. Furthermore, the observation of the
infrared transition with the B quadrupole field o(T dem­
onstrates that the transition is to a predissoeiative state.
Mierowave-inlrared double resonance allowed the deter­
mination of the 7, K assignment of the initial state
involved in the infrared photodissociative process. The
signal strength of the 7 = 0-1, 2-3, and 3-4 microwave
transitions for K = 0 as well as the 7 = 2-3 transition for
K = 1 were unaffected by 984.38 cm -1 infrared radiation
from the C 0 2 laser. The signal strength of 7 = 3-4, K
= I microwave transition, however, was enhanced by
71(5)%. To assign the initial level in the photodissociative
process, the signal strength of the 7 = 3, K = 1, |AA/|
= I and 7 = 4, K = I, |A/W| = I transitions at stonzcro
electric field were also monitored. Only the 7 = 4, K
= I,-|AA/| = I transition was allecled and the signal was
attenuated by 33(6)%. It is certain, therefore, that the
initial level in the photodissociative process is 7 = 4, K
= I. In addition the 7 = 5, K = 1, |AA7| = 1 and 7 = 2,
K = 1, \AM\ = 1 transitions were also investigated, but
no double resonances were observed.
Since NHj-HCCH is a symmetrical top, the infrared
transition at 984.38 cm -1 must be P(4), 0(4), or R(4) of
the K = I parallel band. Since the exact assignment is
uncertain, the most accurate value which we can obtain
for the K = I band origin is 984.4(9) cm"1. The occurrence
of only a single coincidence between the available C 0 2
laser lines and the infrared transitions in the 984 cm -1
band clearly .implies an extremely narrow homogeneous
lincwidth and a correspondingly long predissoeiative life­
time for the complex. To estimate this lincwidth, it is
useful to construct the expected parallel band of the
NHj-HCCH umbrella excitation.
Equating AA in the complex with AC seen in the
corresponding free NH 3 spectrum ( -3 GHz) and assuming
AB for the complex is - 5 MHz (arbitrarily chosen), the
infrared band shown in Fig. 3 is obtained. The intensities
shown are scaled Boltzmann .factors for a 10 K rotational
temperature.37 Examination of this figure shows that at
least five C 0 2 laser lines should overlap the infrared band
since the infrared band covers approximately 6 cm-1.
The observation of only one coincidence is a further
indication of a very narrow linewidth for the infrared
transition. A simple probabilistic model suggests a ho­
mogeneous linewidth of 150 MHz which corresponds to
an excited state lifetime of 1 ns.40
The observed infrared photodissociation of NH3HCCH establishes that the binding energy D0 is less than
2.81 kcal/mol. Frisch, Pople, and Del Bene41 have recently
done a series of electronic structure calculations on NH3HCCH which indicate a slightly higher binding energy.
Using SCF plus their Moller-Plesset perturbation Cl
theories at the MP4SDS/6-31G** level and including
zero-point vibrational energy differences they determined
that Do = 3.6 kcal/mol. The authors indicate that larger
J . Chem. Phys., Vol. 82, No. 6 ,1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fraser e t at.: Weakly bound NH» com plexes
SIMULATED PARALLEL BAND FOR NH^HCCH
5
7 .5
>-
cr
<
cc
♦—
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ir
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hZ
0.0 a
•
2.0
-
1.0
0.0
1.0
2.0
FREQUENCY SHIFT FROM BAND ORIGIN (cm*1)
FIG. 3. Infrared spectrum o f NHj-HCCH assuming A/1 “ - 3 GHz and
A I! ■= - 3 MHz. The intensities arc derived from Rollzmann factors al
10 K. The relative intensities of the A' = 0 and K = I states arc assumed
equal.
basis set calculations suggest a binding energy of 3
kcal/mol.
n h 3- h c n
The microwave spectrum of NHj-HCN has been
previously reported.34 NHj-HCN is a symmetric top with
the HCN subunit hydrogen bonding to the NH3 subunit.
Evidence from the microwave study of this complex
suggests that the NHj-HCN interaction is quite strong.
Specifically, the stretching force constant, the bending
force constant and the induced dipole moment for NH3HCN are all large compared to those measured for NH3HCCH. Also, the hydrogen bond length for NHj-HCN
is 0.2 A shorter than that for NH 3-HCCH. It is, therefore,
not clear whether 1 0 0 0 cm -1 of excitation energy can
photodissociate NH 3-HCN.
Focused beam spectral searches were conducted on
an NHj-HCN molecular beam formed from a mixture
of 1% NH 3 and 1% HCN in Ar. The searches extended
from 984 to 991 cm " 1 and from 1021 to 1060 cm -1 while
monitoring either the HCN+ or the NHj+ mass spectral
peaks. No transitions were observed on either mass peak.
We list three possible explanations for this: (i) the fre­
quency of i>2 of NHj in this complex is between 991 and
1 0 2 1 cm -1 where no CO2 laser tines are available, (ii) the
i*2 vibration in NHj-HCN is less than the dissociation
energy A> for the complex, (iii) the excited state lifetime
is very long. Either explanation (ii) or (iii) would imply
that the transition lincwidth is too narrow to give a
coincidence with the C 0 2 laser lines. This is. not an
unlikely explanation, since in both NHj-HCCH and
NHj-Ar only one rovibrational coincidence has been
found.
4 3
2539
(k = -0.72) in which the NH 3 subunit exhibits effectively
free internal rotation. The ground internal rotor state m
= 0 is described by the usual asymmetrical top formalism
while the excited internal rotor states (|m| > 0 ) require
terms due to the internal angular momentum.
The NH 3-CO 2 beam was formed by a supersonic
expansion of a gas mixture consisting of 1% NH3 and 8 %
C 0 2 in Ar. The NH3+ mass spectral peak has been shown
to be optimal for monitoring NHj-COj .35 For NH 3-C 0 2
a congested parallel infrared band, dominated by A/
= 0, ±1, A K = 0, Am = 0 transitions, is expected. Due
to the large asymmetry of this complex |AA| = 2 transi­
tions may also be present. They will be weak, though,
since the line strengths are a factor of 1 0 0 less than the
corresponding AK = 0 transitions. Further spectral com­
plexity can result from higher order effects which relax
the selection rule on m to |Am| = 0, 3. These transitions
are also expected to be extremely weak since they depend
on high order terms in the expansion of jthe dipole
moment operator in the internal rotor coordinate. Figure
4 shows a simulated parallel band for the ground internal
rotor state of NH 3-CO 2 for an assumed 10 K rotational
temperature.37 For clarity only the AK = 0, Am = 0
transitions are shown. The A, B, and C rotational constants
for the excited state arc assumed to be unchanged from
the ground state values. The band origin used is the
experimentally obtained value discussed below. Also
shown in Fig. 4 is the unfocused beam photodissociation
spectrum of NH3-C 0 2. Note that the photodissociation
spectrum is broad ( ~ 6 cm-1). Microwave-infrared double
resonance experiments were performed to determine
whether the observed lincwidth was due completely to
homogeneous broadening or whether it was dominated
by the underlying inhomogeneous rotational structure.
Figure S displays the results of these double resonance
experiments.
Figure 5 shows that the signal strength of the 7 = 0I microwave transition is attenuated completely by the
NH -CO. INFRARED SPECTRUM
55
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250
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cr
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985
989
FREQUENCY (cm 1 )
n h 3- c o 2
The rotational spectrum of N H j-C0 2 has been pre­
viously measured.35 This complex is an asymmetric top
FIG. 4. Observed unfocused beam infrared spectrum o f NH j-C O j
displayed above a simulated spectrum for this complex. Only the m
- 0 , AA-i - 0 hand is displayed in the simulation.
J. Chem. Phys.. Vol. 82, No. 6 .1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2540
1
.
Frasor ot al.: Weakly bound NHS comploxos
1
should dillcr by approximately 0.1 cm-1. Since the J
= 1 - 2 microwave transitions for both m = 0 and M = 1
arc affected by the same C 0 2 laser lines the rovibralional
transitions must be at least 0.1 cm- ' broad. Furthermore,
the J = 2-3, K = 0 double resonance indicates that the
rovibrational transitions are at least 0 .2 S cm -1 broad,
since F (l) and /?(2 ) arc both overlapped by the laser line
al 987.62 cm- '. The double resonance study on the J
= 3, K = 2 asymmetry doublet shows that, rovibrational
transitions up to 0.3S cm -1 away from a C 0 2 laser line
can be in resonance (though weakly) with that laser line.
These results suggest a linewidth of 0.45(20) cm-1 for the
infrared transitions and a band origin of 987.1(2) cm-1.
The other results shown in Fig. 5 are consistent with this
assignment of the band origin. Microwave transitions
higher in J arc attenuated by C 0 2 laser lines further from
the infrared band origin.
The NH 3 v2 band origin observed in matrix isolated
NH 3-C 0 2 differs remarkably from that observed in this
study. In an Ar matrix the v2 origin of NH3-C 0 2 occurs
at 996.8 cm - ' 42 which corresponds to a frequency shift
of 47 cm -1 from that of uncomplcxed, noninvcrting NH3.
For gas phase NH3-C 0 2 this frequency shift is 37 cm-1.
From the observed photodissociation of NH3-C 0 2, the
dissociation energy D0 is determined to be less than 2.8
kcal/mol. Since the zero point energy of the live van der
Waals modes is approximately I kcal/mol the dissociation
energy D , must be less than 3.8 kcal/mol. This upper
bound on the dissociation energy is clearly in disagreement
with the ab initio SCF calculation of Jonsson and Nelandef43 which determined that De is 7.0 kcal/mol. When
the calculation was redone so that the energy of the free
molecules was calculated in the dimer basis set D , was
determined to be 3.7 kcal/mol. Since configuration inter­
action has not been considered, this latter value can only
be in fortuitous agreement with the upper bound deter­
mined in this study.
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887
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FREQUENCY t e n '1)
FIG. 5. Microwave-infrared double resonance study o f N H j-C O j . The
microwave transitions which were monitored arc indicated. The three
tick marks along the yaxis in each figure indicate 100 %, 0 %, and - 100 %
change in the microwave signal strength. For example, at 985.49 cm ' 1
the 643-641 transition is detuned by 21(6)%. All the transitions arc in the
ground internal rotor state except where otherwise noted.
laser line at 987.62 c m '1. This result alone requires that
the band origin must be within 1 cm -1 or this laser line
since we must be observing cither the /i( 0 ), 1), or /’(I)
infrared transition of the K » 0 band. Combining these
results with the results of the J * 1-2, K ■= 0 double
resonance experiment places F(I) near the laser line at
987.62 cm- ' and P ( 2) near the laser line at 986.S7 cm-1.
This implies that the band origin for the ground internal
rotor state of NH 3-C 0 2 is 987.1 cm-1. Due to the Fm 2 35
term in the rotational energy of NH3-C 0 2 the band
origins of the ground and excited internal rotor states
(tiHih
The microwave spectrum of (NH3)2 has mot been
previously reported. A beam of (NH 3) 2 was formed by a
supersonic expansion of a gas mixture consisting of 1%
NH3 in Ar. Microwave searches from 65 kHz to 91 MHz
and from 3.75 to 23.0 GHz led to the detection of two
transitions, at 10.22 and 20.44 GHz, which are assigned,
respectively, to the J = 0-1 and J = 1-2 transitions of
(NH3)2. The resonances can be observed on both the
NH3+ and N H / mass spectral peaks with the signal
strength being greater on the NH4+ peak by a factor of
1.8. The 10.22 GHz transition is shown in Fig. 6 . It
should be noted that this is the overlap of two hyperfinc
patterns (with three hyperfine components each) of two
different J = 0-1 transitions of the complex. The frequency
separation between the two transitions is 300 kHz and
for the 7 = 1 - 2 transition this separation becomes 600
kHz. It is apparent that we are observing two different
vibrational states of the complex, whose rotational con­
stants differ by 150 kHz. (B + C)/2 is determined from
the frequency of the J - 0-1 transition and is found to
J . Chem. Phys., Vol. 82, No. 8 ,1 6 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2541
Fraser at al.: Weakly bound NHj complexes
TABLE II. Molecular constants o r (NHj)j and (ND5)j .
(NH j )j
J?+ C
2
th
Rem
J=0<— 1
io e e i.e
lO B C O .B
MHz
FIG. 6. High resolution spectrum o f the 7 » 0-1 transition o f (NHj)j.
This is the overlap o f the hyperfine patterns o f two different vibrational
states o f the complex. The hyperfine components o f the two different
vibrational states which were monitored in microwave-infrared double
resonance are indicated by numbers I and 2.
be 5110.0(5) MHz. Using this value of (B + C)/2 and
treating (NH3)2 as a pseudodiatomic molecule leads to a
center of mass separation R m between the two subunits
of 3.4110(2) A. The observed Stark effect of the 7 = 0-1
transition is second order and confirms the assignment
of the transition as K = 0. The corresponding dipole
moment is 0.74(2) D. The Stark effect of the 7 = 1, K
= 0, |AA/| - 1 transition was also examined and found
to be consistent with this dipole moment for the complex.
Table 1 lists the observed transitions of (NH3)2.
We have also observed two transitions for (ND3)2
which have been assigned as 7 = 0-1, K = 0 and 7 = 1 2, K = 0 (at 8.4 and 16.8 GHz, respectively). These
transitions are also listed in Table 1. Due to the added
complexity of the deuterium quadrupole hyperfine struc-
TABLE I. Observed microwave transitions o f (NHj)j.
Transition
7 -O -l.tf-O
J - 1-2. AT - 0
■ /-(M .K -O .M .,-0
E - 1197.9 V/cmb
Frequency (MHz)"
*10 220.600(14)
*10 220.832(9)
••10 220.911(4)
•10 221.030(10)
••10 221.139(16)
••10 221.332(14)
•20 439.494(25)
•20 439.747(25)
••20 440.115(30)
••20 440.379(20)
10 231.282(35)
10 231.486(35)
Observed microwave transitions o f (ND3)j
7 - 0 - 1 , AT-0
7 « 1-2, K - 0
7 - 0-1, AT - 0. M, - 0
■
E - 1996.9 V/cm1'
E - 3012.5 V/cmb
8 380.6(5)
16 760(1)
8 401.0(4)
8 427.3(4)
* • and • • indicate the two vibrational states observed in (NH j )j .
* Electric field known to better than 0.1%.
5110.0(5) MHz
0.74(2) D
3.4110(2) A
(NDj),
4190.3(3) MHz
0.57(1) D
3.4729(1) A
ture, no attempt was made to observe a splitting of the
rotational transitions into different vibrational states as is
observed in (N H ^ . From the 7 = 0-1 transition of
(ND3)2, {Ii + C)/2 is determined to be 4190.3(3) MHz
and
is 3.4729(1) A. The dipole moment of (ND3)2,
measured from the Stark effect of the 7 = 0-1 transition,
is 0.57(1) D. The molecular constants of both (NH3)2 and
(ND3)2 are summarized in Table II.
The structure of (NH3)2 has been the subject of
detailed theoretical studies.4*-53 Electronic structure cal­
culations give a hydrogen bonded minimum in which the
N-H—N arrangement is nearly linear. This structure
requires the electric dipole moment iia for the complex
to be greater than 2 D. The dipole moment components
Ha determined for both (NH3)2 [0.74(2) D] and (ND3)2
[0.57(1) D] are clearly inconsistent with this hydrogen
bonded structure. Furthermore, the observation of a rigid
rotor spectrum for the complex as well as the insensitivity
of the (N H ^ dipole moment to isotopic substitution
shows that the measured dipole moments do not differ
greatly from the equilibrium value. It is apparent that the
accepted hydrogen bonded picture of this complex is
incorrect. Pimentel, Bulanin, and van Thiel54 have pre­
viously suggested that (NH3)2 might display an unusual
type of hydrogen bond since the structure of solid NH355,5A
does not follow a simple hydrogen bonded pattern. At
this time we have not determined a structure for the
complex nor do we understand the nonrigid behavior'
which leads to the nearly complete transparency of (NH3) 2
in the spectral regions searched. The effects of nonrigidity
severely limit our ability to interpret the infrared-spectrum.
Howard, Burdenski, Giese, and Gentry21: have re­
cently examined the photodissociation spectrum of (NH3)2
in the region of the NH 3 v2 umbrella motion using a line
tunable pulsed C 0 2 laser. The photodissociation spectrum
of a seeded molecular beam of NH 3 in He shows a broad
(linewidth of 2 0 cm-1) featureless spectrum centered at
980 cm -1 when the NH4+ mass spectral peak is monitored.
From an examination of the photodissociation intensity
as a function of beam temperature they concluded that
only “hot” (N H ^ can be photodissociated. In addition,
they concluded that the observed linewidth has substantial
homogeneous contributions.
In our experiments, infrared spectral searches were
conducted between 914 and 987 cm -1 on a focused beam
while monitoring either the NH3+ or the NH4+ mass
spectral peak. The spectrum was featureless except in the
frequency range from 969 to 987 cm-1. This spectral
region will be discussed next. In Fig. 7(a) we show the
photodissociation spectrum that was obtained while mon­
itoring the NH4+ mass spectral peak. The C 0 2 laser was
J. Chem. Phys., Vol. 82. No. 6 ,1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2542
Frasor el al.: Weakly bound NH3 coniploxos
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spectra is very similar in appearance to the photodissocia­
tion spectra of (NH3)2 shown in Figs. 7(a) and 7(b).
Undoubtedly, the observed linewidths, conservatively es­
timated at 5.2 and 3.5 cm-1 for the low and high
frequency peaks, respectively, arc not homogeneous but
are due in part to the complicated infrared band structure
expected for such a complex. Since the infrared transition
moment most likely has components parallel and perpen­
dicular to the a axis, the infrared band should be a hybrid
band. With the microwave-infrared double resonance
conditions used here, and, assuming the ground state and
excited stale rotational constants arc identical, the parallel
band is expected to extend approximately 1 cm -1 and the
perpendicular band about 2/3 cm-1. The band separation
should be on the order of the A rotational constant, which
is estimated to be approximately 3 cm-1. Further com­
plicating the expected infrared band is the presence of
two inequivalent NH 3 subunits in the complex, each
contributing a separate infrared spectrum. Inversion mo­
tions and internal rotation will add more complexity to
the spectrum, but without a complete understanding of
the microwave spectrum, they cannot be analyzed. This
complicated band structure might be the source of some
of the other spectral features observed in the double
resonance spectrum. Due to these inhomogeneous con­
tributions to the observed linewidth no upper state lifetime
is reported.
085
A r-N H 3
FREQUENCY (cm-1)
FIG. 7. (a) Infrared spectrum o f (Nllj)j oil an unfocused molecular
beam, (b) Infrared spectrum of (Nl l3)2 on a focused molecular beam,
(c) and (d) Microwave-infrared double resonance study of(NHj)}. The
numbers in the upper right-hand comer indicate which microwave
transition (of Fig. 6) is monitored.
tuned from 969.14 to 986.57 cm -1 with the state selecting
fields off and beam stop not being used. The spectrum
exhibits a diffuse background absorption as well as two
overlapping peaks. Continual refinement in ground state
rotational state selection (via use of the state selecting
fields and microwave-infrared double resonance) shows
that this doublet structure is not an experimental artifact.
Repeating the above experiments with the beam stop in
and the state selecting quadrupole fields set to the voltages
appropriate for observing the 7 = 0 - 1 microwave transi­
tion, the spectrum shown in Fig. 7(b) is obtained. Ex­
amination of this figure shows that both the diffuse
background absorption as well as the doublet persist.
Infrarcd-microwavc double resonance provides in­
sight into the origin of this doublet. As shown in Fig. 6
there arc two vibrational states observed in the / * 0 —1 ,
K = 0 microwave transition of (NHjh. By monitoring
the signal strength of the / = 0 - 1 microwave transition,
for each of these vibrational states, separate infrared
spectra are obtained. These are shown in Figs. 7(c) and
7(d). As seen in these figures, each vibrational state gives
a different nonovcrlapping infrared spectrum. It should
be noted that the composite of the two double resonance
We have begun an investigation of the microwave
and radio frequency spectra of Ar-NH3. In these studies,
as well as in the infrared studies to be described below, a
molecular lieam consisting of 1% NH3 seeded in argon
was formed in a supersonic expansion. Spectroscopy was
carried out while monitoring the NH3+ mass spectral
peak. Spectral searches were conducted from 65 kHz to
91 MHz and from 3.75 to 23.0 GHz. No low frequency
resonances were observed which implies that there are no
degenerate or even nearly degenerate energy levels in ArNH3. The main features of the spectrum are displayed in
Fig. 8 . The observed spectrum is assigned to Ar-NH3,
rather than to (NH3)2, because of the absence of the
resonances when monitoring the N H / mass spectral peak
and because of the presence of the expected hyperfine
structure. Furthermore, the intensity of the transitions
rules out the possibility of higher clusters being responsible.
It should be noted that the parent ion, Ar-NH3+, is not
detected in the mass spectrometer. This is not a surprising
result based on our experience with other NH 3 complexes.
However, Ar-NH3 resonances can be monitored on ArH+,
though the signal intensity there is quite weak.
The spectrum of Ar-NH 3 is quite complex and
difficult to interpret. Although the spectrum is not yet
assigned, we believe that the Ar-NH 3 complex undergoes
large amplitude internal motions in four coordinates. The
transitions clustered between 19 and 20 GHz are suggestive
of a slightly perturbed NH3 inversion spectrum. In free
NH3 the pure inversion transitions for low rotational
states occur near 23 GHz. In addition to inverting, the
J. Chem. Phys., Vol. 82. No. 6 , 1 5 March 1985
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fraser ef al.: Weakly bound NH* complexes
140919
1408V
MHz
GHz
FIG. 8. Observed microwave spectrum o f Ar-N Hj from 13 to 21 GHz.
The spectral regions from 65 kHz to 91 MHz and from 3.75 to 13.0
GHz were also searched but no resonances were found in these regions.
Also shown are two hyperfine components o f the only microwave
transition which was observed in microwave-infrared double resonance.
NH3 subunit internally rotates. A model in which the
NH 3 inverts and simply rotates about its C3 axis cannot
explain the observed Q branch inversion spectrum. A na
dipole moment component which is antisymmetric with
respect to the NH3 inversion is required. The only rea­
sonable model which is consistent with pur results appears
to be one which views the NH 3 molecule as almost free
as a consequence of a nearly isotropic interaction potential.
It will be shown below that the infrared work lends
support to this model. Experimental work and theoretical
studies on the microwave spectrum of Ar-NH 3 are con­
tinuing, since both are required for a full understanding
of this intriguing system.
Based on our microwave model of Ar-NH3, we
expected the NH 3 subunit to behave similarly to free
NH3. Free NH 3 has vibration-inversion transitions at
931.58 and 968.08 cm- 1 .57 The higher frequency transition
is from the symmetric level of the ti = 0 inversion doublet
to the antisymmetric level of the v = I doublet, while the
lower frequency transition is from the antisymmetric level
of the lower doublet to the symmetric level of the upper
doublet. We were, therefore, somewhat surprised that no
transitions could be found when spectral searches were
made on a focused molecular beam. All the available
laser lines between 914 and 987 cm -1 were investigated
while monitoring the NH3+ mass spectral peak and no
features except for the (N H ^ background which begins
around 970 cm -1 were detected. Further spectral searches
were conducted by looking for double resonance connec­
tions between the laser lines near 930 cm' 1 and several
of the Ar-NH 3 microwave transitions. While monitoring
the signal strength of the microwave transition at 14092
MHz (see Fig. 8 ) we attempted to deplete it with the laser
line at 938.69 cm-1. However, rather than attenuating
the resonance, the laser actually enhanced it by 155(7)%.
Attempts were made to find double resonance connections
between this laser line and the Ar-NH 3 microwave tran­
sitions at 13 771, 14006, 14 588, 15 315, 15 387, 16 333,
and 17 368 MHz, but no other double resonance connec­
tions were discovered.
As discussed in the experimental section, the obser­
vation of laser assisted enhancement of a microwave
transition implies that the molecules in the rotational
state with a negative Stark coefficient were being selectively
excited. This also explains why the transition could not
be seen in the focused beam search since in these studies
only molecules in states with positive Stark coefficients
are detected. Repeating the double resonance experiment
with the B field turned off gives a signal which is 87(2)%
as strong as the microwave resonance signal. This dem­
onstrates that the laser is photodissociating the complex,
because it prevents molecules from reaching the detector.
Since the transition is to a predissoeiative state, it was
also possible to detect it in an unfocused beam experiment.
Further searches were conducted in this manner, from
918 to 958 cm-1, but no other resonances were found.
Our model predicts that the infrared transition at
938.69 cm ' 1 must have a higher frequency partner, but
this has not been observed. This result may be^ccounted
for in several ways. The first explanation is that it may
be hidden in the (NH 3)2 background absorption which
stretches from 970 to 985 c m '1. If this is the case,
extensive double resonance searches may be required to
reveal its presence. The second possibility is that the
transition may fall in the null gap of the C0 2 laser
between 958 and 964 c m '1. Finally, the higher frequency
band may have no overlap with the C 0 2 laser. This is
not an unlikely explanation since only one double reso­
nance connection was found with the lower frequency
vibrational band of Ar-NH3.
The observation of only one microwave-infrared
double resonance in Ar-NH 3 also implies that the line­
width of the rovibrational transition is narrow. Unfortu­
nately, the spectroscopy of Ar-NH 3 is not understood
well enough to predict its infrared band shape or to assign
the quantum numbers of the eigenstate that the infrared
transition originates from. Hence, it is not possible to
estimate the linewidth of the transition as accurately as
in the case of NH 3-HCCH. However, there are several
indications that the linewidth is extremely narrow. If the
linewidth of each rovibrational transition were greater
than or equal to IB, then the infrared absorption band
would be continuous and we would see resonances on
adjacent C 0 2 laser lines. Since no other resonances arc
observed, the linewidth of the rovibrational transition
must be less than 2B. The B value for Ar-NH 3 can be
estimated to be about 2.5 GHz. We can, therefore, put
an upper limit of 5 GHz on the linewidth. In the context
of our results on NH3-HCCH it is clear that this number
is overly conservative and a poor guide to the actual
linewidth. The linewidth of the Ar-NH 3 transition is
likely to be of the order of 100 MHz as in NH 3-HCCH.
N H j-O C S
The microwave spectrum of the van der Waals
complex NH3-OCS has not been measured. It is expected
to be analogous to NH 3-C 0 2 and thus have a spectrum
characteristic of a T-shaped complex. The spectrum should
consist of both na and p* type transitions with additional
J. Chem. Phys., Vol. 82. No. 6 . 1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2644
Frasor ot al.: Woakly bound NHj comptoxos
complexity due to internal rotation. Since the structure
and spectrum of NH3-OCS is unknown only a brief
discussion of its infrared spectrum will be presented.
Both free NHj and free OCS have an infrared
transition in the region overlapped by the C 0 2 laser. For
OCS this transition is the 2v2 overtone transition (i/0
«= 1047.04 c m '1) which borrows intensity through a
Fermi resonance with the C-S stretch. The transition
dipole moment for excitation of the NH3 umbrella motion
is 0.23 D58; for excitation of the l v 2 bend on OCS it is
0.039 D.M Previous studies on C 0 2 laser photodissociation
of OCS weakly bound complexes have been undertaken
by Hofibauer, Lui, Gicsc, and Gentry. 17,20 They studied
the binary complexes ArOCS, (OCS)2, OCS-cthane, OCShexanc, OCS-CO4 , and OCS-butane, as well as the
tertiary complex (OCS)j. Except for(OCS)j, only feature­
less spectra with linewidths between 2 - 6 cm ' 1 were
observed.
Figures 9 and 10 show the infrared spectrum of
NH3-OCS measured on a focused molecular beam with
the mass spectrometer, tuned to the NH3+ mass spectral
peak. The expansion consisted of an argon beam seeded
with 1% NH3 and 4% OCS. The spectrum displayed in
Fig. 9 is observed when exciting the NH 3 umbrella motion
in the complex. When the overtone of the OCS bend is
excited the spectrum shown in Fig. 10 is obtained. From
previous characterizations of Ar/NH 3 expansions, the
observed resonances can be safely assigned to an OCS/
NH 3 complex. The assignment of the observed spectral
features at 982 and 1047 cm' 1 to the complex NH3-OCS
is definitive since a larger cluster cannot produce such
intense spectra. Figures 9 and 10 may be directly compared
and show that the beam depletion is a factor of IS greater
when exciting the NH3 umbrella motion than it is when
exciting the 2i/2 overtone in OCS. The transition at 982.10
cm ' 1 is observed to be photodissociative since it can be
detected with the B quadrupole field set to zero potential.
It should be noted that over 10% of the focused molecules
NH.0CS PH0TQ0ISS0CXAT10N SPECTRUM
876.
.8 8 0 ,
668.
680.
FREQUENCY (w*1)
FIG. 9. Focused beam infrared spectrum o f NH j-O CS seen upon
excitation o f the NHj *1 umbrella motion.
MS
W y C S PWOTOPISSOCIATION SPECTRUM
1040
1048
1090
1095
FREQUENCY tea1)
FIG. 10. Focused beam infrared spectrum o f Nllj-OCS. seen upon
excitation o f the OCS(2t'j) bend.
can be removed from the beam at 982.10 c m '1. This
observation cannot be explained by a single rovibrational
transition and suggests either a very dense spectrum or
sufficient homogeneous broadening to allow the simulta­
neous excitation of many rovibrational transitions. The
NH3 v2 band origin is estimated as 981.3(1.5) c m '1. In
addition to the peak at 982.10 cm"1, the spectrum in Fig.
9 shows another feature at 985.49 c m '1. The origin of
this feature is not understood.
n h » - n 2o
We have begun an investigation of the microwave
spectrum of NH3-N 20 . In these studies a 1% NH3, 85 %
N20 seeded Ar beam was expanded through a 25 n
nozzle. Spectra were obtained while monitoring the NH3+
mass spectral peak. Several transitions have been observed,
but arc presently unassigned due to the complicated
hyperfine structure and likely internal rotation.
Interest in the NH3-N 20 complex stems from the
observation that N20 and C0 2 are isoelectronic and
structurally similar. N20 and C 0 2 have the same mass
and nearly the same quadrupole moments and polarizabilities. Since N20 and CX>2 are so similar, one might
expect their complexes to be structurally alike. The weakly
bound complexes Ar-COj,40 and Ar-N 20 61 are, in fact,
very similar. Both are T-shaped and have nearly the same
van der Waals bond length and bending and stretching
force constants. However, there is evidence that the van
der Waals chemistry of N20 and C 0 2 can be different.
The two complexes COy-HF62 and N20 -H F 63 differ
structurally, though in both of these systems the HF unit
behaves as a Lewis acid. The structure and microwave
spectrum of NH3-CD 2 are well understood35; hence, it
would be interesting to study the NH3-N 20 system and
to compare the two complexes. Furthermore, if the struc­
tures of NH 3-C 0 2 and NH 3-N 20 are similar, it would
be instructive to examine the internal rotation in the two
complexes. NH3-C 0 2 is a nearly free rotor with a sixfold
J. Chem. Phys., Vol. 82. No. 6 .1 5 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2545
Fraser et al.: Weakly bound NHS complexes
barrier to internal rotation. NH 3-N 20 will possess a
threefold barrier which might quench the internal motion
more effectively.
Although these questions have not yet been addressed,
and the microwave spectrum is not fully analyzed, it was
decided to perform a preliminary investigation of the
infrared spectrum of NH 3-N 20 . In these experiments a
mixture of argon seeded with 1% ammonia and 9|%
nitrous oxide was expanded through a 7 5 11 nozzle. While
monitoring the NH3+ mass peak, and tuning the C 0 2
laser between 974 and 991 c m '1, both unfocused and
focused beam spectral searches were conducted. Since the
NH 3-N 20 microwave spectrum is not fully assigned,
double resonance searches were not attempted. The results
of the focused beam study are shown in Fig. 11. Although
the underlying rotational structure has not been resolved,
a crude estimate of the NH 3 v2 band origin can be given
as 980(2) cm-1. The photodissociation spectrum obtained
in the unfocused beam study is nearly identical to that
shown in Fig. 11.
CONCLUSION
Table III summarizes the band origins and, when
determined, the excited state lifetimes for the NH 3 com­
plexes studied. (NH3) 2 and Ar-NH 3 results are not in­
cluded in this table because of the likely spectral com­
plexity of both of these species. In our view this prevents
a complete interpretation of the infrared spectrum. Except
for the Ar-NH 3 transition, all of the observed infrared
absorptions fall in the narrow range of 975 to 990 cm"*.
The infrared absorption of Ar-NH 3 at 938.69 cm-1 shows
the uniqueness of this system. It has also been noted that
the observed infrared photodissociation of these complexes
placed an upper bound of 2 .8 kcal/mol on the van der
Waals bond dissociation energy D0. The difference in
frequency of free noninverting NH 3 (950,3 cm-1) from
TABLE III. Infrared band origins, linewidths, and lifetimes.
NHj-HOCH
NH j-CO j
NHj-OCS
NH j-N jO
H>
r
984.4(9) cm’ 1
987.1(2) cm -'
981.5(15) c m -'
980.(2) cm "'
150 MHz
0.45(20) c m -'
• •
T
1 ns
ps
8 -2 0
a
• • •
•••
the band origin of the complex is taken most simply to
be the difference between the binding energy D0 in the
ground v2 state (v = 0 ) and that in the excited state (v
= 1 ). In the cases where band origins are established this
difference is 30-37 cm-1. Do in all of these cases is
greater in the ground state than in the excited state. The
percentage change in binding energy is about 4% assuming
binding energies of 2.5 kcal/mol.
An important result of this study is the determination
of upper state lifetimes for NH3-HCCH and NH 3-C 0 2.
The lifetimes for these two complexes differ by almost
two orders of magnitude, although the van der Waals
stretching force constants for both of these systems are
similar.33,39 This similarity in the stretching force constants
and the observation that the v2 NH 3 vibration in these
species is virtually identical suggest that the strength of
the van der Waals interaction does not necessarily correlate
with the excited vibrational state lifetime. We may
speculate that the shorter lifetime of NH 3-C 0 2 is a
consequence of the 667 cm -1 bending vibration of C0 2
which is in the same symmetry class as v2 NH 3 in the
complex. For the NH3-HCCH complex all of the other
parallel vibrations are higher in energy than v2 NH3. The
range in lifetimes (linewidths) observed in the infrared
spectrum of (HFfe,31 (HCI^ ,® 4 and the present examples
suggests that a wide range of excited state lifetimes exists
in weakly bound complexes.
ACKNOWLEDGMENTS
INFRARED SPECTRUM OF NHftjO
178 r " i ------------------- 1------------------- 1--------- --------- r ”
-
•
ISO
125 -
-
to o -
-
78
•
•
80
-
•
28
0
-
•
t
•
070
080
1
-1 ------- ------- 1—
000
083
FREQUENCY tea*1)
FIG. I t . Infrared spectrum of a focused N H j-N jO beam.
We would like to thank Dr. Harry Radford for his
generous loan of the C 0 2 laser used in these studies. We
also thank Mr. David Wu for computational assistance,
Mr. Thomas Fisher for assistance in the microwave
studies, and Dr. Kevin Lehmann for useful discussions.
1A. Watanabe and H. L. Welsh, Phys. Rev. Leu. 13, 810 (1964).
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3397 (1965).
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1553 (1967).
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(1978).
J. Chem. Phys., Vol. 62. No. 6, 15 March 1985
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2546
Fraser or a/.: WooKly bound NH3 comploxes
15T. E. Cough, R. E. Miller, and G. Scolcs, J. Phys. Chem. 85, 4041
(1981).
“ J. Gcracdls, S. Sctiadi, S. Sloltc, and J. Reuss, Chem. Phys. Lett. 78,
277(1981).
17 M. A. Hofibaucr, K. Liu, C. F. Gicsc, and W. R. Gentry, J. Chem.
Phys. 78, 5567 (1983).
Ia M. P. Casassa, D. S. Bomsc, J. L. Beauchamp, and K. C. Janda, J.
Chem. Phys. 72, 6805 (1980); M. P. Casassa, D. S. Bomsc, and K. C.
Janda, ibid. 74, 5044 (1981).
17 M. A. Ilollbaucr, C. F. Gicsc, and W. R. Gentry, J. C'hcin. Phys. 7 9 ,'
192 (1983).
34 M. A. Hofibaucr, K. Liu, C. F. Gicsc, and W. R. Gentry, J. Phys.
Chem. 87, 2096 (1983).
11M. J. Howard, S. Burdcnslci, C. F. Gicsc, and W. R. Gentry, J. Chem.
Phys. 80, 4137 (1984).
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181 (1984).
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2623(1981).
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35 C. M. Western, M. P. Casassa, and K. C. Janda, J. Chem. Phys. 80,
4781 (1984).
34 J. M. Lisy, A. Tramcr, M. F. Vernon, and Y. T. Lee, J. Chem. Phys.
75,4733(1981).
37 M. F. Vernon, J. M. Lisy, H. S. Kwok, O. J. Kryjnovich, A. Tranter,
Y. R. Shcn, and Y. T. Lee, J. Phys. Chem. 85, 3327 (1981).
31M. F. Vernon, D. J. Kryjnovich, H. S. Kwok, J. M. Lisy, Y. R. Shcn,
and Y. T. Lee, J. Chem. Phys. 7 7 ,4 7 (1982).
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30G. E. Ewing, J. Chem. Phys. 71, 3143 (1979); 72, 2096 (1980).
31 A. S. Pine and W. J. Laffcrty, J. Chem. Phys. 78, 2154 (1983); A. S.
Pine, W. J. Laffcrty, and B. J. Howard, J. Chem. Phys. 81, 2939
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33 R. L. DeLeon and J. S. Mucntcr, J. Chem. Phys. 80, 6092 (1984).
33G. T. Fraser, K. R. Leopold, and W. Klemperer, J. Chem. Phys. 80,
1423 (1984).
34 G. T. Fraser, K. R. Leopold, D. D. Nelson, Jr., A. Tung, and W.
Klemperer, J. Chem. Phys. 80, 3073 (1984).
33 G. T. Fraser, K. R. Leopold, and W. Klemperer, J. Chem. Phys. 81,
2577 (1984).
36 K. Bowen, Ph.D. thesis, Harvard University, 1978.
17 The 10 K rotational temperature o f the van der Waals dimers is
suggested by previous microwave studies o f weakly bound complexes,
for example, in the complex HCN-COj3* we were able to observe a
radio frequency transition across the J “ 12, K - 4 asymmetry
doublet; these two levels have 470 G H z o f rotational energy.
33 K. R. Leopold, G. T. Fraser, and W. Klemperer, J. Chem. Phys. 80,
1039 (1984).
39J. A. Odutola, T. R. Dyke, B. J. Howard, and J. S. Muenter, J. Chem.
Phys. 70,4844 (1979).
40 A computer simulation of the infrared band for several hundred
combinations o f A/I, AB, and band origin assignments (assuming a
50 MHz laser lincwidth) shows that the probability of seeing a second
infrared transition, assuming that one has already been observed, is
40% if the transition line width is 50 MHz, 50% for 150 MHz, 90%
fo r'600 MHz, and 100% for 1350 MHz. Since we do not observe a
second resonance it seems reasonable to estimate the transition lincwidth
as ISO MHz.
41 M. J. Frisch, J. A. Pople, and J. E. Del Bene, J. Chcnt. Phys. 78,4063
(1983).
43 L. Frcdin and B. Nclandcr, Chem. Phys. 15, 473 (1976).
43 B. Jonsson and B. Nclandcr, Chem. Phys. 25, 263 (1977).
44 N. C. Baird, Int. J. Quantum Chcnt. 1 ,49 (1974).
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Righini, J. Chem. Phys. 74, 1211 (1981).
44 Z. Latajka and S. Schcincr, J. Chem. Phys. 81, 407 (1984).
47 P. Kollman, J. McKclvcy, A. Johansson, and S. Rolhcnbcrg. J. Am.
Chem. Soc. 97,955 (1975).
44 W. L. Jorgensen and M. Ibrahim, J. Am. Chcnt. Soc. 102, 3309
(1980).
47 H. Umcyama and K. Morokuma, J. Am. Chem. Soc. 99, 1316 (1977).
MP. A. Kollman and L. C. Allen, J. Am. Chcnt. Soc. 93, 4991 (1971).
31 W. C. Topp and L. C. Allen, J. Am. Chem. Soc. 96, 5291 (1974).
33 K. Ohta, Y. Yushioka, K. Morokuma, and K. Kitaura, Chem. Phys.
Lett. 101, 12 (1983).
33J. A. Pople, Faraday Discuss. Chem. Soc. 73, 7 (1982).
34 G. C. Pimentel, M. O. Bulanin, and M. Van Thiel, J. Client. Phys.
36,500(1962).
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34J. W. Reed and P. M. Harris, J. Chem. Phys. 35, 1730 (1961).
37 G. Hcrzbcrg, Infrared and Ruman Spectra o f Polyatomic Molecules
(Van Nostrand Rcinhold, New York, 1945).
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55, 2822 (1971).
37J. S. Wells, F. R. Peterson, and A. G. Maki, Appl. Opt. 18, 3567
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4095 (1979).
41C. H. Joyner, T. A. Dixon, F. A. Baiocchi, and W. Klemperer, J.
Chem. Phys. 75, 5285 (1981).
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Chem. Phys. 74, 6544 (1981).
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44 N. Ohashi and A. S. Pine, J. Chem. Phys. 81, 73 (1984).
I
J . Chem. Phys., Vol. 02, No. 6 . 1 5 March 1685
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CHAPTER 2
WEAKLY BOUND COMPLEXES OF HCK
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5*2
Rotational spectrum and stru ctu re of the com plex HCNC02a)
K. R. Leopold, G. T. Fraser, and W. Klemperer
Department o f Chemistry, Harvard University, Cambridge, Massachusetts 02138
(Received 21 September 1983; accepted 18 October 1983)
Radiofrequency and microwave rotational spectra of the complexes HCN C 0 2 and DCN C 0 2 have been
obtained using molecular beam electric resonance spectroscopy. The spectra are characteristic of prolate
asymmetric rotors. The spectroscopic constants obtained are
H
^ ) ] (mhz)
( a i e ) (MH*»
^
)
(MHz )
A j (kHz)
6k (kHz)
Pa <D>
eqQ? (MHz)
HCNC02
dcnco2
9817(86)
9750(650)
2044.056(10)
1929.53(24)
182.42(60)
162(4)
...
0.0070(6)
137(50)
229(32)
3.2279(29)
3.2067(32)
...
-4 .0 7 5 (1 4 )
These are shown to be consistent with a C2, structure in which the nitrogen of the HCN bonds to the carbon
of the C 0 2 with a weak bond length of 3.00 A. The HCN subunit subtends an average angle of 17.4 (2)' with
the line joining the centers of mass of the two submolecules, and the average bending vibrational amplitude of
the C 02 is 11(1)'. The difference between the average amplitudes of the in-plane and out-of-plane bending
vibrations of the HCN is less than 4*. The stretching force constant for the weak bond is 0.049 mdyn/A in
HCNCOj, and the induced dipole moment is 0.361 D.
INTRODUCTION
Over the past decade, high resolution rotational sp ec­
troscopy of hydrogen halide complexes has played a cen­
tral role in the study of weakly bound m olecular com ­
p lexes. These sim ple dipolar probes have been bonded
to a variety of sp ecies, ranging from inert gases and
sim ple inorganic m olecules, to moderately sized hydro­
carbons and the resulting structural and dynamical in­
formation has provided considerable insight into the
nature of weak inter m olecular forces. A numer of in­
vestigations have extended the se t of system s studied
to those containing the molecule hydrogen cyanide, which,
like the hydrogen halides, is also a dipolar probe having
an acidic proton bound to an electronegative group. Un­
like the hydrogen halides, however, HCN has not only
an acidic proton at one end, but a basic nitrogen atom
at the other end. Moreover, while the lowest unoccupied
m olecular orbital of HX is a* centered on the HX bond,
that of HCN is w* centered on the CN bond and has little
density on the hydrogen. One might expect that the extra
chem ical complexity built into the HCN system would
permit a variable and therefore interesting structural
chemistry for HCN com plexes to exist. A quick survey
of the known HCN com plexes, however, shows that in
• ’T h is w ork w as supported by the N ational Science Foundation.
J. Chem. Phys. 80(3), 1 Feb. 1984
m ost cases HCN behaves very much like HF (or HX)
in its weak bonding interactions. Recent studies of the
complexes of HF, HC1, and HCN with acetylene , 1-3
ethylene , 4-8 and cyclopropane 7-9 for example, have dem­
onstrated that a ll these van der Waals dimers have struc­
tures in which the HX or HCN hydrogen bonds to the tt
system or “bent bond’ of the hydrocarbon. Moreover,
in their com plexes with H 20 , both HF10 and HCN11 hydro­
gen bond to the oxygen. It would appear, at lea st super­
ficially, that in these sy stem s, the substitution of the
halogen by CN has little effect on the van der Waals in­
teractions in the com plexes. The basic nitrogen of the
HCN has been observed to be active with hydrogen
halides , 12,13 but clearly, in the wider variety of s y s ­
tem s mentioned above, it is the acidic proton which
dominates the van der Waals structural chem istry.
Since the electronic structures of HX and HCN differ
considerably, additional comparisons between HX and
HCN system s w ill be important in an attempt to under­
stand the relationship between the structure and prop­
erties of the complex, and the electronic structure and
physical-chem ical properties of the constituent sub­
m olecules.
A number of recent studies in our laboratory 14-17 have
been concerned with the structures of van der Waals
clusters of CO* and the isoelectronic m olecule N20 . 18,19
0021-9606/84/031039-08$02.10
© 1983 American Institute of Physics
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1039
1040
L e o p o ld , F ra se r, a n d K le m p e rer: S p e c tru m a n d s tru c tu re o f H C N C O j
Attempts to understand the binding in these system s have
left som e puzzling questions unanswered. The linear,
hydrogen bonded structures of C 02HF and C0 2HC1 for
instance, are difficult to reconcile with the nonlinear,
hydrogen bonded structure of N2OHF. Because C 0 2 and
NsO are so sim ilar, any explanation of their structures
based solely on lone pair or electrostatic arguments
would have to predict very sim ilar geom etries for these
sy stem s. An attempt to clarify this situation by study­
ing the complex of C0 2 with BF 3,16 a strong sim ple Lewis
acid whose interactions are presumably w ell understood,
has led to still further confusion. Both HF and BF 3 are
sim ple Lew is acids which accept electron density along
their axes of sym metry. Thus, given the linear struc­
ture of COjHF, C 0 2BF 3 would be expected to be a sym ­
m etric rotor in which the COz axis is coincident with the
symmetry axis of the BF3. Surprisingly, C 0 2BF 3 has
an asym m etric structure from which it can be concluded
that a sim ple argument based on analogy with HF is not
adequate to understand the binding in this system .
In a further attempt to study the interactions of COz
with sim ple Lew is acids, we have investigated the com ­
plex of C 0 2 with HCN. If HCN were to behave like HF,
its complex with C0 2 would also be expected to have a
linear, hydrogen bonded structure. We have obtained
the rotational spectrum of the HCNC02 van der Waals
m olecule using the m olecular beam electric resonance
technique and have found that this is not the case. In­
stead, HCNC02 has a T-shaped geometry in which the
HCN nitrogen binds to the carbon of C 0 2 and this is the
subject of the present paper.
EXPERIMENTAL
TABLE I. O bserved z e ro field tra n s itio n s of HCNCOj and
d c n c o 2.
J
*>
*0
F
J
Kp
*0
B
9
10
2
11
12
3
4
4
4
' 4
4
4
4
5
1
2
2
2
2
2
3
3
3
3
4
4
4
2
4
4
2
4
2
2
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
4
5
6
0
7
B
1
2
2
2
2
2
2
2
3
1
2
2
2
2
2
3
3
3
3
9
10
2
11
3
4
2
3
4
4
2
4
2
2
0
0
3
6
0
7
F
i'(.'VTffz)
HCNCOj
B
9
10
2
11
12
3
4
4
4
4
4
4
4
5
0
1
1
1
1
1
2
2
2
2
4
4
4
2
4
4
2
2
2
2
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
5
6
7
B
9
2
3
3
3
3
3
3
3
4
0
1
2
2
2
2
4
3
5
4
5
4
3
2
0
2
2
1
3
3
3
2
3
4
4
3
5
4
3
2
1
3
1
3
4
2
2
1.215(41
3.159(31
7.361(2)
1 0 .105(2)
15.730(21
31.373(5)
50.472(2)
151.613(3)
150.349(3)
150.409(3)
151.754(3)
151.051(3)
151.051(3)
151.051(3)
350. 001 (4)
4009(2)
01 6 4 .6 0 0 (0 )
0 1 6 4 .0 7 0 (1 0 )
01 6 5 .9 0 7 (1 0 )
0 1 6 6 .7 0 7 (7 )
0 1 6 7 .9 3 4 (0 )
12 221.912(7)
12 223. 265(9)
12 223.742(5)
12 225.043(5)
DCNCO;
9
10
2
11
3
4
1
2
4
4
2
4
2
2
0
0
6
7
1
&
2
3
1
2
2
2
3
1.932(2)
4.501 (4)
7.954(4)
9.632(4)
39. 743(4)
110.994(2)
7 7 10.0(10)
11 545(1)
J = 0 - 1 , 1 -2 , and 2 -3 transitions.
A beam of HCNC02 was produced by expanding a m ix­
ture of 1/2% HCN, 10% COj in argon through a 30 p
nozzle at room temperature. Stagnation p ressu res were
typically 20 psig. Radiofrequency and m icrowave spectra
w ere taken using the molecular beam electric resonance
technique with the spectrom eter operated in the flop-out
mode, and the m ass spectrom eter tuned to the parent
ion HCNC02 (or DCNCOP. Though m ost spectra were
obtained in this way, it was eventually discovered that
an increase in sign al-to-n oise of about a factor of 4
could be realized by monitoring the HCN* or DCN* m ass
peaks. HCN was purchased from Fumico, Inc . 20 and
DCN was produced by reaction of KCN with
D3P 0 4(85% in D 20 ).
Initial spectral searches w ere carried out at low
radiofrequencies. F ive resonances w ere found which
could be assigned to the K .t = 4, J = 8 , 9, 10, 11, and 12
asymmetry doublets, based on their characteristic ratios
expected for a prolate asym m etric rotor. Subsequent
searches yielded frequencies for the K = 2 , J = 2, 3, and
4 doublets. Prelim inary calculations showed the fre­
quencies and assignm ents to be consistent with a T shaped structure, and gave initial estim ates of B and
C. It is interesting to note that though the rotational
energy of the 124 lev els is 470 GHz, corresponding to a
temperature of 23 K, the 1249-1 2 4a transition could still
be observed.
Low resolution m icrowave searches located the K =0,
The latter two tran­
sition s were investigated at high resolution, each pro­
viding a consistent value of XM(N), the projection of the
nuclear quadrupole coupling constant of the l4N nucleus
along the a axis of the complex. The high resolution
data also provided accurate line centers, thus giving
(B + C )/2 and centrifugal distortion information. Deu­
terium isotopic substitution was used to confirm that the
structure was T shaped with the nitrogen atom pointed
toward the C0 2 carbon. Microwave transitions of
DCNCOa w ere observed using a broadened oscillator,
and no attempt was made to m easure xaa(N) or xM(-Dh
Once spectroscopic constants were known with suffi­
cient accuracy to predict the spectrum , attempts were
made to observe asymmetry doublets between lev els
with K .i = 1 or 3. In no instance have transitions involv­
ing odd K levels been observed, and, recalling that 160
is a sp inless nucleus, this is strongly suggestive of a
C tv structure for this complex.
Stark effect measurements to obtain the dipole m o­
ments of HCNC02 and DCNCOj, were performed on the 3 2
asym metry doublet where the nuclear quadrupole hyper­
fine structure vanishes.
RESULTS
The zero field transition frequencies for HCNC02 and
DCNC0 2 are given in Table I along with their a ssign ­
m ents, and a typical resonance is shown in F ig. 1. Hy­
perfine structure due to the ,4N nucleus was resolved in
J. Chem. Phys., Vol. 80, No. 3 ,1 February 1984
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L e o p o ld , F ra se r, a n d K le m p e rer: S p e c tru m a n d s tru c tu r e o f H C N C O j
SH
1041
be ignored, the final values of xaa and xM being chosen
as those obtained from fitting all the hyperfine data
simultaneously. Finally, using these values for xaa and
Xib and the fact that Xaa + Xbb + X« = °> we calculate that
X n - X e e - 89(150) kHz. Clearly, the asymmetry in the
quadrupole coupling constant for this system is too
sm a ll to be measured.
hcnco2
t20‘ 22l
- 4 Khz
The line centers obtained in the above analysis, to­
gether with the radiofrequency data were next fit to
Watson’s Hamiltonian for an asym metric rotor:
iams
H = [ ( ^ ) " A' j2] j2 + [A ~ ( ^ ) " A^ j2
I0.H5
MHz
+ [ ( ^ f £ ) “ 26jj2] ( j' " J' )
FIG. 1. The 2jo— tra n sitio n of HCNC02. T his is the average
of th ree scans using a 10 s tim e constant.
the 10i - 2o2, 202- 303, and
transitions of HCNC02.
The Oqq—Iqi transition was observed only at low resolu ­
tion, and due to poor sign al-to-n oise, no hyperfine
structure was resolved. The radiofrequency transitions
which are listed without reference to the F quantum
number are the three A F = 0 components of the stated
asymmetry doublets. Only for the J = 4, K = 2 doublet
were searches for the A F * 0 components conducted.
For the other doublets, only the AF = 0 components were
measured. Within the resolution of our spectrom eter,
these occur at the line center of the transition, so the
frequencies listed may be taken as hyperfine-free.
The data for HCNC02 were fit using a two step proce­
dure. F irst, for transitions with resolved hyperfine
structure, the frequencies were fit using the usual ex­
pression for the hyperfine energy:
nr w
0
-o* rj C (C + l)-J(J+l)-J(J+l)1
£ 1 ( 2 7 -1 ) 7 (2 /-1 )
J ’
( 1)
where C =F (F + 1) - J ( J + 1 ) - 1 ( 1 + 1), w ith F = I+ J , and
1 = 1 is the spin of the nitrogen nucleus. q} was evalu­
ated using the usual first order perturbation treatment ,21
from which values of X m = eQqaa, x bb = eQ qbb, and line
centers were obtained.
A few comments about the reported uncertainties are
appropriate here. The uncertainties quoted in Table II
represent two standard er ro rs. Of the 16 hyperfine
components treated in the first part of the analysis, the
residuals for 12 of these are within the estim ated exper­
imental uncertainty, while the remaining four calcu­
lated frequencies fall no m ore than 1 kHz outside the
quoted error lim its. If the K = 0 and K = 2 data are
treated separately, the values x 00 = - 4.068(14) MHz
and xw = 2.10(26) MHz are obtained for K = 0, and xaa
= -4.107(16) MHz and xt* = 2.00(6) MHz are obtained
for AT= 2 , and a ll frequencies are reproduced to within
the stated experimental error. We note that while the
values of xaa for K = 0 and K = 2 strictly fall within 95%
confidence lim its of each other, they do so only m ar­
ginally. Whether this is an artifact, or a bonefide
centrifugal distortion effect on xaa is not clear. If real,
the effect is obviously not well determined, and so w ill
- 5 k[J2(J2 - J2) + (J2 - J 2)J2] .
(2)
The form of Eq. (2) makes clear which of the spectro­
scopic constants are determinable from the available
data. (B + C)/2 and its distortion constant A j are deter­
mined from the transitions which change the total angu­
lar momentum of the molecule, i. e . , the O00- l 01, 1012(12, and 2M- 3 ro. From the second term in Eq. (2), it
i s clear that the rotational constant A is not well deter­
mined unless transitions involving changes in K .( can be
observed. As discussed below, this complex has C2v
sym metry and therefore only a-type transitions are pos­
sib le. A K . i = 1 transitions do not occur, and the weak
AK.i = 2 transitions which are possible for an asym ­
m etric rotor were not observed. Hence, A is poorly
determined. Since odd K lev els do not exist for this
complex, a direct measure of (B - C ) from the A' = 1
asym metry doublet is not possible. This situation
leaves both (B - C) and [A - (B + C)/2] to be deconvolved
from the frequencies of the K = 2 and if = 4 asymmetry
doublets, and thus introduces considerable correlation
between these constants. The deviation of the relative
positions of these K stacks from that computed for a
rigid rotor requires that 6 *. also be fit. Inspection of
Eq. (2) shows that AJK and A* are not determined from
the available data and so were set to zero. Since A is
large and poorly determined anyway, this does not in­
troduce any serious error. The rotational constants ob­
tained from a fit of (B + C )/2, (B - C )/2, [ A - ( B + 0 / 2 ] ,
A j and 6 * are given in Table II. (B + 0 / 2 and A} are
TABLE n. Spectroscopic constants of HCNC02 and DCNC02.
( £ = £ ) < M H z>
A j (kHz)
6jr(kHz>
P a(D)
e(]Q% (MHz)
HCNCOj
DCNCO;
9817(86)
9750(650)
2044.056(10)
1929.53(24)
182.42(60)
0.0070(6)
137(50)
3.2067(32)
- 4 .0 7 5 ( 1 4 )
J. Chem. Phys., Vol. 80, No. 3 ,1 February 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
162(4)
...
229(32)
3. 2279(29)
...
S'S*
L eo p o ld , F ra se r, a n d K lem p erer: S p e c tru m a n d s tru c tu re o f H C N C 0 2
1042
TABLE III. S tark effect data for the 32
doublet of HCNCOj and DCNCOj.
E (V/cm)
v(MHz)
ing analysis, we make the usual assumption that the in­
dividual subm olecules remain unchanged upon complexation, so that these are the only coordinates which must
be treated. In term s of these coordinates, the inertial
tensor in the coordinate system shown in Fig. 2 is given
by22
Af-AJ'
HCNC02
0
9.988(6)
9.988(6)
9.981(6)
39.981(24)
69.895(40)
50.472(2)
50.754(2)
51.592(10)
52.990(10)
54.854(6)
62.942(8)
1 -1
2 -2
3 -3
1 -1
1 -1
/..s J jS in 2? + /2sin2x ,
I„=MaRl.n. + /* cos2x + / t cos2y + / 1sin2ysin 2 <p, (4)
DCNCOj
0
4.995(3)
9.983(6)
39.925(24)
69.875(42)
39.743(4)
39.833(3)
40.106(3)
45.243(5)
54.881(5)
(3)
1 -1
1 -1
1 -1
1 -1
w ell determined from the K = 0 data, though it should be
em phasized that the quantities [A - (B + C )/2], (B - C ) / 2 ,
and &K, which are determined from the rf data, are cor­
related. These values of the spectroscopic constants
satisfactorily reproduce the observed spectra except for
the 1249- 1248 transition for which the calculated fre­
quency i s 20 kHz too low. This m ost likely a r ise s from
neglect of the 6 j term in the Hamiltonian. Since this
parameter is so poorly determined, the final values of
the spectroscopic constants chosen are those obtained
from a fit in which the 124 doublet frequency was omitted
and Sj was set to zero.
The dipole moment for HCNC02 was obtained by ob­
servation of the Stark effect on the 32 doublet, where the
nuclear hyperfine structure vanishes. The Stark effect
data for HCNC02 are given in Table ED. The observa­
tion of a number of Stark components is used to confirm
their assignm ents, but the best value of p is taken as
that obtained from the Af = 1 - 1 component at 69.895
V /cm . The data were treated using the usual expres­
sion 21 for the Stark energy for a two level system with
the coupling matrix element (322, AfI p ,l 3 2i, Af) evaluated
in an asym m etric rotor b asis. The dipole moment ob­
tained is also given in Table II.
The treatment of the data for DCNCOj is sim ilar to
that for HCNC02 except that, since no hyperfine struc­
ture was resolved, microwave line centers were not
known with sufficient accuracy to warrant the inclusion
of the A j term in Watson’s Hamiltonian. The resulting
rotational constants have correspondingly greater un­
certainty, but are still useful for the elucidation of
structure, as discussed in the next section. The rota­
tional constants obtained are also listed in Table n .
/ w = JW4fi 2.m. + /2+ /iS in 2y co s2 tp + It cos* y ,
(5)
I „ = / „ = - / i sin2y cos
( 6)
(fi
sin cp ,
l xt = I a = I t cosy sin y cos i p - l 2 cos x sin x ,
(7)
IKI= I f t = I l s in y cosy sin <p .
(8)
To begin the structural analysis, we might initially
want to make the simplifying assumption that cp = 0 ,
i. e . , that HCNC02 is a planar complex. The inertial
defect A = I CC- I aa —/(.j,, calculated from the rotational
constants in Table II, has the value 1 .9 amuA 2 which,
though somewhat large, is not unreasonable for an ap­
proximately planar complex. In the past, neglect of
vibrational averaging of the off diagonal inertial ten­
so r elem ents has often led to the m isleading representa­
tion of many system s in which the a axis of the complex
has been assumed to be rotated on the average a few de­
g rees from the z axis. Here this would result from
evaluating
at tp = Q and som e nonzero value of y
derived from xM (the observed projection of the 14N cou­
pling constant onto the a axis). Assuming that at equi­
librium, y = 0, proper attention to the vibrational aver­
aging shows, however, that J „ = / „ = 0 since (siny cosy)
= (sinx cos x) = 0. Hence, the average position of the a
axis is coincident with the z axis. The average angle
that the HCN subunit makes with the a axis is then deter­
mined directly from x„a< v*2 Xoa =
5XHcn<3cos 2y - l >
0
H ere, xHcn is the quadrupole coupling constant along the
HCN bond in free HCN which we have assumed to be un­
changed upon complexation.
The assumption that cp = 0, however, seem s almost
certain to be incorrect. The bending motions of the
HCN described by the angles <p andy may equivalently
be described by the in-plane and out-of-plane bending
angles
and £out, which are the projections of the angle
com
STRUCTURAL INTERPRETATION
The coordinates needed to describe the structure of
HCNC0 2 are shown in Fig. 2. R c.m, is the line joining
the centers of m ass of the two subm olecules, y is the
angle that the HCN subunit makes with the z axis (chosen
to be coincident with Rc.m.), x is the corresponding angle
for the C 02, and <p is the dihedral angle. In the follow -
)
cm
FIG. 2. Coordinate sy stem used to specify the stru c tu re of
HCNCOj.
J. Chem. Phys., Vol. 80, No. 3.1 February 1984
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L eo p o ld , F raser, a n d K lem p erer: S p e c tru m a n d s tru c tu r e o f H C N C O j
1043
and Itl = hi/8 v 2A , one computes that sin' 1[(sin 2x)1/2]
= 79(1)°.
Finally, if Eq. (4) is added to Eq. (5), term s involv­
ing the coordinate <p vanish. Thus, using the values of
(cos 2y> and (sin 2x) determined above, and Iib and l cc
computed from Table II, the value
=3.5923(18) A
is computed.
.(9 0 -X)
cmFIG. 3. R epresentation of the vibrationally averaged stru c tu re
of HCNCOj.
formed between the HCN axis and the a axis onto the X Z
and YZ planes, respectively, viz.
sin £,„= sin y cos <p/[cos2y + sin2y cos 2 <p]1/2 ,
( 10)
sin £ou, = sinysin<p/[cos2y + sin 2y s in 2 (p]1/2 .
( 11)
For an harmonic bender, we have
ri2
(12)
where
is the equilibrium value of | (reasonably a s ­
sumed to be zero for both £tn and | out). kb is the force
constant for the bending vibration, and / HCN is the m o­
ment of inertia of the HCN. This equation, if applied
to both the in - and out-of-plane bending vibrations of the
HCN shows that if (£2ut)2
the force constant for the
out-of-plane bend is essentially infinite compared with
that for the in-plane bend. While these two force con­
stants certainly cannot be identical, it seem s more rea­
sonable that they would be nearly equal than widely
disparate. Moreover, it is the difference between the
amplitudes of the in - and out-of-plane bending vibrations
which would give rise to asymmetry in the quadrupole
coupling constant. Thus, consistent with our inability
to observe any such asymmetry, it seem s more rea ­
sonable to envision the complex HCNC02 as shown in
Fig. 3. Here, the vibrational motions of the two sub­
units are represented by cones which describe their
average angular positions in the complex. With this
figure in mind, we can perform the vibrational averag­
ing over Eqs. (3)—(8). If we can assum e that the coor­
dinates y, x, and <p are uncoupled, so we may write
term s like (sin"y cos"^ ) as (sinny)(cosmcp), the inertial
tensor described by Eqs. (3)—(8) becom es diagonal since
(sin tp) —(c o s <p) = 0. The z axis, therefore, is again the
a axis of the complex, and the angle that the HCN rod
m akes with this axis is equal to y obtained from the ob­
served nuclear quadrupole coupling constant. Using the
value of xoa given in Table n , a value of 0.9102(17) is
obtained for (cos 2y>. If we proceed in the usual manner
and operationally define y as cos ' 1[(cos 2y)1/2], a value
of y = 17.4(2)° is obtained. The choice of the acute
angle w ill be discussed below.
To obtain the remaining coordinates x and Hc.m., we
note first that once (cos 2y> is known, (sin 2x) can be de­
rived from / „ using Eq. (3). With (cos 2y> = 0.9102(17)
The choice of the acute angle for y can be made by
examining the rotational constants for DCNC02. From
Eqs. (4) and (5), and the measured rotational constants,
the value of Hc.m. = 3.652(7) A is obtained for DCNC02.
In computing this value, (sin 2x> was taken as the
HCNC02 value (since A is better determined for the protonated form) and y was scaled with the rotational con­
stants of HCN and DCN using Eq. (12), v iz. yD= y HUHCN/
JDCN]1/4 = 1 6 .5°. These are sm all corrections and do not
introduce any seriou s error. Assuming the complex has
the HCN nitrogen bound to C02, the van der Waals bond
lengths are 2.996 and 2.998 A for HCNC02 and DCNC02,
respectively. If the complex were hydrogen bound, the
C-H weak bond distances computed from the rotational
constants would be 1.970 and 2.089 A for HCNC02 and
DCNC02, respectively, unambiguously establishing that
the nitrogen of HCN is bound to the C 02. Structural
constants for HCNC02 and DCNC02 are summarized in
Table IV.
Table IV also includes values of the induced dipole
moment and stretching force constant. The induced
dipole moments were computed using y = 17.4° for
HCNC02 and 16.5° for DCNC02. The stretching force
constant was obtained from the relation
32 TrHMA.n, )2 [B4 + C4]
h
A,
(13)
The asymmetry in the quadrupole coupling constant
has been shown to be too sm all to measure in this s y s ­
tem . The most sensitive indicator of this quantity in
the spectrum is the splitting between the AF = 0 compo­
nents of the asymmetry doublets. Since no splitting
could be observed between these transitions, the ob­
served line widths must be used to obtain lim its on its
magnitude. Assuming that a 3 kHz splitting in the 4224 23 transition could have been observed, calculations
show that - 0 .2 0 MHz<xt» -X 5e < + 0 '0 3 MHz. Using
Xbi-X cc = - ° - 2 MHz gives ?,a- ^ out<4° thus placing an
TABLE IV. D erived constants fo r HCNCO, and
DCNC02.
hcnco2
^B.B.
f^N-C (A)
3.5923(18)
2.998
dcnco2
3.652(7)
2.996
y Meg)
17.4(2)
16.5*
X Meg)
79(1)
79”
kt (mdyne/A)
0.049(4)
A p11(I(D>
0.361
• ••
0.362
•C alculated value. See the text for d iscussion.
’’A ssum ed.
J. Chem. Phys., Vol. 80, No. 3,1 February 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1044
L eo p o ld , F ra se r, a n d K lem p erer: S p e c tru m a n d s tr u c tu r e o f H C N C O j
upper lim it on the average difference between the in and out-of-plane bending vibrational amplitudes in this
system .
TABLE V. C om parison of s tru c tu ra l p a ra m e te rs of various
nitrogen bonded com plexes of HCN.
R
Finally, it is seen that the value of the induced dipole
moments for HCNCOj and DCNCOj obtained using y H
= cos‘ 1[<cos2y >]1/2 for HCNCOj and yD = y H[/HCH/ / DCN]1/4
are the sam e. Stated differently, the value of
cos *1[(cosy)] obtained from measurement of the dipole
moment of the complexes sca les roughly as expected for
sim ple harmonic oscillations about y„ = 0. Though in­
duced dipole moment is not always a reliable m easure
of angle, the internal consistency obtained here lends
further support to the physically reasonable assumption
of a planar, C2„ equilibrium geometry.
vd »
>HCN ,cleS '
* g ^mdynfe>'A^,
At* lart>Di
H C N -C O .*
3 .00
1 7.4
0 . 0 40
0 .3 0
HCN~HCNb
2 .2 3
17
0 .0 6 1 4
0 . 77
H C N -H B r'
2.16
2 .0 9
16.1
0 . 074
H C N -H C ld
17
0. 002
0.04
H C N -H F*
1.67
17
0 .14
1.1
•This w ork,
’’R eference 25.
•R eference 26.
‘’R eference 12.
•R eference 13.
’F o rc e constants fo r the lin e a r m olecules w ere recalculated
fro m o riginal data using the method of Ref. 30.
DISCUSSION
The weakly bound complex HCNCOj has been shown
to have a T-shaped structure in which the nitrogen of the
HCN bonds to the carbon of the C02. One of the most
interesting asp ects of this observation a r ise s from a
comparison with the complex COjHF. Unlike HCNCOj,
COjHF has a linearly hydrogen bonded structure . 15
Though this structure lias in itself been a source of great
puzzlement, a comparison of the structures of a number
o f HF and HCN com plexes would suggest that COjHCN
would also have a linearly hydrogen bonded structure in
which the HCN proton bonds to the oxygen of C02. For
example, the complexes of HF and HCN with acetylene,
ethylene, and cyclopropane 1-9 have recently been shown
to be hydrogen bonded sp ecies in which the acidic proton
of the HF and HCN bonds to the ir electron density of
HCCH and H2CCH2 or to the electron rich “bent bond” of
cyclopropane. H2OHF, which has been the subject of
much investigation, has a structure in which the HF
hydrogen bonds to the water. The complex was orig i­
nally described as having a "planar or effectively
planar” structure , 10 though subsequent work on its ex­
cited vibrational states 23 has shown the equilibrium
structure to be nonplanar. A recent preliminary report
on the rotational spectrum of H2OHCNu has shown the
HCN to be hydrogen bonded to the oxygen and has de­
scribed the structure of this complex, too, to be planar
or effectively planar. With HC1, on the other hand,
neither HF24 nor HCN12 form s hydrogen bonds. Although
the equilibrium structures for HFHC1 and HCNHC1 are
probably different, the atomic ordering in these com ­
p lexes is the sam e. Thus, it appears that [with the
exception of (HF)2, (HCN)2i and HCNHF, which for the
purposes of this comparison are trivial cases] HF and
HCN are quite sim ilar in their weak bonding interac­
tions. It would, therefore, seem reasonable to expect
C 02HF and COjHCN to have sim ilar structures, making
the T-shaped geometry of HCNC02 particularly in terest­
ing. The HF and HCN com plexes with C 0 2 com prise the
first example in which these two sp ecies behave qualita­
tively differently toward a common binding partner.
The complex HCNCOj may be compared with other
com plexes in which HCN is nitrogen bonded, and this is
done in Table V. HCNCOj appears to be the first ex ­
ample in which the HCN nitrogen form s a weak bond to
anything but hydrogen. We see from the table, that as
judged from the stretching force constants, the hydrogen
bonded com plexes form stronger bonds. It is quite r e ­
markable that while the stretching force constants in
this se r ie s vary by about a factor of 3, the average
bending angle of the HCN subunit rem ains essentially
constant. Thus, we see that whether the HCN is bend­
ing against a C 0 2 m olecule or a hydrogen bonding acid,
it undergoes very sim ilar angular motions. Interest­
ingly, a s previously noted by Aldrich e t a l . , 3 a com ­
parison of a number of hydrogen bound HCN complexes
shows a sim ilar constancy of HCN bending angle, this
angle being 12.4°, 12.8°, 12.4°, 10.2°, and 11.2° for
the HCCH, H2CCH2, cyclopropane, H20 , and HCN com ­
plexes, respectively. The sm all 1° variation in bending
angle for the nitrogen bound com plexes corresponds to
a variation in bending force constant of only about a fac­
tor of 1 .3 . We see, therefore, that for nitrogen bound
HCN, the angular portion of the potential is much le ss
sensitive to the nature of the binding partner than is the
radial part.
In the previous section it was remarked that only if
the difference between the in - and out-of-plane bending
vibrational amplitudes were greater than about 4° could
asym m etry in the quadrupole coupling constant be ob­
served. A s seen in Table V however, this is greater
than the average deviation in the HCN angle among dif­
ferent system s. It is therefore reasonable that the in
and out of plane bending vibrations of HCNC0 2 would
also differ from one another by le s s than 4°, so the unobservably sm all asymmetry in the quadrupole coupling
constant is not unexpected.
The nitrogen-carbon bond length in HCNC0 2 is dif­
ficult to compare directly with the other distances given
in Table V since these are bond lengths to hydrogen. In
order to facilitate the comparison, we can compare the
bond lengths of C 0 2, HCN, HBr, HC1, and HF with a
second common binding partner, namely argon. The
data are shown in Table VI. ArHCN has been put in
parenthesis, since this system has been shown to have
an unexpectedly short bond length for a linear hydrogen
bonded system . We see, however, that for the other
m em bers of this se r ie s, the bond shortening in the HCN
com plex relative to the argon complex parallels the
stretching force constant of the HCN complex.
J . C h e m . P h y s ., V o l. 8 0 , N o . 3 , 1 F e b r u a r y 1 9 8 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
L e o p o ld , F ra se r, a n d K le m p e rer: S p e c tru m a n d s tr u c tu r e o f H C N C 0 2
1045
TABLE VI. C om parison of bond lengths and fo rce constants f o r argon and HCN com plexes.
Ryuw (A)
k, (mdyne/A)
Synw
ft,(mdyne/A)
3.49
0.0174
0 .49
(2.72)
...
(0.49)
ARvcw
HCNC02*
3.00
0.049
A rC 0 2*
HCNHCN"
2.23
0.081
(ArHCN)*
HCNHBr*
2.16
0.074
ArHBr*
2.73
0.0076
0.57
HCNHCl"
2.09
0.092
ArHCl*
2.73
0.0117
0.64
HCNHF*
1.8 7
0.14
A rH FJ
2.63
0.0142
0.76
•T his w ork.
•R eference 25.
“R eference 26.
‘•Reference 12.
•R eference 13.
'R e fere n ce 14.
*Reference 27.
•'Reference 28.
'R e fere n ce 29.
*Reference 30.
While the structure of HCNC02 is surprising for the
reasons discussed above, it is also sensible when com­
pared with several other van der Waals com plexes in
which C 0 2 binds to sim ple Lewis b ases. Table VII lis ts
som e of the structural param eters for four such com­
plexes, all of which are T-shaped with the basic atom
bonded to the C 0 2 carbon. It is possible to rationalize
the structures of these com plexes in term s of the usual
HOMO-LUMO model. The lowest unoccupied molecular
orbital of C0 2 is v* and one may imagine these com­
p lexes as forming through donation of electron density
from the basic donor into this orbital. We see that, as
judged by the force constant and induced dipole moment,
H3N C 0 2 appears to be a more strongly bound complex
than HCNC02. This is in agreement with intuitive pre­
diction, since NH3 is generally more basic than HCN.
M oreover, as judged by k „ H20 appears of comparable
basicity to NH3, and argon, of course, is the weakest
base of all. It is noteworthy, here, that the weak bond
lengths for HjNCOj and HCNC02 are nearly identical.
From a donor-acceptor viewpoint, a shorter bond length
would have been expected for the complex which shows
the stronger force constant and larger induced dipole
moment, and we may take this as an indication that the
important interactions in these complexes are probably
m ore complicated than suggested by a simple HOMOLUMO model. Indeed the failure of orbital pictures in
reconciling the structures of C 02HF andN 2OHF, while
correctly predicting qualitative structure, and even
som e of the quantitative trends in Table VII, ra ises
TABLE VII. C om parison of C 02 com plexes with sim ple
Lew is b a se s.
fivnw 1^1
A p „ d (D)
k , (mdyne/A)
h 3n c o 2*
3 .0 0
0.41
0.066
h c n c o 2b
3 .0 0
0.36
0.049
h 2o c o 2*
2.84
> 0.175
0.064
A rC 0 2d
3 .4 9
0.068
0.017
•R eference 31.
•This w ork.
•R eference 17.
“•Reference 14.
questions about how, when, and to what extent the
HOMO-LUMO picture of weak intermolecular interac­
tions can be applied. Nonetheless, this picture has been
the m ost su ccessfu l one so far, and has provided a u se­
ful language in which to d iscu ss a wide variety of com­
plexes. We thus guardedly interpret the structure of
HCNC02 in these term s.
•w . H. Read and W. H. F ly g are, J . Chem . Phys. 78, 2238
(1982).
2A. C. Legon, P . D. A ldrich, and W. H. F ly g are, J . Chem.
Phys. 76, 625 (1981).
3P . D. A ldrich, S. G . Kukolich, and E. J . Cam pbell, J . Chem.
P h y s . 78, 3521 (1983).
4J . A. Shea and W. H. F ly g a re , J . Chem. Phys. 76, 4857
(1982).
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Phys. 75, 2126 (1981).
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Phys. 78, 3552 (1983).
tL . W. Buxton, P . D. A ldrich, J . A. Shea, A. C. Legon, and
W. H. F ly g a re, J . Chem . Phys. 75, 2681 (1981).
"A. C. Legon, P . D. A ldrich, and W. H. F ly g are, J . Am.
Chem. Soc. 104, 1486 (1982).
9S. G . Kukolich, J . Chem. P hys. 78, 4832 (1983).
•°«J. W. Be van, Z . K isie l, A. C. Legon, D. J . M illen, and S.
C. R o g e rs, P ro c . R. Soc. London S e r. A 372, 441 (1980).
mA. J . F ille ry -T ra v is , A. C. Legon, and L . C. Willoughby,
Chem. P hys. L ett. 98, 369 (1983).
12A . C. L'egon, E . J . Cam pbell and W. H. F ly g are, J . Chem.
Phys. 76, 2267 (1982).
“ A. C. Legon, D. J . M illen, and S. C. R ogers, P ro c . R. Soc.
London S e r. A 370, 213 (1980).
14J . M. Steed, T . A. Dixon, andW . K lem p erer, J . Chem . Phys.
70, 4095 (1979).
15F . A. B aiocchi, T . A. Dixon, C. H. Jo y n er, and W. Klem ­
p e re r , J . Chem . Phys. 74, 6544 (1981).
16K. R. Leopold, G . T . F r a s e r , and W. K le m p e rer, J . Am.
Chem . Soc. (to be published).
I2K. I. P e te rs o n and W. K le m p e rer, J . Chem . P h y s . (to be
published).
,SC .H . Jo y n e r, T . A. Dixon, F . A. B aiocchi, andW . Klem ­
p e re r, J . Chem . Phys. 74, 6550 (1981).
1SC. H. Jo y n e r, T . A. Dixon, F . A. B aiocchi, and W. Klem ­
p e re r, J . Chem . P hys. 75, 5285 (1981).
20Fum ico C orporation, A m a rillo , T exas.
21C. H. Townes and A. L . Schalow, Microwave Spectroscopy
(Dover, New Y ork, 1975).
22F . A. B aiocchi, P h .D . th e s is , H arvard U niversity, C am -
J . C h e m . P h y s., V o l. 8 0 , N o . 3 , 1 F e b r u a r y 1 9 8 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1046
L e o p o ld , F ra se r, a n d K lem p erer: S p e c tru m a n d s tru c tu re o f H C N C O j
b rid g e, M a s s ., 1982.
a Z . K isie l, A. C. Legon, and D. J . M illen, P ro c . R. Soo.
London S e r. A 381, 419 (1982).
y K. C. Janda, J . M. Steed, S. E . Novlck, and W. K lem p erer,
J . Chem. P hys. 87, 5162 (1977).
25L . W. Buxton, E . J . C am pbell, and W. H. F ly g a re , Chem.
Phys. 88, 399 (1981).
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Phys. 78, 3494 (1983).
J,K. R . Leopold, G . T . F r a s e r , and W. K le m p e rer (manu­
sc rip t in preparation).
fflM. R. Kennan, E . J . C am pbell, T . J . B a lle , L . W. Buxton,
T . K. Minton, P . D. Soper, and W. H. F ly g are, J . Chem.
Phys. 72, 3070 (1980).
»S . E . Novick, P . D avies, S. J . H a rris , and W. K lem perer,
J . Chem. Phys. 59, 2273 (1973).
30T . A. Dixon, C. H . Jo y n e r, F . A. B aiocchi, and W. Klem ­
p e re r, J . Chem . Phys. 74, 6539 (1981).
51G . T . F r a s e r , K. R. Leopold, and W. K lem perer (m anuscript
in p re p ara tio n ). .
J. Chem. Phys., Vol. 80, No. 3,1 February 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IcO
M icrowave an d radiofrequency Stark sp ectru m of ArHCN: A highly
nonrigid m oleculea)
K. R. Leopold,1” G. T. Fraser, F. J. Lin, D. D. Nelson, Jr., and W. Klemperer
Department o f Chemistry, Harvard University, Cambridge, Massachusetts 02138
(Received 22 June 1984; accepted 14 August 1984)
The rotational spectrum of the weakly bound complex ArHCN has been observed using
molecular beam electric resonance spectroscopy. The spectrum is superficially characteristic of
that of a linear molecule with both unusually large centrifugal distortion (requiring a J 6 dependent
distortion term to fit the data) and an unexpectedly large bending amplitude. The spectroscopic
constants are
ArH
ArH
ArH
ArD
ArD
ArD
,2C
l3C
,2C
,2C
l3C
l2C
,4N
l4N
”N
l4N
,4N
l3N
B (MHz)
D j (kHz)
H j (Hz)
<90™ (MHz)
#»(D)
1609.832(6)
1583.714(8)
1556.996(6)
1574.794(2)
1551.971(6)
1525.19(3)
172.3(6)
152.(2)
158.0(6)
101.8(3)
92.7(20)
90.5(10)
323(18)
244(26)
311(14)
152(20)
118(16)
118(8)
-2.856(18)
-2.878(47)
...
- 3.160(14)
...
2.6254(2)
2.6394(11)
2.6542(4)
2.7495(10)
The centrifugal distortion constant D j is remarkably large and abnormally sensitive to isotopic
substitution. Using the usual model, the stretching and bending force constants obtained from
these data are an order of magnitude smaller than those similarly computed for the hydrogen
halide complexes of argon. The calculated stretching and bending frequencies are 10 cm- ',
predicting that excited vibrational levels should be populated in the beam. Three transitions have
been observed which appear to correspond to an excited vibrational level of ArDCN, but poor
signal-to-noise has prohibited their unambiguous assignment. While seemingly, the data support
a hydrogen bonded structure for this complex, they require an anomalously short bond length of
2.7 A, despite the apparent weakness of the bond. The vibrationally averaged molecular geometry
and force constants are seen to be unexpectedly sensitive to isotopic substitution. Our conclusion
is that the observed behavior of this system is best interpreted in terms of strong coupling between
the radial and angular degrees of freedom associated with the weak bond. The amplitude of
oscillation in the two coordinates is large, making the “structure” of this complex nebulous.
INTRODUCTION
Binary van der Waals complexes containing argon are
in principle the simplest systems in which to study the nature
of weak intermolecular forces. Detailed spectroscopic stud­
ies of such systems have provided much information about
the geometry and internal dynamics of a variety of weakly
bound dimers. Moreover, because argon is a virtually struc­
tureless probe, we have regarded its complexes with other
molecules as useful references with which to compare more
complicated systems. Recently, a large number of papers
have appeared characterizing the van der Waals interactions
of HCN with a variety of substances including hydrogen
halides, 1-3 hydrocarbons,4-6 H20 ,7 and COz .8 Invariably,
HCN has been seen to form bonds along its axis either by
formation of a linear hydrogen bond, or by use of the lone
pair of electrons on the nitrogen atom. In no instance has a
complex been observed in which the rr* orbitals are involved.
This observation is particularly interesting in light of the
known T-shaped structures of the isoelectronic complex
ArHCCH9 and the isovalent complex ArClCN. 10 By ana•'Supponed by the National Science Foundation.
Present address: National Bureau of Standards, Boulder, Colorado 80302.
4922
J. Chem. Phys. 81 (11), 1 December 1984
logy with these systems, it might be expected that ArHCN
would also be a T-shaped complex, thus providing an exam­
ple of a system in which the n* orbitals of HCN are active. A
different conclusion is reached, however, by comparison of
complexes of HCN with those of the hydrogen halides. It has
been previously noted that HCN and HX frequently behave
quite similarly in their van der Waals interactions. Hence, by
analogy with the known linearly hydrogen bonded struc­
tures of the ArHX complexes, a linear hydrogen bound
structure for ArHCN would be anticipated.
Some insight into this problem has already been pro­
vided in a recent publication by Campbell, Buxton, and Le­
gon in which the microwave spectrum of the closely related
complex KrHCN was reported. 11 An intense spectrum char­
acteristic of a linear molecule was observed and the rota­
tional constants obtained for the isotopically substituted spe­
cies H ,2C 14N, H ,2C I5N, and D 12C I4N were regarded as
consistent with a hydrogen bonded structure. Though qual­
itatively the KrHCN spectrum is quite simple, examination
of the spectroscopic constants obtained reveals some
remarkable peculiarities. Most pronounced is the unusually
large centrifugal distortion which was observed. The linear
molecule distortion constant D j obtained for KrHCN was
0021-9606/84/234922-10$02.10
© 1984 American Institute of Physics
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Leopold etal. : Stark spectrum of ArHCN
TABLE I. Observed zero field transitions of ArHCN.
v(MHz)
J
F
TABLE 1 [continued).
J'
F'
ArH l2C "N
3 219.126(5)
3 220.405(10)
6433.184(10)
6433.946(5)
6 435.306(12)
9 639.948(15)
9 640.731(10)
9 640.901(10)
9 642.162(12)
12 835.630(15)
12 836.613(30)
12 837.830(10)
16 018.4(10)
19 184.1(18)
22 332.9(10)
•0
0
1
1
1
2
2
2
2
3
3
3
4
5
6
...
1
1
2
2
2
3
3
3
3
4
4
4
5
6
7
v(MHz)
J
F,‘
J'
F{
0
0
0
1
2
2
2
3
4
5
6
1
1
1
...
1
3
2
1
1
1
2
3
3
3
4
5
6
7
2
2
0
...
2
4
2
1
1
0
2
1
3
1
3
2
4
4
3
2
0
1
3
1
3
2
4
2
4
5
3
•
...
ArD l2C l4N
3 149.330(I0)b
3 149.360(7)c
3 150.761(4)**
6296.42(80)
9437.847(9)
9 438.034(5)
9 439.432(10)
12573.0(15)
15 700.0(12)
18 817.0(20)
21922.6(30)
ArD n C “ N
9 141.50(20)
12 178.95(20)
15 208.80(25)
18229.5(15)
24240.8(10)
2
3
4
5
7
3
4
5
6
8
6205.1(5)
9 301.9(10)
12 392.64(50)
15475.63(50)
18 549.0(15)
21 612.6(10).
24664.9(10)
1
2
3
4
5
6
7
2
3
4
5
6
7
8
v(MHz)
J
A rD ,5C ,4N
F
J'
ArH ,JC l3N
3113.372(7)
6222.986(10)
9 325.378(15)
12416.714(10)
15496.856(12)
0
1
2
3
4
1
2
3
4
5
F'
ArH ” C ,4N
3 166.965(15)
3 168.260(6)
9485.6(10)
12 632.15(13)
15 765.5(13)
21 988.0(10)
25075.4(15)
0
0
2
3
4
6
7
1
1
3
4
5
7
8
2
3
4
3
4
5
2
0
m /e = 69'
9 537(4)
12706.75(220)
15 871.25(125)
*F, = J + 1W;F = F, + Ic .
bF ' = y
' F ' = 2.
* F '= 1.
'Weak, unassigned transitions observed at m /e — 69 from an ArD l2C MN
beam. These lines are fit with an effective rotational constant and distortion
constant B — 1590.6(3) MHz and Dj = 70(7) kHz.
over a factor of 2 greater than that for KrHCl and the inclu­
sion of a J 6 distortion term in the Hamiltonian was neces­
sary. Furthermore, the unexpectedly large D j observed was
found to be extremely sensitive to isotopic substitution, de­
creasing by a factor of 1.7 upon deuteration of KrH 12C l4N.
The unusual behavior of this system clearly calls for addi­
tional work on rare gas-HCN complexes.
We have undertaken a study of the complex of ArHCN
using the molecular beam electric resonance technique and
have determined the spectroscopic constants for the com­
plexes of six isotopically substituted forms of HCN. Like
that of its krypton analog, the rotational spectrum of
ArHCN can be fit to a Hamiltonian appropriate for a linear
molecule with large J 4 and J 6 distortion terms. The general
features of the ArHCN spectrum are found to be the same as
those observed for the KrHCN system, but the peculiarities
are even more striking. The value ofD j obtained for ArHCN
is a full order of magnitude greater than that of ArHCl, and
its value, like that for KrHCN, also decreases by a factor of
1.7 upon deuteration. Moreover, attempts to interpret the
spectroscopic constants by usual methods lead to results
which are dramatically inconsistent with expectations based
on present knowledge about other weakly bound complexes.
The hydrogen bond length, e.g., appears to be roughly 0.3 A
shorter than expected by comparison of a number of HF and
HCN complexes, yet the weak bond stretching force con­
stant, obtained by assuming separability of the parallel and
perpendicular vibrations, is an order of magnitude less than
that similarly computed for other van der Waals systems. In
addition, the structural parameters derived from the spec­
troscopic constants show an unusually strong isotopic de­
pendence. We conclude that this behavior is best interpreted
in terms of strong coupling between the radial and angular
degrees of freedom associated with the weak bond. It is inter­
esting to note that work on this system was originally begun
with the intent of resolving the question discussed above of
whether ArHCN has a linear or a T-shaped geometry. Ironi-
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42-
Leopold eta t: Stark spectrum of ArHCN
4924
ArH C N
J '2 — 3
FIG. 1. T hey = 2-3 transition
of ArH l2C l4N at low resolu­
tion. This spectrum is a single
sweep using a 10 s time con­
stant, but was readily observ­
able without phase sensitive de­
tection.
9650
9630
M Hz
cally, as will be shown below, the strong coupling between
the wide amplitude radial and angular motions in this sys­
tem makes the definition of “the structure” of the complex
nebulous and the quantitative interpretation of the spectro­
scopic data presents a formidable theoretical problem.
EXPERIMENTAL
A beam of ArHCN was produced by expanding a mix­
ture of 1/2% HCN in argon at 3 atm behind a 25 ft nozzle at
room temperature. Rotational spectra were obtained using
the molecular beam electric resonance technique with the
spectrometer operated in the flop-out mode and with the
mass spectrometer tuned to the parent ion (ArHCN+ or its
isotopic variants).
Extremely intense transitions were observed, many of
which could be seen without phase sensitive detection. With
the exception of three unassigned transitions observed while
monitoring m /e = 69, the spectra for all isotopic species
studied were characteristic of a linear molecule, though, as
discussed in detail below, the values of the spectroscopic
constants obtained were quite unexpected. For all isotopically substituted species studied, K = 0, \AJ | = 1 transitions
were observed at zero electric field. For all MN containing
species with the exception of ArD l3C I4 N, nitrogen hyperfine structure was resolved in at least one J —J + 1 transi­
tion, providing a value of eqQa„, the projection of the nuclear
quadrupole coupling constant onto the n-inertial axis of the
complex. Other transitions were observed at low resolution
using an oscillator broadened with white noise.
The dipole moment component along the a axis of the
complexes was measured by examining the Stark effect of
th e7 = 0-1 transitions. For ArH l2C ''’N and ArH l2C l5N,
the dipole moment was also measured by observation of the
J = 1, M j = 0 — ± 1 transition at nonzero electric field.
The assignment of the K = 0 spectra is unambiguous
since the J = 0-1 transitions were observed and fit smoothly
into the series formed by the higher J transitions. Further
support comes from the nonzero electric field measurements
which show the characteristic second order Stark effect. In
addition, for isotopes in which nitrogen hyperfine structure
was resolved in more than one microwave transition, the
“effective” quadrupole coupling constant eqQ [3K2/
J(J + 1) — 1] was found to be independent of J.
For ArH l2C MN, zero field radiofrequency searches
between 3 and 100 MHz were performed in an effort to ob­
serve transitions involving levels with K ^ 0 . A number of
microwave searches for such transitions were also conduct­
ed, but in no instance were K ^ 0 transitions seen. In con­
trast, however, as noted above, while monitoring the parent
mass peak of ArD 12C 14N three microwave transitions
(/ = 2-3,3-4,4-5) were observed which cannot be assigned
to K = 0 ArDCN and are presumably due to an excited vi­
brational state of this complex. These transition frequencies
are given at the end of Table I under m /e = 69. Poor signal
to noise has presently precluded high resolution study of
these three transitions. It is noteworthy that this is in accord
with the observations of Campbell et al. who were also un­
successful in their efforts to observe AT# 0 levels of the close­
ly related complex KrH ,2C ,4 N."
RESULTS
Table I lists the observed zero-field transitions for the
six isotopically substituted forms of ArHCN studied. Figure
1 shows th e / = 2-3 transition of ArH I2C l4N at low resolu­
tion. The large signal to noise obtained was typical while
studying this molecule and is taken as an indication that
substantial quantities of the complex are formed in the adia­
batic expansion.
The spectral data were fit using the Hamiltonian
(1)
H = H0 + H q
with
H 0= B 3 2- D
j J*
+ H jJ6
and
TABLE II. Spectroscopic constants for isotopically substituted forms of ArHCN.
21(MHz)
D j (kHz)
H j (Hz)
(MHz)
ArH ,JC ,4N
1609.832(6)
172.3(6)
323(18)
-2.856(18)
ArH l3C ,4N
ArH l5C l3N
1583.714(8)
1556.996(6)
152(2)
158.0(6)
244(26)
311(14)
-2.878(47)
***
ArD ,JC ,4N
ArD ,3C l4N
ArD l2C l!N
1574.794(2)
1551.971(56)
1525.19(3)
101.8(3)
92.7(20)
90.5(10)
152(20)
118(16)
118(8)
-3.160(14)
...
a (D)-
2.6254(2)
2.6270(11”
2.6394(11)
2.6542(4)
2.6563(4)b
2.7495(10)
...
*Unless otherwise noted, dipole moments are obtained from the J = 0—1 transition.
bDetermined from the J = 1, A J = 0, AM j — ± 1 transition.
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2 )
63
Leopold etal. : Stark spectrum of ArHCN
He =
- eqQa
2 /(2 7 - 1)(2J - \ ) ( 2 J 4- 3)
(3)
where C = F ( F + l ) - / ( / +
1),F = I + J, and
/ = 1 is the spin of the l4N nucleus. H Q was first used to fit
the hyperfine frequencies in transitions with resolved hyperfine structure, yielding eqQaa and hyperfine free line centers.
For the 7 = 0-1 transitions ArD l2C l4N, where hyperfine
structure due to the deuterium was resolved, the deuterium
quadrupole Hamiltonian analogous to Eq. (3) was included
and treated by first order perturbation theory.
The high resolution line centers obtained in this way
were fit together with the assigned low resolution data, pro­
viding values for B, D j, and 77,. The need to include an 77,
4925
term in H0 was evident, as, e.g., it accounted for as much as 6
MHz in th e / = 7-8 transition of ArH nC l4N. The spectro­
scopic constants obtained are given in Table II.
Table III gives transition frequencies measured at non­
zero electric field. These were analyzed by including the
Stark Hamiltonian
Hs = 77 —jx • E
in Eq. (1). 773 was set up in MF blocks including levels off
diagonal in J by three and diagonalized to yield energies and
thus frequencies. The dipole moment was obtained by an
iterative procedure until the best fit to the data could be
obtained and the results are also listed in Table II. For
ArH ,2C 14N and ArH 12C 15N the dipole moment was mea­
sured for both the J —0-1 transition, and the J — 1, AMj
= + 1 transition and, as seen in the table, slightly different
TABLE III. Nonzero electric field data for isotopically substituted forms of ArHCN.
E (V/cm)
v(MHz)
J
F
3219.126(5)
3220.405(10)'
3264.528(9)
3265.362(3)
3608.825(65)
3609.455(65)
8.884(20)
9.761(4)
10.156(2)
10.554(9)
11.012(14)
14.142(2)
14.580(3)
38.866(4)
39.707(3)
40.135(4)
40.972(2)
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
2
2
2
2
2
0
3266.965(15)
3168.260(6)
3244.170(15)
3243.346(40)
0
0
0
0
1
1
1
1
3113.372(7)
3174.378(10)
3192.271(10)
42.358(10)
163.405(50)
0
0
0
1
1
3150.761(4)
3162.784(5)“
3162.742(7)b
3201.050(15)*
3201.01 l(5)b
0
0
0
0
0
Mj
J'
F'
M ’f
M 'j
0,±1
0,±1
0, + l
0, ± 1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
0
2
2
1
1
1
2
1
2
2
1
1
±1
0
± 1
0
0
0
1
0
1
2
1
0
2
1
1
0
J
0
±1
+1
+1
±1
±1
±1
±1
±1
±1
±1
+1
...
...
0, ± 1
o, ± 1
...
0
0
1
1
1
1
2
0
0
2
...
0
1
0
0
0
0
0
0
1
1
1
1
1
...
0
0
0
0
1
1
1
1
1
ArH 1JC l4N
0
399.586
399.586
1201.877
1201.877
249.570
249.557
249.574
249.568
249.526
299.489
299.471
499.125
499.110
499.102
499.125
ArH l3C l4N
0
0
511.800
511.7
ArH IJC ,3N
0
499.213
511.723
499.12
998.30
0
0
±1
±1
ArD IJC l4N
0
199.62
399.24
1
1
1
1
1
0,±1
0,±1
0, ± 1
0,±1 I
(4)
0
0
0
0
0
...
0
0
0
0
0
0
0
0
M f?= ±1.
bM?=0.
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Leopold et at.: Stark spectrum ot ArHCN
4926
K
Ar
'em
FIG. 2. Coordinate system used to describe the structure and dynamics of
ArHCN.
values were obtained. The uncertainties quoted for the di­
pole moments are relative uncertainties which arise primar­
ily from errors in measuring the frequencies of the zero field
and Stark shifted transitions. Since the uncertainty in the
electric field is 0.06%, the absolute uncertainty in the mea­
sured dipole moments is roughly 0.0015 D larger than stated
in the table. Since it is the relative values of p. which are of
interest for the various isotopically substituted forms of
ArHCN, the estimates of precision given in Table II are con­
sidered to be more useful.
The discrepancy between the dipole moments deter­
mined from the 7 = 0-1 transition, and the 7 = 1 , AMj
= ± 1transition for ArH l2C 14N and ArH l2C '5N is seen
to be small but significant. The data can be accommodated
by a single dipole moment for each species if the observed
frequencies are corrected for the presence of a perpendicular
moment coupling the ground vibrational state to the first
excited bending level. Using the formulation of Howard,
Dyke, and Klemperer, 12 the values of p \ / A W of 0.19 D2/
cm" 1 and 0.22 D 2/cm - 1 are obtained for ArH 12C 14N and
ArH 12C 15N, respectively, where A W is the energy differ­
ence between the ground and first excited bending states.
The corresponding corrected dipole moments of these spe­
cies are 2.6244 and 2.6530 D, respectively.
The spectroscopic constants obtained can now be used
to derive vibrationally averaged structural parameters for
the ArHCN complex. Since the observed spectrum is at least
superficially characteristic of that of a linear molecule, we
shall, in the treatment that follows, discuss ArHCN as if the
equilibrium geometry were linear. As discussed in the next
section, however, the internal dynamics of this complex will
probably require that a more sophisticated treatment be used
to interpret available data, but the analysis given here will
serve well to illustrate the fundamental aspects of the prob­
lem.
The coordinates used to describe the complex ArHCN
are shown in Fig. 2. R c m is the line joining the argon atom
with the center-of-mass of the HCN, and y is the angle that
the HCN forms with the z axis which is chosen to be coinci­
dent with Rcm . In accord with the stated assumption of a
linear equilibrium geometry, the cylindrical symmetry of the
system requires that the a axis, on the average, coincide with
the z axis. Thus, the angle y (or more properly (cos2 y ) ) may
be directly determined from the measured values of the I4N
nuclear quadrupole coupling constants, viz.
eqQaa =
hcn
<3 cos2 y —1>,
(5)
where eqQ%Cn *s the quadrupole coupling constant of the
nitrogen in free HCN, which is assumed to be unchanged
upon complexation. For the isotopic forms of ArHCN for
which eqQaa was measured, the operationally defined angles
y = cos- 1[(cos2 y )]'/2] obtained from Eq. (5) are listed in
Table IV. For the ,5N species, as well as ArD 13C 14N, the
angles given in Table IV are estimates determined from scal­
ing the measured ArH(D)12C ,4N constants with the mo­
ments of inertia of the HCN subunits, e.g., y{ ArD l3C 14N)
= 7^ArD 12C I4 N)[/(D ,2C ,4N)//(D ,3C ,4N )],/4 and are
calculated primarily for the purpose of computing Rc m ’s
from Eq. (6 ) below. To assess the validity of this procedure,
we note that the angle predicted for ArH 13C 14N using this
method is 30.6°, which is in excellent agreement with experi­
mental observation. Since this scaling is only performed
between complexes ofthe same hydrogen isotope, it amounts
to a small correction and no serious error is expected to be
introduced.
_
Using the values of (cos2 y) obtained above, R c m., the
vibrationally averaged value of R c.m., may be computed for
each of the isotopically substituted forms of this complex
from
hb=
= K R l . m. + j l , 11 + (cos2 y) ] ,
where M, = M licriM AT/(M HCK + AfAr) and /, is the mo­
ment of inertia of the HCN subunit. The values of R c^ so
obtained are also given in Table IV. The decrease in R c m
upon deuteration of each of the three ArHCN species sup­
ports an atomic ordering Ar-HCN, and hence Table IV also
includes estimated argon-hydrogen bond lengths for an as­
sumed linear equilibrium geometry. It is seen that these com­
puted Ar-H bond lengths vary among the isotopic species by
0.049 A. If the complex had been assumed to be nitrogen
bound, the corresponding variation in the Ar-N bond length
would be 0.15 A, and so the comparatively consistent bond
lengths obtained for the hydrogen bonded form further sup­
port the stated atomic ordering. In absolute terms, however,
a 0.049 A variation in van der Waals bond length is some­
what more than would be expected based on experience with
TABLEIV. Derived molecular constants of ArHCN*
* .« .( A)
ArH
ArH
ArH
A rD
A rD
ArD
,2C ,4N
,3C MN
l2C l5N
12C HN
,3C HN
12C l5N
4.3432(1)
4.3310(3)
4.3693(1)
4.3278(1)
4.3149(2)
4.3531(1)
(6 )
* a,-h (A)
?tdeg)
A:,(mdyn/A)
<u,(cm-1 )
fct (mdyn/A)
<u.(cm~')
2.721
2.729
2.726
2.764
2.768
2.767
30.8(2)
30.6(4)
30.6(4)”
27.9(2)
27.8(4)”
27.7(4)”
0.000 991(3)
0.00109(2)
0.000999(4)
0.00) 593(5)
0.001 71(4)
0.001 66(2)
10.22(1)
10.6(1)
10.15(2)
12.81(2)
13.1(2)
12.95(8)
0.000 70(2)
0.000 70(4)
10.2(2)
10.1(3)
0.000 85(2)
10.2(1)
...
...
...
‘ Reported uncertainties include errors in the spectroscopic constants only.
”Estimated.
‘ Using y — 30.6°.
J. Chem. Phys., Vol. 81. No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•4/rmd(D)
’ 0.062(5)
0.071(11)
0.085(10)c
0.107(5)
Leopold et at.: Stark spectrum of ArHCN
other van der Waals systems, and provides only weak evi­
dence for a hydrogen bound system. Guided by chemical
intuition, however, and supported by a decrease in Rc m.,
upon deuteration, we shall continue to regard the hydrogen
as being between the argon atom and the center-of-mass of
the HCN.
Harmonic stretching and bending force constants are
computed from the centrifugal distortion constants and
average bending angles, respectively, using the usual expres­
sions in which the bending and stretching motions are as­
sumed to be uncoupled oscillations, viz.
,
{AnfM ]R ] mB 4
k,
------------------------------
7
2hDj
kb=
Ji:
(8)
4 ^ / HCn i r )
Corrections to kb which arise from replacement of / HCN by a
more sophisticated form of the bending reduced mass13 do
not produce significantly different results. The calculated
force constants together with the corresponding vibrational
frequencies are also listed in Table IV. We note here that, as
discussed below, the values obtained from these expressions
are expected to be particularly unreliable. They will, none­
theless, be useful in discussing the nature of the internal dy­
namics in this system. It is interesting to note that iffi for this
complex is taken as roughly ^ HCN sin y = 1.5 D, the values
of A W obtained from fi]/A W determined above are 12 and
10 cm - 1 for the 14N and l5N species, respectively. Though
these values are remarkably close to the bending vibrational
frequencies listed in Table IV, we refrain from overinterpret­
ing this calculation, since it seems likely that a simplistic
interpretation of a small effect in such a dynamically com­
plex system will be misleading. Moreover, with the data
available, it is not possible to rigorously reject a distortion
effect on the dipole moment as the origin of the observed
difference between the rf- and microwave-determined dipole
moments. Computing RQm from Bctt= B — DJJ(J + 1)
and estimating d y /d R to be 3°/0.047 A (as determined from
the isotopic data in Table IV), the change in projection of
4927
/^hcn due to centrifugal stretching is estimated to be 0.0009
D. Since this number is of comparable magnitude to the dif­
ference in the two values of(i in question, the physical origin
of this small effect is not unambiguously determined, but
clearly, it is not inexplicable either.
DISCUSSION
ArHCN has been shown to have a spectrum character­
istic of a linear molecule, and the spectroscopic constants
obtained have been used to compute values for vibrationally
averaged molecular constants according to standard proce­
dures. It is now useful to more carefully examine both the
spectroscopic constants themselves and the structural pa­
rameters derived from them.
The most striking feature of the data presented above is
the magnitude of the quantities associated with vibrational
effects. First we consider the stretching coordinate. It is seen
that the values of D} obtained are an order of magnitude
greater than those observed in any van der Waals complex of
argon studied to date, and the need to include an
term in
the Hamiltonian has precedent in van der Waals systems
only in the related complex KrHCN. Equally remarkable is
the extreme sensitivity of the centrifugal distortion constants
to isotopic substitution. It is seen, for instance, that Dj for
ArHCN decreases by a factor of 1.7 upon deuteration. Since
this quantity is expected to scale roughly as 1/M ], a de­
crease of only 4% would be predicted and is in marked con­
trast with experimental observation.
The centrifugal distortion constants for the six isotopic
forms of ArHCN have been used to compute potential pa­
rameters based on a model in which the bending and stretch­
ing motions associated with the weak bond are assumed to be
uncoupled. Not unexpectedly, the large D j values give rise
to extremely small stretching force constants and vibrational
frequencies. Close examination of the constants obtained,
however, evokes suspicion as to whether these numbers can
be correct. Table V compares the stretching force constants
and hydrogen bond lengths of a number of hydrogen bound
hydrogen cyanide complexes and it is seen that the value of
TABLE V. Comparison of hydrogen bond length and stretching force constants of complexes of HF, HC1, and
HCN.
HF
Ar
HCCH
H j CCH j
Cyclopropane
HCN
■Reference 15.
bReference 16.
'Reference 17.
d Reference 18.
'Reference 1.
f Reference 19.
•Reference 20.
"Reference 21.
‘Reference 22.
HC1
HCN
R h -b
k,
m
AR?
R h -b
k,
AR*
^H-B
k,
(A)
(mdyn/A)
(A)
(A)
(mdyn/A)
(A)
(A)
(mdyn/A)
2.630*
2.196"
2.218°
2.095"
1.870°
0.0142
0.091
0.398
0.429
0.318
0.361
2.732r
2.415*
2.440"
2.286'
2.094*
0.0117
0.067
0.061
0.087
0.092"
-0 .0 1 1
0.179
0.207
0.127
0.137
2.721"
2.594'
2.647"
2.413"
2.231°
0.000 991
0.053
0.046
0.062
0.0814"
...
...
0.23
0.245
JReference 2.
"This work.
'Reference 4.
"Reference 5.
"Reference 6.
"Reference 23.
PA R — R& -ncs — R b- hx •
"Recalculated from original data using method of Ref. 15.
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4926
Leopold etal.: Stark spectrum of ArHCN
ks for ArHCN is about an order of magnitude smaller than
that for any of the other complexes listed. Comparison with
other van der Waals complexes of argon similarly shows k,
to be anomalously small. It is particularly noteworthy that
the force constant and vibrational frequency of Ar2 are
1X 10~ 2 mdyn/A and 26 cm- respectively. 14 Comparison
with the corresponding quantities calculated for ArHCN
(1X 10~ 3 mdyn/A and 10 cm- *, respectively) would suggest
the counterintuitive conclusion that the bond in ArHCN is
actually weaker than that in Ar2. We emphasize, however,
that extremely intense spectra were observed for ArHCN,
though the complex was produced from a mixture in which
the Ar.’HCN ratio was 200:1. If the bond in Ar2 were stron­
ger than that in ArHCN, the formation of the mixed com­
plex would not be expected to be competitive with that of the
homogeneous dimer. Thus, the intensity of the observed
spectra (which may be taken as evidence that substantial
quantities of ArHCN are formed in the expansion) creates
further doubt that the calculated force constants (and
stretching frequencies) for ArHCN are physically realistic
numbers.
Second, with regard to the angular coordinate, the
bending vibrational amplitudes determined from the nuclear
quadrupole coupling constants are of unexpected magni­
tude. Under the assumption used above that the bending and
stretching motions are separable, the vibrationally averaged
HCN angles also give rise to bending force constants which
are an order of magnitude smaller than would be expected.
The vibrational frequencies calculated from these constants
are also 1 0 cm- 1 and thus similar objections to those made
above may be raised. Moreover, since K # 0 states of an
asymmetric rotor correlate with excited bending vibrational
states of a linear rotor, failure to observe such levels in
ArHCN would mean that no vibrationally excited bending
state was observed. Since the temperature in the beam is
estimated to be 10 K, a 10 cm- 1 bending state would be
expected to be populated. Failure to observe such a state in
ArHCN may thus be indicative of substantial error in the
estimate of the bending vibrational frequency. Indeed, as­
suming that the three weak transitions observed on m /
e — 69 are from an excited vibrational of the complex
ArDCN it remains puzzling that such a low vibrational state
exists. Moreover, in light of the discussion which follows, the
validity of Eqs. (7) and (8 ) must be questioned and their ap­
parent ability to predict such a low energy vibration as for­
tuitous. Thus, regardless of the identity of the unassigned
transitions, it is clear that the behavior of this system is not
straightforwardly analogous to that of other van der Waals
systems studied to date, other than the closely related
KrHCN.
Further examination of the data given in Table V re­
veals still additional peculiarities. Specifically, it is seen that
the hydrogen bond length obtained for ArHCN is signifi­
cantly shorter than that which would have been predicted by
comparison of other complexes of HCN with the corre­
sponding complexes of either HF or HC1. This short bond
length, while surprising in itself, appears particularly anom­
alous in light of the small stretching force constant discussed
above. The relationship between the stretching force con­
stant and the hydrogen bond length may be examined in
more detail. Figure 3 shows a plot of ks as a function of the
hydrogen bond length for all the isotopically substituted
forms of ArHCN studied. It is seen not only that the force
“constant” is nearly a monotonic function of the hydrogen
bond length, but that as the bond gets longer, the vibrational­
ly averaged force constant gets larger.
In light of the apparently anomalous behavior of this
system, it is reasonable to question whether in fact the ob­
served spectrum is truly that of a linear rotor with large
centrifugal distortion, or rather, just the/if = 0, a-type spec­
trum of an asymmetric rotor.25 Approximating Iaa for an
asymmetrical form of ArHCN by 1a = / HCN(sin2 y), the
value of B — C necessary to reproduce the observed devia­
tions from a rigid rotor spectrum is on the order of 1 0 0 0
MHz. As y is varied from 0° to 90°, the value of Rc m neces­
sary to give B — C = 1000 MHz varies from 2.1 to 1.1 A,
corresponding to a variation of B + C from 13 358 to 27 770
MHz. These values of R cm are not only entirely unreason­
able from a physical standpoint, but clearly give B -f C val­
ues which are in sharp disagreement with that which is ob­
served. Thus, there is no asymmetric rotor structure for
ArHCN capable of accounting for the observed spectrum.
Further evidence refuting an asymmetric rotor struc­
ture for ArHCN comes from the apparent lack of a zero-field
radiofrequency spectrum. For an assumed asymmetric
structure in which R c m = 4.34 A (the value necessary to
reproduce the observed B + C) and y — 30° (the value con­
sistent with the experimentally determined eqQaa), the cal­
culated value of B —Cis 14 MHz. Hence, the K — \ , J — 1,
2, and 3 asymmetry doublets would be expected to fall within
the 3-100 MHz range which was searched. These levels all
have calculated rotational energies less than 200 GHz and
would therefore be expected to be populated in the beam.
Failure to observe these transitions in this frequency range
may be taken as further evidence that asymmetry is not re­
sponsible for the observed deviations from a linear rigid ro­
tor spectrum.
Thus, close examination of the spectroscopic constants
and derived structural parameters for this system has shown
a number of remarkable peculiarities. Before proceeding to
15
«t 14
■ to
2.72
2.73
2.74
2.75
2.76
2.77
2 78
'» r - H < * 1
FIG. 3. Plot of the stretching force constant computed from Eq. (7) as a
function of estimated hydrogen bond length.
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Leopold etal.: Stark spectrum of ArHCN
offer an interpretation for the behavior of the ArHCN sys­
tem, we summarize the important observations which have
been made:
(i) ArHCN has an intense spectrum characteristic of a
linear rotor with unusually large centrifugal distortion and
unexpectedly wide bending vibrational amplitude. The
stretching and bending vibrational frequencies computed by
assuming separability of these motions are each 10 cm(ii) The large centrifugal distortion constants observed
are extremely sensitive to isotopic substitution. The harmon­
ic stretching and bending force constants obtained from
them are an order of magnitude smaller than those for all
other van der Waals complexes of argon, and the stretching
force constants vary by a factor of 1.7 among the isotopically
substituted forms studied. The HCN bending amplitudes
similarly give rise to a bending force constant and vibrational
frequency which are significantly smaller than those ob­
served in other weakly bound systems.
(iii) The hydrogen bond length is unexpectedly short
based on comparisons between other complexes of HCN and
the analogous complexes of HF and HC1. The hydrogen
bond length varies by 0.047 A among the isotopic species
studied and a nearly monotonic relationship exists between
the hydrogen bond length and the stretching force constant:
As R (Ar-H) gets longer, the stretching force constant gets
larger.
Some insight into the problem may be gained by exami­
nation of Fig. 4 in which the centrifugal distortion constant
of the argon complex is plotted against the rotational con­
stant of the HCN subunit. It is seen from this plot that the
dramatic changes in Dj which accompany isotopic substitu­
tion are strongly correlated with the concomitant changes in
the rotational constant of the HCN moiety. Since, in an har­
monic approximation, the moment of inertia of the HCN is
closely related to the reduced mass for the bending vibration,
the correlation with the centrifugal stretching constant of
the complex is indicative of a strong coupling between the
stretching and bending degrees of freedom associated with
the weak bond.
It may be noted, too, that the ,3C and l5N data on this
plot establish that the observed behavior is not a result of the
average nonlinearity of the HCN itself. While the average
H-C-N angle in HCN is sensitive only to substitution of the
hydrogen, the value of Dj of the complex is seen to be unex­
pectedly sensitive to isotopic substitution of any of the atoms
of the HCN.
Additional evidence for strong angular radial coupling
in this complex is contained in Table VI in which structural
parameters for argon and krypton complexes of H(D)CN,
H(D)C1, and H(D)F are compared. We see that for the hy­
drogen halide complexes, an 8 ° change in the average HX
bending angle upon deuteration is accompanied by a change
in the bond length of —0.004 and + 0.023 A for HF and
HC1, respectively. For HCN, however, a change in the bend­
ing angle of only 3° is associated with a 0.043 A change in
R (Ar-H), further demonstrating the strong interdependence
between the radial and angular motions in this system. It is
worthy of mention, here too, that the behavior of ArHCN is
not solely due to the wide amplitude of the motion, since the
HX systems undergo even wider amplitude oscillations, but
do not exhibit the behavior observed for the hydrogen cyan­
ide case.
A number of other interesting comparisons may be
made with reference to Table VI which show the behavior of
ArHCN to be qualitatively similar to, though even more
dramatic than, that of KrHCN. First, it is seen that both the
stretching and bending force constants of ArHCN are about
a factor of 2 smaller than those of KrHCN. Moreover, we
note that the decrease in bond length upon deuteration of
KrHCN is 0.028 A, while that for ArHCN is 0.047 A. In
fact, of all the hydrogen bond lengths listed in Table VI, that
of ArHCN is seen to be most sensitive to isotopic substitu­
tion. Interestingly, though, despite the differences between
ArHCN and KrHCN, the behavior of their stretching force
constants upon deuteration is quite similar; the ratio of ks for
the protonated and deuterated forms of KrHCN is the same
as that for the protonated and deuterated forms of ArHCN.
The tendency of the argon complex of HCN toward
more extreme behavior than that of KrHCN is further exem­
plified by comparison of the complexes of the two rare gases
with another common binding partner HC1. It is seen that
for argon, the stretching force constant decreases by a factor
of 12 as the binding partner is changed from HC1 to HCN,
while the corresponding change for the complexes of kryp­
ton is only a factor of 8 . It is interesting to note, however, that
TABLE VI. Comparison of A rand K r complexes of H(D)CN, H(D|C1, and
H(D)F.
180
160
120
100
80
34
36
38
40
42
44
48
b „ C N (G Hz )
FIG. 4. Plot of the centrifugal distortion constant of the complex ArHCN
as a function of the rotational constant of the HCN subunit.
ArHCN*
ArDCN
ArHF*
ArDF
ArHCl'
ArDCl
“ KrHCN11
"K rD C N
“ KrHCl'
"K rD C l
r(Ar-H)|A)
rtdeg)
k, (mdyn/A)
2.721
2.764
2.630
2.626
2.732
2.755
2.898
2.926
2.827
2.844
30.8
27.9
41.1
33.0
41.4
53.!
26.7
24.5
3f.C
30.9
0.000 991
0.001 59
0.014 2
0.016 8
0.0117 ,
0.013 4
0.001 84
0.003 08
0.015 4
0.017 0
“This work.
b Reference 15.
'Reference 19.
d Reference 11.
'Reference 24.
J. Chem. Phys., Vol. 81, No. 11.1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
k b{mdyn A)
0.000 70
0.000 85
0.003 1
0.003 9
0.001 5
0.001 8
0.0012
0.001 4
0.002 2
0.002 5
4930
Leopold etal.: Stark spectrum of ArHCN
the ratio of ks for the protonated and deuterated forms of
ArHCN and KrHCN are nearly the same (1.60 and 1.67,
respectively), though this ratio is quite different from that of
either ArHCl or KrHCl (1.15 and 1.10, respectively).
Further comparisons may be made with regard to bond
lengths. It is seen from the table that for HC1 complexes, the
hydrogen bond length to argon is 0.12 A shorter than that to
krypton. The similar comparison for the HCN complexes
shows that the hydrogen bond length to argon is 0.18 A
shorter than that to krypton. Thus, we see again how the
behavior of ArHCN is qualitatively similar to, though more
dramatic than, that of KrHCN.
A physical explanation for the origin of the strong an­
gular radial coupling in this system may be suggested. To do
so, we return to the question of what structure would have
been predicted for the ArHCN complex. By analogy with
ArHX, a linear hydrogen bound structure would have been
predicted, while by analogy with ArHCCH, a T-shaped ge­
ometry would be expected. Realizing that HCN is both a
polar protonic acid (like a hydrogen halide) and a species
which is isoelectronic to HCCH (in which the lowest unoc­
cupied molecular orbital is ir*), it is possible to imagine that
near the linear configuration, the argon atom experiences a
potential similar to that due to a hydrogen halide, but that
near the T-shaped configuration, the potential energy sur­
face is more like that due to acetylene. We note that Rcm. for
ArHCCH is 3.2 A which is considerably shorter than the 4.6
A value which would have been predicted for ArHCN near
y — 0 (or, for that matter, considerably shorter than the ob­
served value of 4.3 A). Keeping this in mind, it is possible to
envision that as the HCN undergoes wide amplitude oscilla­
tions away from a potential energy minimum at or near the
linear configuration, it begins to experience an acetylenic
potential which draws it towards the C-C bond. In this man­
ner, the coupling between the radial and angular coordinates
could be explained. We note, also, that this picture offers the
intriguing possibility that a double minimum exists in the
potential energy surface of this system, with one minimum
near the linear configuration, and another near the T-shaped
configuration. Though difficult to verify, this picture is quite
physically appealing.
Whether or not the above discussion of the origin of the
observed angular radial coupling is correct, the existence of
such coupling seems clear. The decrease in R c m. near the Tshaped configuration contributes to the vibrationally aver­
aged hydrogen bond length in such a way as to make it unex­
pectedly short. The sensitivity of average bond length to
isotopic substitution is also expected, since changes in the
moment of inertia of the HCN are tantamount to changes in
the reduced mass for the bending vibration, and hence the
amplitude of oscillation. The deuterium isotopes, whose
bending motion is attenuated relative to that of the protonat­
ed forms, incorporate greater contributions from the linear
configuration in their vibrationally averaged bond length,
and hence exhibit the longer R [Ar-H(D)].
The inverted relationship between the stretching force
constant and hydrogen bond length may also be rational­
ized. Since the bond in ArHCCH is almost certainly weaker
than that in an ArHX complex, isotopic forms of ArHCN
with the smaller vibrational amplitudes (i.e., those which, on
the average appear more like the ArHX systems) will have
the larger vibrationally averaged stretching force constants.
Such isotopic forms, however, are those associated with the
longer bond length and hence the anomalous relationship of
Fig. 3 may be understood.
In this spirit, even the results of the “isotopic substitu­
tion” of Kr for Ar are sensible. While the increase in polarizability of the rare gas is expected to have only a small effect
on the energy of the T-shaped (or near T-shaped) configura­
tion, the dipole-induced dipole energy near y = 0 will be
larger for krypton than for argon. The HCN is consequently
more directed toward the rare gas and samples less of a re­
gion of the angular potential which is associated with the
shorter R c,m.. The system thus begins to converge (though
not completely) on the usual behavior expected in the ab­
sence of strong angular radial coupling making the behavior
of KrHCN similar to, though not as dramatic as that ob­
served for ArHCN.
A more exact, quantitative interpretation of the spec­
troscopic constants is far less intuitive. To the best of our
knowledge, the problem of wide amplitude oscillations in
more than one coordinate has not been adequately treated
and it appears that such a treatment will be necessary for the
proper interpretation of the ArHCN spectrum. As demon­
strated by the magnitude of the stretching and bending force
constants which have been calculated, any simple model in­
volving uncoupled small amplitude oscillators is grossly ina­
dequate. Moreover, the complicated internal dynamics of
ArHCN which gives rise to isotopically sensitive geometri­
cal parameters makes the “structure” of this complex a neb­
ulous concept. Thus, an improved description of systems
undergoing wide amplitude motions in more than one coor­
dinate is an important goal with direct bearing on the proper
interpretation of spectroscopic data. We hope that this sys­
tem will motivate further work in this area.
Lastly, the suggestion that a double minimum may exist
in the potential energy surface has been made. If this is the
case, this system illustrates how the existence of two inequi­
valent local minima does not necessarily guarantee the oc­
currence of two separate spectra.26 Whether or not such a
situation exists in this case, the possibility raises questions as
to what the spectral consequences of such a potential would
be. In principle, a sufficiently high barrier between two such
minima in a potential would give rise to distinct isomers, but
the existence of isomeric forms of small van der Waals mole­
cules has not yet been established by rotational spectroscopic
methods. Simple calculation shows that at 10 K, an energy
separation of only 30 cm - 1 between two such forms would
give a population ratio of 100:1. Thus, since a typical van der
Waals binding energy is several hundred cm- ', the observa­
tion of two separate forms would require a fortuitous match­
ing of their energies to within a relatively small fraction of
the binding energies. If inequivalent minima separated by a
high barrier exist in other van der Waals systems, it is not too
surprising that they have not been observed. This does not,
however, exclude the possibility of more than one minimum
separated by a low barrier. If this is indeed the case in
ArHCN, the severity of its spectroscopic consequences un­
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Leopold e ta l.: Stark spectrum ot ArHCN
derscores the need for a better understanding of wide ampli­
tude oscillations in more than one coordinate. We hope that
progress in this direction, together with potential energy sur­
face calculations for ArHCN, will provide further insight
into this dynamically complex system and lead to more so­
phisticated methods with which to treat spectroscopic data
in other weakly bound systems.
ACKNOWLEDGMENTS
The authors wish to thank Dr. E. J. Campbell and Pro­
fessor J. S. Muenter for private communications concerning
this system.
’A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R. Soc. London Ser. A
370,213 (1980).
2A. C. Legon, E. J. Campbell, and W. H. Flygare, J. Chem. Phys. 76,2267
(1982).
3E. J. Campbell, A. C. Legon, and W. H. Flygare, J. Chem. Phys. 78,3494
(1983).
4P. D. Aldrich, S. G. Kukolich, and E. J. Campbell, J. Chem. Phys. 78,
3521 (1983).
3S. G. Kukolich, W. G. Read, and P. D. Aldrich, J. Chem. Phys. 78,3552
(1983).
*S. G. Kukolich, J. Chem. Phys. 78,4832 (1983).
7A. J. Fillery-Travis, A. C. Legon, and L. C. Willoughby, Chem. Phys.
Lett. 98,369 (1983).
*K. R. Leopold, G. T. Fraser, and W. Klemperer, J. Chem. Phys. 80,1039
(1984).
*R. L. DeLeon and J. S. Muenter, J. Chem. Phys. 72,6020 (1980).
,0M. R. Keenan, D. B. Wozniak, and W. H. Flygare, J. Chem. Phys. 75,631
(1981).
4931
"E . J. Campbell, L. W. Buxton, and A. C. Legon, J. Chem. Phys. 78, 3483
(1983).
I!B. J. Howard, T. R. Dyke, and W. Klemperer, J. Chem. Phys. (to be pub­
lished).
I3E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations
(McGraw-Hill, New York, 1955).
“ E. A. Colboum and A. E. Douglas, J. Chem. Phys. 65, 1741 (1976).
I5T. A. Dixon, C. H. Joyner, F. A. Baiocchi, and W. Klemperer, J. Chem.
Phys. 74,6539 (1981).
'*W. G. Read and W. H. Flygare, J. Chem. Phys. 76,2238 (1982).
I7J. A. Shea and W. H. Flygare, J. Chem. Phys. 76,4857 (1982).
18L. W. Buxton, P. D. Aldrich, J. A. Shea, A. C. Legon, and W. H. Flygare,
J. Chem. Phys. 75, 2681 (1981).
I9(a) S. E. Novick, P. Davies, S. J. Harris, and W. Klemperer, J. Chem. Phys.
59,2273 (1973); (b) S. E. Novick, K. C. Janda, S. L. Holmgren, M. Waldman, and W. Klemperer, ibid. 65,1114 (1976).
“ A. C. Legon, P. D. Aldrich, and W. H. Flygare, J. Chem. Phys. 75, 625
(1981).
2IP. D. Aldrich, A. C. Legon, and W. H. Flygare, J. Chem. Phys. 75, 2126
(1981).
22A. C. Legon, P. D. Aldrich, and W. H. Flygare, J. Am. Chem. Soc. 104,
1486(1982).
23L. W. Buxton, E. J. Campbell, and W. H. Flygare, Chem. Phys. 56, 399
(1981).
2<(a) T. J. Balle, E. J. Campbell, M. R. Keenan, and W. H. Flygare, J. Chem.
Phys. 72, 922 (1980); (b) A. E. Barton, T. J. Henderson, P. R. R. Langridge-Smith, and B. J. Howard, Chem. Phys. 45,429 (1980).
2,In the former case, the unassigned transitions, if truly from ArDCN,
would correspond to vjtQ, while in the latter case, we would regard them
as A' y^O states.
26We acknowledge, of course, the possibility that the unassigned transitions
could be due to an isomeric form of ArDCN. However, since the existence
of complex internal dynamics has been established from the assigned spec­
trum, a simple explanation involving two well separated minima is not
favored.
J. Chem. Phys., Vol. 81, No. 11,1 December 1984
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CHAPTER 3
ROTATIONAL SPECTROSCOPY OF MOLECULAR COMPLEXES OF BF^ WITH
KCCH. C02 , and 1I20
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71
R e p rin te d from th e J o u r n a l o f th e A m erican C hem ical S ociety, 1984,106,897
C opyright © 1984 by th e A m e ric an C hem ical S ociety a n d r e p rin te d by p erm ission o f th e c o p y rig h t o w n er
Rotational Spectroscopy of Molecular Complexes of BF3
with NCCN, C 0 2, and N 2Ot
K. R. Leopold, G. T. Fraser, and W. Klemperer*
Contribution fro m the Department o f Chemistry, Harvard University.
Cambridge, Massachusetts 02138. Received Ju ly 2 7 ,1 9 8 3
Abstract The microwave spectrum of the van der Waals complex NCCN-BFj has been obtained by molecular beam electric
resonance spectroscopy. This molecule is shown to be a symmetric rotor. The rotational constants for the "B and ,0B species
are B0 = 672.2 (2) and 675.6 (2) MHz, respectively. These values are consistent with a B-N bond length of 2.647 (3) A.
Radio-frequency and microwave transitions of the complex C 0 2-BF3 have been observed and establish that this molecule is
an asymmetric rotor. One radio-frequency transition observed for N 2OBF3suggests an asymmetric structure for this complex
as well.
Introduction
Addition complexes of the strong Lewis acid-BFj are funda­
mental in classical donor-acceptor chemistry. Recently the van
der Waals complexes of BF3 with Ar, CO, and N 2 have been
formed in an adiabatic expansion and structurally characterized
by their microwave spectra.1 The van der Waals bonds fonn along
the C3 axis of the BF3 in a manner analogous to the binding in
the ‘‘classical complexes”. This behavior seems chemically rea­
sonable and suggests that the van der Waals interaction may also
be viewed in terms of a Lewis acid-base model. Such a picture
has successfully provided an intuitive understanding of van der
Waals interactions in a variety of weakly bound systems.
In view of the chemical character of weakly bound systems it
seems reasonable to consider whether, in fact, there is a smooth
transition between van der Waals and covalent bonding. Despite
structural similarities between the covalent and van der Waals
complexes of BF3, for example, dramatic differences exist. The
B-N bond length in BF3-amines is 1.6 A while that in N 2-BF 3
is 2.9 A. Such a large variation in bond length with nitrogen donor
may permit, at least in principle, the observation of a smooth
transition between “covalent” and “van der Waals” binding,
provided the nature of the nitrogen donor were properly chosen.
Two classes of nitrogen donors which may be used for this purpose
are the amines and the cyanides. Microwave data for a number
of the gas-phase amines are available, but the analogous data for
the cyanides are lacking. With the simplest of these, HCN and
CH 3CN, BFj forms solid compounds. Cyanogen, on the other
hand, does not form a solid with BF3, and so was chosen as an
interesting system to study.
The structure of NCCN-BF3is also of interest for comparison
with a number of other previously studied “van der Waals”
molecules. Recent rotational spectroscopic studies of C 0 2-HFJ
and NCCN-HF,3as well as SCOHF 4 and COr HC!,4 have shown
these complexes to have linear, hydrogen bonded structures. The
linear structures of the CQ2-HX complexes are not readily un’ This work was supported by tbe National Science Foundation.
0002-7863/84/1506-0897501.50/0
derstandable from consideration of oxygen lone pairs on C 0 2, as
might be expected if chemical reasoning were applicable.
Moreover, the geometry of the closely related, isoelectronic species
N 2OHF is quite different, having a bent, hydrogen bonded
structure. In view of the similarities between C 0 2 and N zO and
the dissimilarities in their complexes with HF, a simple
HOMO-LUMO approach does not appear applicable to these
systems, since any argument based on lone pairs would have to
predict the same structure for N 2OHF and C 0 2HF. In contrast,
HF and BF3 appear quite similar in their weak interactions. For
example, studies of the complexes of CO and N 2 with HF and
BF3show that HF and BF3 behave similarly as simple Lewis acids.
Specifically, viewed as electron-pair acceptors, both HF and BF3
accept electrons along their symmetry axes. Thus, given the
oberved behavior of C 0 2 with HF, the complex C 0 2BF3 is ex­
pected to be a symmetric top in which the C 0 2 axis is coincident
with the symmetry axis of the BF3. Likewise, the linear structure
of NCCN-HF suggests a similar geometry for NCCN*BF3.
We have studied the complexes NCCN-BF3, C 0 2-BF3, and
N 20-BF 3 by rotational spectroscopy using the molecular beam
electric resonance technique. The spectra show that the complex
NCCN*BF3 does indeed have the anticipated C*, structure, while
C 0 2-BF3 and N 20*BF3 do not. This result further emphasizes
the complexity of the binding in C 0 2 and N20 systems.
Experimental
A beam of NCCN-BF3 was formed by expanding a mixture of 1%BF3
and 25% N CCN in Ar through a 25-/un nozzle at room temperature.
The stagnation pressure was typically 2.5 atm. Under these conditions.
(1) K. C. Janda, L. S. Bernstein, J. M. Steed, S. E. Novick, and W.
Klemperer, J. Am. Chem. Soc., 100, 8074 (1978).
(2) F. A. Baiocchi, T. A. Dixon, C. H. Joyner, and W. Klemperer, J.
Chem. Phys., 74, 6544 (1981).
(3) A. C. Legon, P. D. Soper, and W. H. Flygare, J. Chem. Phys., 74,4936
(1981).
(4) R. S. Altman, T. A. Dixon, M. D. Marshall, and W. Klemperer, J.
Chem. Phys., 77, 4344 (1982).
© 1984 American Chemical Society
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 1
898
Leopold, Fraser, and Klemperer
J. A m . Chem. Soc.. Vol. 106, N o. 4. 1984
Table I. Observed Zcro-l:ield Transitions o f NCCNBI:3°
J
J'
4
5
6
7
8
5
6
7
8
9
"BFj-NCCN
6722
8068
9412
10752
12095
(2)
(2)
(2)
(3)
(5)
10BFj-NCCN
9459 (3)
12158 (5)
0 All frequencies given in MHz.
prominent mass spectral features included BF2+ and NCCN BF2+, but
ArBF2+ and B2F3+ were conspicuously absent. At lower NCCN con­
centrations (e.g., ~12% ) both ArBF2+ and NCCNBF2+ were observed,
while B2F3+ still was not. Both the NCCNBF2+ and BF2+ mass peaks
were observed to be polar, but about four times more focussed beam
could be obtained on the latter. Therefore, as with previously studied
complexes of BF3, spectroscopy was performed monitoring m /e 49 (or
48 for l0BF2+). Interestingly, in the absence of any N C C N , B2F3+ was
formed in abundance and was found to be nonpolar in agreement with
a previous observation. From the nonpolarity of (BF2)2 and the lack of
ArBF2+ in the mass spectrum it can be concluded that most if not all of
the focussed beam on the BF2+ peak was due to NCCNBF3. In exper­
iments with C 0 2BF3 and N 2OBF3, 25% C 0 2 or N 20 with 1% BF3 (in
Ar) was also used, and no ArBF2+ was formed. Mass spectral and
focussing data in these systems indicate that the observed resonances
must arise from the 1:1 complexes of BF3 with C 0 2 or N 20 . All spectra
were taken by using the molecular beam electric resonance technique
with the spectrometer operated in the flop-out mode.
A quick, and therefore useful, way to test whether a molecule is a
symmetric rotor may be applied to these BF3 systems. The quadrupole
coupling constant of "B ( / = 3/ 2) in ArBF3 and COBF3 has been de­
termined1to be 2.75 MHz. This value, identical with that in solid BF3,M
is seen to be unchanged upon van der Waals complexation. If no ad­
ditional quadrupolar nuclei are present, any axially symmetric complex
of "B F 3 will have the J = 2, K «= 2, F = ' / 2 — 3/ 2, and F = J/ 2 — 7/ 2
transiions a t lU(eqQ) *= 680 kHz. This transition, which is electric dipole
allowed since K yt 0, will occur a t this frequency regardless of the
rotational constants of the complex. Thus, direct observation of these
transitions affords a method of determining if a molecule is a symmetric
rotor. Indeed a strong resonance is observed a t 680 kH z with COBF3,
but despite extensive effort, no such resonance could be observed for
C 0 2BF3. Instead, four radio-frequency frequency transitions between
2 and 7 M Hz and seven microwave transitions which do not fit a sym­
metric rotor pattern were observed. We note that considering only states
which are expected to be populated in our beam, the largest pure quad­
rupole splitting produced by a spin 3/ 2 nucleus on the axis of a symmetric
top occurs between the F = !/ 2 and F *= 3/ 2 levels of J = 1 and K = 0
and corresponds to OASeqQ ( * 1.24 M Hz for "B F 3). Direct transition
between these levels, however, is electric dipole forbidden since K = 0.
Thus, the observed radio-frequency transitions are too high in frequency
to be pure qaudrupole transitions. N o radiofrequency transitions other
than the pure quadrupole transitions are passible a t zero electric field if
this is a rigid symmetric rotor, and inversion of a symmetric C 0 2BF3 does
not appear to be sensible motion. The radio-frequency transitions are
those of an asymmetric rotor which are, perhaps, complicated by internal
rotation. The inability to fit the microwave lines to a symmetric top
spectrum lends further support to this interpretation. The possibility of
internal rotation in C 0 2BF3 makes this molecule especially interesting,
but no further discussion of its structure other than the fact that it is an
asymmetric rotor will be given here.
A transition at 2.6 M Hz was also observed for N 2OBF3. The zerofield pure quadrupole spectrum (calculated for a symmetric top structure)
contains no transitions above ~ 1.5 MHz. Thus, it seems likely that this
molecule is also an asymmetric rotor. In experiments with OCS-BF3, no
m>/**tl(F transition could be observed.
The quadrupole coupling constants in NCCN -HF have previously
been determined3 to be -4.28 and -4.56 M Hz for the bonded and non­
bonded nitrogens, respectively. Due to the complex hyperfine structure
expected for NCCN-BF3, no attempt was made to observe a “V ^ C "
transition, but a Iow-resolution microwave spectrum characteristic of a
symmetric top was quickly found by using an oscillator broadened to 3
M Hz with white noise.
9380
M hz
Figure 1. The J = 6 « - 7 transition of "B F 3-NCCN. This is a single
sweep, using a 10s time constant.
data clearly show that NCCNBF 3 is a symmetric rotor. Note
that the observed line widths are too broad to be accounted for
by quadrupole hyperfine structure or oscillator line width and are
likely due to a Z>JKterm in the energy expression. A small "Dj"
value of 3 kHz can be fit to the frequencies given in Table I. While
this value is quite reasonable, lack of knowledge of Z)JK as well
as uncertainty concerning the distribution of K levels being fo­
cussed in the spectrometer preclude a meaningful interpretaton
of this number. Thus, the B value used for calculation of the weak
bond length was just that obtained from the lowest frequency
transition (where the centrifugal distortion would be the least)
and computed assuming a nondistortable rotor. The values ob­
tained are 672.2 (2) and 675.6 (2) MHz for the "B and >°B
isotopes, respectively. If the 3-kHz Ds were considered, the
corrected B values would be 672.5 and 676.0 MHz for the "B
and 10B species, respectively. With use of the known rotational
constant1of NCCN and known bond lengths85 and the assumption
that the NCCN is along the BF3 axis, a boron-nitrogen bond
length of 2.647 (3) A is obtained. If the rotational constants
obtained by including the D j term were used, the boron-nitrogen
bond length would be only 0.002 A lower than the above stated
value. A more detailed treatment of the internal motions in this
complex is not justified with the resolution of these data.
The signal-to-noise ratio of the observed transitions was not
adequate to resolve the complex structure arising from nuclear
quadrupole and Dj* centrifugal distortion effects. Consequently,
no Stark measurements were performed. Transitions involving
lower J, where this structure would be simpler, were at best
difficult to observe, even at low resolution.
The two rotational constants obtained for the isotopically
substituted species permit, in principle, the determination of the
degree of out-of-plane deformation of the BF3. The data obtained
are consistent with a FBN angle of 90°, but due to the relatively
low resolution of the spectra, the data cannot preclude angles less
than about 100s . We feel, however, that comparison with other
similar systems indicates that the out-of-plane distortion of BF3
in NCCNBF 3 is negligible. This was found to be the case in the
weakly bound complexes BF3CO and BF3N 2 where the higher
resolution spectra set the out-of-plane bending angle at less than
1°. Since the nitrogen-boron bond length in the cyanogen system
is quite comparable to the van der Waals bond length in other
weakly bound systems, and since under the scrutiny of higher
Results
The observed transitions of NCCN*BF3 are given in Table I.
Figure 1 shows the J = 6 * - 7 transition of NCCN-,IBF3. The
(5) P. A. Casabella and T. Oja. J. Chem. Phys., 50,4814 (1969).
(6) H. M. Kriz and P. C. Taylor, J. Chem. Phys. 55, 2601 (1971).
(7) A. Maki, J. Chem. Phys., 43, 3193 (1965).
(8) Y. Morino, K. Kuchitsu, Y. Hori, and M. Tanimoto, Bull. Chm. Soc.
Jpn., 41, 2349 (1968).
(9) C. Brown and J. Overend, Can. J. Phys., 46, 977 (1968).
(10) P. D. Soper, A. C. Legon, W. G. Read, and W. H. Flygare, J. Chem.
Phys., 76, 292 (1982).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
R o ta tio n a l Spectro scopy o f M o lecu la r C om p lexes o f B F 3
T abic II. C om parison o f van der Waals Bond Lengths to Nitrogen
Nj
NCCN
c h 3c n
HCN
B l'j (B-N)
HI t l —N)
2.88°
2 .6 5 b
1.64c,h
•>
3 .08d
2.86*'
2.759^
2.796*
0 R eference 1. b T his w ork. c Reference 12. d R eference 10.
e R eference 3. ^ Reference 13. * R eference 14. h Solid-state
value.
resolution these other systems show little or no deformation of
the BF3 upon complexation, we shall assume that the BF3 moiety
is planar in NCCN-BF3 as well.
Discussion
The nitrogen-boron bond length in NCCN-BF3 may be com­
pared with the van der Waals bond length in several other com­
plexes containing van der Waals bonds to nitrogen. These data
are summarized in Table II. It is seen that with both HF and
BF3, NCCN forms bonds which are about 0.22-0.23 A shorter
than those formed with N 2. In this context, the B-N bond length
in NCCN-BF3 is not surprising. Interestingly, BF3 forms solids"
with HCN and CH3CN, and an X-ray crystallographically
study,2of the latter compound has shown it to consist of individual
BF3-NCCH3 units with a B -N distance of 1.64 A. Clearly, the
substitution of CN with CH3 produces a tremendous change in
the radial potential between BF3and NC-R. With HF, however,
this is not the case, the N -H bond lengths in CH3CN-HF and
NCCN-HF being 1.833 and 1.936 A, respectively. This difference
between HF and BF3 undoubtedly occurs because it is possible
to form a covalent bond to BF3 without violating the octet rule,
while such bonding is not possible for HF. In this sense, it would
seem that the BF3 systems provide a rare opportunity for exam­
ining the transition between van der Waals and covalent bonding
if the nature of the substituent were properly varied. The rela­
tionship between the stability of the adduct and electron-withdrawing capabilities of the donor substituent is well known for
the classical addition complexes of BF3. Interestingly, the B-N
lengths in H3N-BF3, CH3H?N-BF3, and (CH3)3N-BF3 are 1.60,
1.57, and 1,59 A, respectively. The contraction relative to
CH3CN-BF3 has been interpreted in terms of greater stability of
the amines. The relative similarity of these distances, however,
compared with the 2.64-A length in NCCN-BF3 underscores the
dramatic nature of the increase in bond length with NCCN-BF3.
It would appear that at least in principle there is not reason
to expect an abrupt transition between “covalent” and “van der
Waals” binding as the donor molecule is varied, though the adducts
of BF3 with CH3CN and NCCN are apparently two extreme
(11) H. S. Booth and D. R. Martin, “Boron Trifluoride and Its
Derivatives*, John Wiley and Sons, Inc. N. Y., 1949, and references therein.
(12) J. L. Hoard, T. B. Owen, A. Buzzell, and O. N. Salmon, Acta.
Crystallogr., 3, 130 (1950).
J. A m . Chem . S o c ., Vol. 106, N o. 4. 1984
899
cases. The complex between BF3 and CH3CN shows significant
electronic reorganization within the BF3 moiety: The FBN angle
in the solid is 103°, indicating a 13° distortion of the initially
planar BF3, and the boron atom may be thought of as approaching
an sp3 configuration. Whether this process can occur on its own
in an isolated pair of molecules or must be concomitant with the
appearance of the long-range stabilizing forces present in the solid
is an open question. Clearly, it would be interesting to prepare
a “van der Waals” complex of CH3CN-BF3. The vapor phase of
this material is completely dissociated above 50° C,15 so that
adiabatic expansion in an argon carrier above this temperature
should provide a gas-phase sample of CH3CN-BF3. It will be
interesting to see if under these conditions this adduct more closely
resembles NCCN-BF3 (long bond length, planar BF3), or if it
remains essentially unchanged from its configuration in the crystal.
The structural characterization of the other BF3*NC-R complexes
with a variety of substituents may also be useful in trying to
observe a continuous transition from covalent to van der Waals
bonding.
While both HF and BF3 show some degree of regularity in their
binding to N 2 and NCCN, it is of interest to observe that there
is a striking dissimilarity between the binding of HF and BF3 to
C 0 2. COyHF is axially symmetric, while C 0 2-BF3 is not. One
might have naively expected an asymmetric structure for C 02-BF3
from consideration of lone sp2 electron pairs of C 0 2, but such a
description would fail to account for the linear structure of
C 0 2*HF. One frequently tends to think of van der Waals binding
in terms of donor-acceptor picture, and HF and BF3 are two
simple Lewis acids which accept electrons along their axes of
symmetry. The difference in structure between their C 0 2 com­
plexes illustrates the complexity of the behavior of C 02 as a Lewis
base. The contrast between the structures of HF with C 02 (linear
complex) and isoelectronic N zO (nonlinear complex) has already
been discussed2’16,17 and further emphasizes that the binding of
C 0 2 complexes is probably rather subtle. Further work in our
laboratory18,19 shows still other binding patterns of C 0 2 when
bound to simple Lewis bases, and the structural chemistry of C 02
van der Waals complexes appears quite rich. Clearly a more
complete structural characterization of C 02BF3 as well as com­
plexes of C 02 with other Lewis acids in desirable in order to better
understand binding in this system.
Registry No. BF3, 7637-07-2; 10BF3, 15875-25-9; "B F3, 20654-88-0;
NCCN , 460-19-5; C 0 2, 124-38-9; NjO, 10024-97-2.
(13) J. W. Bevan, A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R.
Soc. London, Ser. A, 370, 239 (1980).
(14) A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R. Soc. London,
Ser. A, 370, 213 (1980).
(15) A. W. Laubengayer and D. S. Sears, J. Am. Chem. soc., 67, 164
(1945).
(16) C. H. Joyner, T. A. Dixon, F. A. Baiocchi, and W. Klemperer, J.
Chem. Phys., 74, 6550 (1981).
(17) A. M. Sapse and J. M. Howell, J. Chm. Phys., 78, 5738 (1983).
(18) K. R. Leopold, G. T. Fraser, and W. Klemperer, J. Chem. Phys., in
press.
(19) K. I. Peterson and W. Klemperer, J. Chem. Phys., in press.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 4
ELECTRIC DIPOLE MOMENTS OF H F - C ^ , H F - C ^ , AMD
h f - c 3h6
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ELECTRIC DIPOLE MOMENTS OF H F -C gH g, HF-C2 H4l AND
h f - c 3h 6
D. D. N elso n , J r.
G. T. F r a s e r , a n d W. K le m p e r e r
D e p a r tm e n t of C h e m is try
H a rv a rd U n iv e rs ity
C a m b rid g e , MA 02138
* S u p p o r te d b y t h e N a tio n a l S c ie n c e F o u n d a tio n f N a tio n a l S c ie n c e
F o u n d a tio n P r e d o c to r a l Fellow
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ABSTRACT
E le c t r ic
a c e ty le n e
d ip o le moments o f H F -cyclop ro p an e ,
and
HF-
have been d eterm ined u s in g th e m o le c u la r beam e l e c t r i c re s o ­
nance te c h n iq u e .
are
H F -e th yle n e ,
2 .5 0 8 4 (2 8 )
The d ip o le
D,
2.3 8 39 (4 5 )
moments o f H F -C .ft.,
5 o
D,
and
2.3 6 81 (2 8 )
HF-C -H .,
2 4
and HF-C„H„
2 2
D r e s p e c t iv e ly .
The
induced d ip o le moments o f these system s are d is c u s s e d , a lo n g w ith
th a t
o f HF-benzene w hich has been p re v io u s ly d e te rm in e d .
moments
do
not
s c a le
s im p ly
w ith
hydrocarbon
The induced d ip o le
p o la r iz a b ilitie s .
M oreover, th e y do n o t c o r r e la t e w e ll w ith th e fre q u e n cy s h i f t s o f th e HF
subm olecule s t r e tc h in g v ib r a t io n measured i n m a tr ix is o la t io n s tu d ie s .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
IHTRODUCTIOH
The n a tu re o f the in t e r a c t io n o f hydrocarbons w ith
h y d rid e s ,
t iv e
th e
fir s t
HF, H^O, and NH^ i s an area o f c o n tin u a l i n t e r e s t .
d ynam ical s im p li c it y
c h o ic e s f o r
of
HF complexes makes th e se
p r e c is io n s t r u c t u r a l s tu d ie s .
th e w eakly bound com plexes, HF-CgHg [ 1 ] ,
HF-C^H^ [ 3 ] ,
microwave
HF-C^H^,
and HF-C^H^ [4 ]
s p e c tro s c o p y .
and
H F -C ^ ^
hydrogen bonds to
The r e la ­
sp e c ie s
fir s t
The g e o m e tric s t r u c t u r e s o f
HF-CgHg (H F -cyclo p ro p a n e )
[2 ],
have been determ ined u s in g h ig h r e s o lu t io n
As shown by
are
row
T-shaped
th e C-C bond
of
F ly g a re
and
complexes i n
th e
co w o rkers,
w hich
u n s a tu ra te d
HF-CgHg,
th e HF s u b u n it
h yd ro ca rb o n .
ground v ib r a t io n a l s ta te o f HF-CgHg has a v ib r a t io n a lly
The
averaged, sym­
m e t r ic a l to p s t r u c t u r e i n w h ich th e hydrogen atom o f the HF s u b u n it i s
p o in te d
w it h
tow ards
th e
benzene.
The la rg e
a m p litu d e n o tio n s
th e HF s u b u n it have p re ve n te d a d e te rm in a tio n
of
th e
a s s o c ia te d
e q u ilib r iu m
s t r u c t u r e o f t h i s complex and th u s i t i s n o t known w hether th e HF h yd ro ­
gen bonds to the c e n te r o f th e benzene r in g o r to a C-C bond.
An exami­
n a tio n o f th e s t r u c tu r e s o f th e se complexes shows th a t th e hydrogen bond
le n g th s in c re a s e i n
th e o rd e r : CgHg-HF < C2H2~HF < C2H4~HF < CgHg-KF.
W ith th e e x c e p tio n o f CgHg-HF, th e bond le n g th s in c re a s e w it h d e cre a sin g
bond o rd e r o f th e C-C bond.
t io n
in
bond le n g th found i n
It
has been suggested
the se systems i s
[1 ] t h a t th e v a r ia ­
n o t a measure o f d i f f e r ­
ences i n in t e r a c t io n s tre n g th b u t r a th e r a measure o f th e s p a t ia l e x te n t
o f th e e le c tr o n d e n s ity .
The e l e c t r i c d ip o le moment in duced upon c o m p le xa tio n appears to
e m p ir ic a lly
by Bowen,
c o r r e la te d
L e o p o ld ,
w ith
in t e r a c t io n
and K lem perer
[5 ].
s tr e n g th .
be
T h is has been noted
They showed t h a t
fo r
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van
der
Waals complexes th e m agnitude o f
th e induced d ip o le moment c o r r e la te s
w ith th e weak bond s t r e t c h in g fo r c e c o n s ta n t.
T h is r e s u lt i s
seen more
c le a r ly in an e xa m in a tio n o f th e SCF in t e r a c t io n energy by Horokuma [ 6 ] .
Morokuma analyzed van der Waals b in d in g energy
ta tic ,
charge
t io n s .
tra n s fe r,
p o la r iz a t io n ,
term s o f
e le c tr o s ­
and exchange re p u ls io n c o n tr ib u ­
Horokuma's r e s u lt im p lie s t h a t la rg e induced e l e c t r i c m u lt ip o la r
moments
can r e s u lt
whenever
th e
p o la r iz a t io n e n e rg ie s are la r g e .
is
in
a measure o f in t e r a c t io n
e le c t r o s t a t ic ,
If
charge
th e induced e l e c t r i c
tra n s fe r,
and
d ip o le moment
s tr e n g th , i t would be in t e r e s t in g to see i f
a tre n d , s im ila r to th a t fo u n d i n th e hydrogen bond le n g th s , i s observed
in
th e
e le c tr ic
d ip o le
d ip o le
moments o f
moment o f HF-CgHg has been
these HF-hydocarbon com plexes.
p re v io u s ly
measured
[1 ].
The
In
th is
s tu d y we r e p o r t th e d ip o le moments o f HF-C2H2 , HF-Cj H ^ and HF-C^Hg.
EXPERIMENTAL AND RESULTS
The d ip o le moments were measured u s in g th e m o le c u la r beam e le c t r ic
resonance te c h n iq u e .
A beam o f
th e a p p ro p ria te complex was formed by
e xpanding, a t room te m p e ra tu re , a m ix tu re o f 1
carbon i n
atm .
Ar th ro u g h a 100 p n o z z le .
HF and 3 % - 5 To hydro­
The s ta g n a tio n p re ssu re was 1.3
The mass peaks m o n ito re d were IJ( C2 H2 ^ + f o r
^2H4* anci ^3H5+ *'o r ^ ”^3^6*
^2 K3+ *'o r
*n e a °k c a se t *ie
Mj=0» AMj=0 tr a n ­
s i t i o n was measured a t two n o n -z e ro v a lu e s o f th e e l e c t r i c f i e l d .
d ata
a re
n u c le a r
summarized
s p in - s p in
in
T a b le
in t e r a c t io n
I.
of
The h y p e rfin e
th e
HF
s tru c tu re
s u b u n it
was
not
These
due to
th e
re s o lv e d .
D ip o le moments were found by d ia g o n a liz a tio n o f th e K a m ilito n ia n m a tr ix
( in c lu d in g le v e ls up to J= 3) and a re ta b u la te d , to g e th e r w it h th e d ip o le
moment o f HF-CgHg [ 1 ] , in Ta ble I I .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
79
Discussion
The induced d ip o le moments o f these complexes are c a lc u la te d from
^induced = 11
HHF<c°s9>.
In t h i s e x p re s s io n p^p i s th e d ip o le moment o f HF (1.8265 D
is
th e
a x is .
bending
a n g le o f
The a ve ra g in g
2 1/2
<cos 0>
which i s
complex [ 1 - 4 ] .
th e HF s u b u n it measured fro m
is
o ve r
v ib r a t io n s .
<cos0>
is
[7 ]
th e
) and 0
a - in e r tia l
approxim ated
by
o b ta in e d from th e HF s p in - s p in in t e r a c t io n i n each
T h is i s a s ta n d a rd a p p ro x im a tio n w hich a llo w s com paris­
ons to be made between s im ila r com plexes.
A lth o u g h i t s
a b s o lu te v a l i ­
d i t y has n o t y e t been w e ll te s te d , i t i s s t i l l
expected to be u s e fu l in
making
s m a ll
such
com parisons.
a p p ro x im a tio n i s e x a c t.
II.
In
th e
lim it
of
o s c illa t io n s
The induced d ip o le moments a re l i s t e d
in
th is
Table
We a ls o l i s t hydrogen bond le n g th s [ 1 - 4 ] , HF s t r e t c h in g fre q u e n c ie s
and HF bending fre q u e n c ie s
f o r each com plex.
The HF s t r e t c h in g
fre q u e n c ie s and bending fre q u e n c ie s were measured i n an argon m a tr ix by
Andrews and cow orkers [ 8 ,9 ] and T ru s c o tt and A u lt
[1 0 ].
The r e s u lt s i n
T a ble I I
in d ic a t e t h a t HF has th e weakest in t e r a c t io n w it h benzene and
th a t i t s
in t e r a c t io n s tre n g th i s n e a rly th e same w ith e th y le n e and ace­
t y le n e .
The data on HF-CgHg though are somewhat p e r p le x in g .
s h o rt
bond
s t r e t c h in g
le n g th ,
fo rc e
la rg e
induced
c o n s ta n t_ (k g =
c o r r e la t e w e ll w ith \)g o r V^.
van
der
moment,
0.23
and
mdyn/A
la rg e
[2 ])
van
The ve ry
der
Waals
o f HF-CgHg do n o t
Due to th e la c k o f any d ir e c t measure o f
Waals bond d is s o c ia tio n
r e la tiv e
bond d is s o c ia t io n
m ole cule
s tr e tc h in g fre q u e n c ie s ,
e n e rg ie s th e
r e lia b ilt y
e n e rg ie s from in d uce d d ip o le
o f in f e r r in g
moments,
sub­
and bond le n g th s has n o t been te s te d .
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20
The r e s u lt s l i s t e d
in
Table
alw ays be a p p ro p ria te .
p o l a r i z a b ilt y
It
II
is
o f benzene i s
in d ic a t e
th a t
in t e r e s t in g
such in fe re n c e s may n o t
to n o te t h a t even though the
tw ic e t h a t o f e it h e r a c e ty le n e o r e th y le n e
(th e t e n s o r ia l component a lo ng th e van der Waals bond a x is i s b eing com­
pared h e re , see Table I I
le s s th a n t h a t seen i n
) th e induced d ip o le moment i n HF-C..H, i s 0 .1 D
O6
th e e th ly e n e o r a c e ty le n e
com plexes.
be noted t h a t a tte m p ts to account f o r th e m agnitude
moments by u s in g lo w
I t should
o f induced d ip o le
o rd e r e le c t r o s t a t ic
argum ents have n o t been suc­
For CgHg, th e re i s a c le a r d iffe r e n c e
between th e m a tr ix is o la t io n
c e s s fu l.
measurements and th e m o le c u la r c o n s ta n ts o b ta in e d from microwave spec­
tro s c o p y .
Repeated s tu d ie s have shown th e s e lf- c o n s is te n c y o f th e
phase m o le c u la r c o n s ta n ts .
T h is i s
gas
c le a r ly seen by e xa m in a tio n o f th e
s t r e t c h in g fo r c e c o n s ta n ts , in d uce d d ip o le moments, and (where a p p lic a ­
b le ) hydrogen bond le n g th s o f th e fo llo w in g s e r ie s o f com plexes: HF-HH^,
HCN-NH3 . HCCH-NH3 [ 1 3 ] ; HCN-HCK, HCN-HBr, HCN-HC1, HCN-HF [1 4 ];
and A r-
A r, Ar-C02> Ar-B Fg, A r-C IF , A r-S 03 [ 5 ] . Though th e data are lim it e d , th e
m a tr ix
r e s u lt s ,
r e s u lt s .
s u r p r is in g
in
g e n e ra l,
a re
a ls o
c o n s is te n t
w it h
th e
microwave
Thus, i n l i g h t o f these exam ples, th e r e s u lt s on HF-CjH^ are
and c a l l
fo r
a
c lo s e r
e xa m in a tio n
of
r e la te d
hydrocarbon
s e r ie s .
The KC1 complexes o f C f o
form one such s e r ie s .
[ 1 5 ] , C2H4 [ 1 6 ] , CgHg [ 1 7 ] , and CgH6 [1 8 ]
Though th e y are s t r u c t u r a ll y analogous to th e HF
com plexes, th e y d is p la y some u nique c h a r a c t e r is t ic s .
The hydrogen bond
le n g th s and weak bond s t r e t c h in g fo r c e c o n s ta n ts are shown i n Table I I I .
A lso shown are th e d iffe r e n c e s i n hydrogen bond le n g th s between th e HF
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
SI
and HC1
s it u a t io n ,
complexes of each
th e
r e s u lt s
in
hydrocarbon.
Ta ble
h y d ro c a rb o n -a c id in t e r a c t io n s .
Rather than
III
clarifying the
in d ic a t e th e
c o m p le x ity
The van der U aals bond s t r e t c h in g fo rc e
c o n s ta n t and bond le n g th f o r HCl-CgHg suggest t h a t t h i s
s tr o n g ly bound th a n H C l-C ^ ^ and HC1-C2H4 .
o f th e HF r e s u lt s .
In fa c t,
T h is i s
HF complexes
complex i s
more
s u r p r is in g i n l i g h t
th e fo r c e c o n s ta n t o f HCl-CgHg i s a c t u a lly
g re a te r th a n t h a t o f HF-CgHg (lcg = 0.073 m dyn/A ).
s in c e
of
(e x c lu d in g
tho se
w ith
ra re
T h is
i s d is t u r b in g ,
gases)
a re
g e n e ra lly
observed to have s t r e t c h in g fo r c e c o n s ta n ts w hich are a t le a s t a f a c t o r
o f two g re a te r th a n th o se fou n d i n th e c o rre s p o n d in g HC1 com plexes.
The
o b s e rv a tio n t h a t th e hydrogen bond le n g th changes by o n ly 0 .1 0 A between
HF-CgHg and HCl-CgHg i s
in
fo r c e
c o n s ta n t.
th e HF r e s u lt s .
c o n s is te n t w it h th e c o rre s p o n d in g s m a ll change
O ther a sp e cts o f th e KC1 r e s u lt s a re analogous to
The r e s u lt s noted h e re ,
suggest t h a t
knowledge o f HF- and H C l-h ydroca rb on in t e r a c t io n s
is
a more com plete
n ece ssa ry.
Such
knowledge w i l l be v a lu a b le i n d e v e lo p in g o u r u n d e rs ta n d in g o f th e im p o r­
t a n t w a te r-h y d ro c a rb o n in t e r a c t io n .
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REFERENCES
1.
F .A . B a io c c h i, J .H . W illia m s , and W. K le m p ere r,
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A.C. Legon, P.D.
A ld r ic h ,
and W.H. F ly g a re , J.Chem.Phys.
A ld r ic h ,
and W.H. F ly g a re , J.Chem.Phys.
A ld r ic h ,
and W.H. F ly g a re , J.Am.Chem.Soc.
75, 625 (1 9 8 1 ).
1 6.
A.C. Legon, P.D.
75, 2126 (1 9 8 1 ).
1 7.
A.C. Legon, P.D.
102, 7584 (1 9 8 0 ).
1 8.
U.G. Read, E .J . Cam pbell,
and G. Henderson, J.Chem.Phys.
78, 3501 (1 9 8 3 ).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T ab le I.
Frequencies of the J = 0-1, M j - 0, Mfj=0 transitions
m easured at nonzero electric fields for CgHg-HF, CgH^-HF, and CgHg-HF
HF-C3 H6
HF-CgH4
HF-CgH g
E (V /cm )a
Frequency(MHz)
4 9 5 .9 7
5 3 3 2 .6 3 0 (1 0 0 )
9 9 8 .2 6
5 4 5 0 .1 9 8 (8 0 )
7 4 8 .6 5
8 3 1 8 .5 8 0 (5 0 )
1006.00
8 3 6 0 .0 9 6 (1 2 0 )
9 98.41
88994477.1
.11100(5
(555))
1097.92
8 9 6 4 .7 4 0 (6 0 )
a) Electric field known to b e tte r th an 0.1%.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T a b le II.
M o le c u la r c o n s t a n t s of s e v e r a l H F - h y d r o c a r b o n c o m p le x e s . I n c lu d e d a r e
d ip o le m o m e n ts , in d u c e d d ip o le m o m e n ts , h y d ro g e n b o n d le n g th s , h y d r o c a r b o n
p o la r iz a b ilitie s , HF s t r e t c h i n g f r e q u e n c ie s , HF b e n d in g f r e q u e n c ie s a n d
w c alt b o n d s t r e t c h i n g f o r c e c o n s t a n t s .
A6 (D)
^•induced (D)
R h - b (A)
o3
« ii (-^ ) J
r s ( c m '1)
!/„ ( c m -1 )
k s ( m d y n /A )
6
2 .2 4 4 (4 ) a
0 .5 9 a
2 .2 5 a
6 .4 h
3795 b
253 b
HF-CgHg
2.30131(20)
0 .6 5 (1 )
2 .1 9 u
2 .4 h
3747 d
404- d
-
-
h f -c 2h 4
2 .3 0 3 9 (4 5 )
0 .0 7 (2 )
2 .2 2 c
3.6
h
3732 d
41 0 d
-
-
h f - c 3 i -i g
2 .5 0 0 4 (2 0 )
0 .7 0 (2 )
2 .0 9 f
6 .0 1
3753 g
3 02 8
h f - c gh
0 .073a
0 .2 3 f
a) R e fe re n c e 3
b) R e f e r e n c e 0.
c) R e f e r e n c e 4.
d) R e fe re n c e 9.
e ) R e f e r e n c e 3.
f) R e f e r e n c e 2.
g) R e f e r e n c e 10.
h) R e f e r e n c e 11.
i) R e f e r e n c e 12.
j) D iag o n a l p o la r iz a b ilitie s a lo n g IIF d ir e c tio n .
(T-
T a b le III.
H y d ro g e n b o n d le n g th s a n d v.-eak b o n d s t r e tc h in g fo r c e c o n s ta n ts
o f s e v e r a l K C i-h y d ro c arfc o n c o m p le x e s . Also lis te d a r e t h e d ifle re n c
in h y d ro g e n b e n d le n g th s fo r th e HF a n d HC1 c o m p le x e s of e a c h h y d r o c
R h - s fA )
k-s (m d y n e /.4 )
a
2.35
O.GSO
0.10
KC1-C2H2 b
2.41
0.057
0.22
HC1-C2H4
c
2.44
0.051
0.22
HCl-CgH6 d
2.29
0.079
0.20
k c i-c 6 h 6
a)
b)
c)
d)
R e fe re n c e
R efe ren c e
R e fe re n c e
R efe ren c e
R b - hcl~R b -J:F
18.
15.
15.
17.
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CHAPTER 5
THE MICROUAVE AND RADIOFREQUENCY ROTATIOH-INVERSIOH SPECTRUM
OF (S02 ) 2
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T H E MICROW AVE A N D R A D IO F R E Q U E N C Y
R O T A T IO N -IN V E R SIO N S P E C T R U M O F ( S 0 g ) 2 *
D. D. Nelson, Jr.^, G. T. Fraser, and W. Klemperer
D epartm ent of Chemistry
Harvard University
Cambridge, HA 02138
t National Science Foundation Predoctoral Fellow
®Supported by the National Science Foundation.
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ABSTRACT
The radiofrequency and microwave spectrum of (SOg)g has
been m easured using th e m olecular beam electric resonance tech­
nique. The spectrum is ch aracteristic of an asym m etric top in
which the two nonequivalent SOg subunits interchange roles
through a low frequency (70 kHz) tunnelling motion. The spectros­
copic constants obtained for SOg dim er are:
B + C ( MHz )
2
3 - C
2
A
( MHz )
( MH z )
026.160(2)
22.3207(1)
6032.3(6)
A, (MHz )
0.00217(2)
Anr ( MHz )
0.0995(1)
A*, ( MHz )
0.070(1)
Ha ( D)
1.4052(13)
The average distance betw een th e c e n te r of m asses of th e two
subunits, Rcu< is 3.625(10) A. The m agnitude of th e weak bond
e
stretching force constant, ks , is 0.0264(4) m dynes /A . The relative
orientation of th e subunits is not well determ ined, b u t is dem on­
s tra te d to be unlike the orientation of the n e a re s t neighbors in the
sulfur dioxide crystal.
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INTRODUCTION
I t h a s lo n g been hoped t h a t
ro ta tic n a lly
r e s o lv e d
s p e c tr o s c o p ic
s t u d i e s o f g a s p h a se m o le c u la r c l u s t e r s w i l l l e a d , w ith l a r g e enough
c l u s t e r s , t o a f u l l u n d e rs ta n d in g o f t h e condensed p h a s e .
High r e s o l u ­
t i o n s t u d i e s o f g a s p h a se d im e rs h a v e , i n f a c t , been v e ry s u c c e s s f u l and
to
d a te
n e a rly
a
h u n d red
b in a r y
com plexes
have
been
in v e s tig a te d .
U n f o r tu n a te ly , t o t h e b e s t o f o u r know ledge, a tte m p ts t o s tu d y l a r g e r
c lu s te rs
at
ro ta tio n a l
re s o lu tio n
have
been
m if o r m ly
u n s u c c e s s f u l.
H ence, i t w ould be w ise t o t r y t o e x p l o i t t h e in fo rm a tio n p r e s e n t i n t h e
dim er s t r u c t u r e s i n
p hases.
o rd er
to
fu rth e r
our
in d e r s ta n d in g
of
condensed
Homogeneous condensed p h a s e s a r e t h e e a s i e s t t o s tu d y ; t h e r e ­
f o r e . t h e s tu d y o f homogeneous g a s p h a se d im e rs i s o f s p e c i a l im por­
ta n c e .
Ue h av e u n d e rta k e n t h e m icrow ave s p e c tr o s c o p ic s tu d y o f t h e s t r u c ­
t u r a l a n d dynam ical p r o p e r t i e s o f t h e s u l f u r d io x id e d im e r ic com plex.
S o l id s u l f u r d io x id e h a s b e e n d e s c r ib e d a s one o f t h e few t r u e m o le c u la r
c ry s ta ls
[ 1 ,2 ].
T h is s u g g e s ts t h a t in fo r m a tio n c o n c e rn in g t h e S02 p a i r
p o t e n t i a l m ig h t b e p a r t i c u l a r l y u s e f u l i n t h e u n d e rs ta n d in g o f i t s s o l i d
s ta te .
In p a rtic u la r,
i t w ould b e re w a rd in g t o o b s e rv e a c l e a r r e l a ­
t i o n s h i p betw een t h e g a s p h a se dim er s t r u c t u r e and t h e n e a r e s t n eig h b o r
c r y s t a l s t r u c t u r e o f S02 .
Knowledge o f S02 p o t e n t i a l s u r f a c e s , an d o f t h e S02-S 0 2 s u r f a c e i n
p a r t i c u l a r , m ig h t a l s o b e h e l p f u l i n m o d elin g p o s s i b l e p h o to o x id a tio n
m echanism s f o r a tm o s p h e ric S02 .
The o b s e r v a tio n t h a t S02 p h o to o x ia iz e s
o r d e r s o f m agnitude f a s t e r i n p o l l u t e d a i r th a n i n c le a n a i r [ 3 ] , su g ­
g e s t s t h e p o s s i b i l i t y o f t h e in v o lv e m e n t o f a n S02 g a s p h a s e com plex.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
F u rth e rm o re , i n one s tu d y , d i r e c t p h o to o x id a tio n o f S02 dim er t o s u l f u r
t r i o x i d e i n lo t; t e n p e r tu r e oxygen m a tr ic e s was s e e n , w h ile t h e S02 mono­
mer w as fo u n d t o be p h o to c h e m ic a lly i n a c t i v e under t h e same c o n d itio n s
[4 ].
S h is s u g g e s ts t h a t S02 dim er c o u ld be im p o rta n t i n s tu d y in g t h e
" a c i d r a i n " phenomena, s in c e i t
is
known t h a t g a s p h a se S03 form s an
H2S04 a e r o s o l i n t h e p re s e n c e o f w a te r v ap o r 1 5 ].
S he s tu d y o f S02 dim er i s a l s o i n t e r e s t i n g b e c a u se i t
geneous com plex. (HF)2 [ 6 ] ,
( ! I Q ) 2 (7 1 , <HCN)2 [ 8 ] ,
i s a homo­
(H jO ^ [9 1 , (EHg)2
[ 1 0 ] , (00) 2 [ i i ] a n d (I3D) 2 [12] a r e o th e r homogeneous sy ste m s w hich have
been i n v e s t i g a t e d w ith
ro ta tio n a l
r e s o lu tio n .
The exchange symmetry
p r e s e n t i n homogeneous d im e rs im p lie s t h e p o s s i b i l i t y o f i n v e r s io n tu n ­
n e l l i n g when t h e s u b u n its a r e n o t e q u iv a l e n t .
In v e r s io n t u n n e l l i n g h a s
been c l e a r l y o b se rv e d i n (HF>2 [6] a n d i n (HC1) 2 [ 7 ] . S02 dim er p r o v id e s
a n o p p o r tu n ity t o s tu d y i n v e r s io n t u n n e l l i n g i n a complex whose s u b u n its
h av e r a t h e r l a r g e re d u c e d m a s s e s .
In te re s tin g
dynam ics h av e a lr e a d y
b een o b s e rv e d i n a n o th e r S02 com plex. A r-S02 h a s been shown t o be a T
sh ap ed com plex, i n w hich t h e S02 u n i t tu n n e l s betw een tw o c o n f ig u r a tio n s
by r o t a t i n g a b o u t i t s a i n e r t i a l a x i s [ 1 3 ] . The in v e r s io n fre q u e n c y f o r
th is
m o tio n
is
9 7 5 .1 (9 )
MHz.
It
is
n o t s u p ris in g ,
th e re fo re ,
(S02 ) 2 a l s o shows i n t e r n a l t u n n e l l i n g dynam ics.
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th a t
93
emsflaam
The s p e c t r a w ere o b ta in e d u s in g t h e m o le c u la r beam e l e c t r i c r e s o ­
nance te c h n iq u e .
The d e t a i l s o f t h e m o le c u la r beam s p e c tro m e te r have
been d e s c r ib e d p r e v io u s ly an d w i l l n o t be d is c u s s e d h e r e [ 1 4 ] .
An S02
dim er beam w as form ed by a s u p e rs o n ic e x p a n sio n o f a m ix tu re o f i s s u l ­
f u r d io x id e i n a rg o n th ro u g h a 75|i n o z z le a t
s ta g n a t io n p r e s s u r e was 2 .3 a tm o sp h e re s.
d u c te d w h ile m o n ito rin g t h e
room te m p e ra tu re .
The
S p e c tr a l s e a r c h e s w ere con­
(S02 >2+ m ass s p e c t r a l peak
(m /e =
128).
R esonances c o u ld a l s o b e d e te c te d on t h e S02 + m ass p e a k , how ever, th e
s i g n a l t o n o is e r a t i o w as s m a lle r t h e r e th a n on t h e p a r e n t p e a k .
Beam
d e f l e c t i o n e x p e rim e n ts (ev en w ith a n e a t S02 beam) showed S02 tr im e r t o
be n o n p o la r .
Hence, t h e s p e c t r a c o u ld b e unam biguously a t t r i b u t e d t o
S02 d im e r.
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9W
RESULTS
H ie o b se rv e d z e r o - f i e l d
T a b le I .
tra n s itio n s
of
(S02 >2 a r e
p r e s e n te d
in
A ll o f t h e s e t r a n s i t i o n s s a t i s f y a - ty p e s e l e c t i o n r u l e s and
ca n be f i t t o a H a m ilto n ia n ,
»0 ■ Ba - (- 1)Kp + K° (^ 2 E)
where 6 ^
is
a n e x p e r im e n ta lly
d e te rm in e d c o n s ta n t t o
b e d is c u s s e d
below an d Ha i s a s e m i - r i g id r o t o r H a m ilto n ia n f o r a n a sym m etric t o p
[1 5 ],
Ha “ S ~2TC£2 * (A " E^
C )£2
d
H ie quantum number a s s ig n m e n ts i n T a b le I c o r r e l a t e t o t h e n c n p e rtu rb e d
a sym m etric r o t o r .l a b e l s d e r iv e d fro m Ha .
H ie ^ p e c tr o c o p ic c o n s ta n ts o f
(S02 >2 w ere d e te rm in e d fro m a n o n lin e a r l e a s t s q u a r e s f i t o f t h e f r e ­
q u e n c ie s c a l c u l a t e d fro m HQ t o t h e o b se rv e d t r a n s i t i o n f r e q u e n c ie s .
H ie
s p e c tr o s c o p ic c o n s ta n ts o b ta in e d a r e p r e s e n te d i n T a b le I I .
H ie se co n d te rm i n H0 in v o lv e s 6 ^
a n d d e s c r i b e s a s h i f t i n each
e n e rg y l e v e l o f t h e com plex d i e t o i n v e r s io n t u n n e l in g .
H ie s e s h i f t s
c a n b e v iew ed a s t h e r e s u l t o f t h e s p l i t t i n g o f e a c h r o t a t i o n a l s t a t e o f
th e
sy ste m i n t o tw o r o f a t i c n - i n v e r s i c n s t a t e s w hich a r e s e p a r a te d i n
fre q u e n c y by 6 ^ ^ .
u re 1 .
H ie r e s u l t i n g e n e rg y l e v e l d iag ram i s s h a m i n F ig ­
As i s i n d ic a te d i n t h i s f i g u r e , we o b s e rv e c n ly cne h a l f o f t h e
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a - ty p e t r a n s i t i o n s e x p e c te d f o r t h a t l e v e l s t r u c t u r e .
p a ir
of
le v e ls ,
one
of
th e
ro ta tio n -in v e rs ic n
Hence, f o r each
s ta te s
( th e
cue
r e p r e s e n te d by d ash ed l i n e s ) m ust be a b s e n t.
The c h o ic e o f w hich s t a t e
is
of
m is s in g
depends s o l e l y
upon t h e
p a rity
th e
sum,
+
K
e x p re s s e d i n HQ.
. as
K
IT
^
T h is i m p l ie s t h a t r o t a t i o n a l s t a t e s w hich a r e sym­
m e tr ic w ith r e s p e c t t o a n o v e r a l l r o t a t i o n o f t h e com plex a b o u t t h e b
i n e r t i a l a x i s by n a r e p a i r e d w ith t h e s y n m e tric (low er e n e rg y ) in v e r ­
s io n s t a t e an d t h a t a n ti- s y m m e tr ic r o t a t i o n a l s t a t e s a r e a s s o c i a te d w ith
t h e a n t i - s y m e t r i c (h ig h e r e n e rg y ) in v e r s io n s t a t e .
I t i s n o t u n rea so n ­
a b le t h a t h a l f o f t h e s t a t e s i n S02 dim er s h o u ld be u n o b se rv e d .
Each
n u c le u s i n t h i s s p e c i e s i s a q ? in z e r o b o so n .
h ig h
d e g re e
of
s y m e try
w a v e fu n c tic n s
s ta te s .
w ith
S in p le
p re s e n t,
th e
it
p ro p er
may n o t
exchange
g ro u p t h e o r e t i c a l
be
B ecause o f
p o s s ib le
p ro p e rtie s
to
fo r
th e
th e
c o n s tr u c t
m is s in g
arg u m en ts s u g g e s t t h a t t h i s e f f e c t
c o u ld b e p r e s e n t i n t h e s p e c tr o s c o p y o f S02 d im e r.
U n f o r tu n a te ly , t h e
s t r u c t u r e an d dynam ics o f t h i s sy ste m a r e n o t w e ll enough u n d e rs to o d t o
d e m o n s tra te t h i s c o n c lu s i v e l y .
None t h e l e s s ,
th e f a c t
th a t
ro ta tio n -in v e rs ic n
tra n s itio n s
a re
o b s e rv e d i n a n a - t y p e s p e c tru m im p lie s t h a t ji- i s a n t i - s y n m e t r i c w ith
resp ect to
th e
70 kHz i n v e r s io n m o tio n .
S in c e t h e
b etw een e q u iv a le n t c o n f i g u r a t i o n s . |ifl m ust be t o t a l l y
com plex tu n n e l s
a n ti-s y i(n e tric ,
a n d t h e in v e r s io n m o tio n a t 70 kHz m ust in v o lv e t h e in te r c h a n g e o f two
n o n - e q u iv a le n t S02 s u b u n it s .
O b s e rv a tio n o f t h e p u re i n v e r s io n t r a n s i ­
t i o n o f S02 dim er i s n o t p o s s i b l e s in c e a l l t r a n s i t i o n s m ust s a t i s f y a fy p e s e l e c t i o n r u l e s f o r b o th r o t a t i o n a n d i n v e r s i o n . The t r a n s i t i o n s
w hich we o b s e rv e , t h e r e f o r e , o c c u r a t f r e q u e n c ie s V w here.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94
V - Iv0 4 ( - 1) ^ + \
I n t h i s e x p r e s s io n ,
j
an d KQ l a b e l t h e low er s t a t e i n t h e p u re r o t a ­
t i o n a l t r a n s i t i o n a n d \)Q i s t h e fre q u e n c y o f t h i s u n p e rtu rb e d r o t a t i o n a l
tra n s itio n .
S in c e 8 ^
i s o n ly 7 0 (1 ) kHz, i t i s a v e ry s n a i l p e r t u r b a ­
t i o n t o t h e f r e q u e n c ie s o f t h e m icrow ave t r a n s i t i o n s p r e d i c t e d frctn K .
O
However, H_ a l s o p r e d i c t s t h e e x is t a n c e o f r a d i o fre q u e n c y t r a n s i t i o n s
CL
a c r o s s a sy n m e try d o u b l e t s .
fiany o f t h e s e w ould h av e t r a n s i t i o n fre q u e n ­
c i e s below 5 kHz i f i t w ere n o t f o r t h e 6 ^
of
th is
te rm
im p lie s
th a t
(S02 >2 n u s t
te rm i n H0 .
e x h ib it a
C o n s id e ra tio n
s tr o n g
a b s o r p tio n
betw een 65 an d 75 kHz w hich c o n s i s t s o f a s u p e r p o s itio n o f marry o v e r la p ­
p in g r e s o n a n c e s .
F ig u re 2 .
T h is a b s o r p tio n i s , in d e e d , s tr o n g a n d i s d is p la y e d i n
S in c e t h e u n p e rtu rb e d r o t a t i o n a l l e v e l s , i n t h e s e c a s e s , a r e
n e a r l y d e g e n e r a te ,
tio n s s lig h tly
d o u b le ts
one c a n v i e ; t h e s e re s o n a n c e s a s i n v e r s io n t r a n s i ­
d is p la c e d by t h e r o t a t i o n a l s p l i t t i n g s .
in v o lv e d
The asy n m etry
i n t h i s s u p e r p o s i ti o n in c lu d e a l l o f t h e p o p u la te d
d o u b le ts w ith K2.4, p i t s t h e K»3 d o u b le ts f o r J “ 3 . 4 . a n d 5 .
I t w ould b e s a t i s f y i n g a n d p h y s i c a l l y m ean in g fu l t o d e r i v e from t h e
t m n e l l i n g fre q u e n c y an e s ti m a t e o f t h e h e i g h t o f t h e b a r r i e r t o in v e r ­
s io n .
fa c e ,
I f t h e r e w ere o n ly tw o e q u iv a le n t m inima i n t h e p o t e n t i a l s u r ­
th e
pro b lem c o u ld b e t r e a t e d
in
one d im e n sio n .
U n f o r tu n a te ly
t h e r e a r e f o u r e q u iv a le n t m inim a i n t h e p o t e n t i a l s u r f a c e .
S in c e t h e
p o t e n t i a l s u r f a c e n e e d s t o b e m odeled i n a t l e a s t tw o d im e n s io n s , our
u n c e r t a i n t y o f t h e n a tu r e o f i t s sh a p e p r e v e n ts a m e a n in g fu l e s tim a tio n
o f t h e t m n e l l i n g p a th an d t h e c o rre s p o n d in g b a r r i e r h e i g h t .
T he a a x ro o n e n t o f t h e d i p o le moment o f
(S02 >2 was d e te rm in e d by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
91
m easu rin g t h e S ta r k e f f e c t o f t h e 321(|M j |= 2) t o 3J 2 ( |l lj |= 2 ) asy n m etry
d o u b le t t r a n s i t i o n .
W iese d a ta a r e sum m arized i n T a b le I I I .
T r a n s i­
t i o n s in v o lv in g o th e r Mj com ponents w ere a ls o m easured t o a i d i n our
a ssig n m e n t o f t h e S ta r k s p e c tru m .
The a p p r o p r ia te H a m ilto n ia n i s
H ® H - |i«E
o
~ ~
w here |i i s t h e m o le c u la r d i p o le moment a n d E i s t h e e l e c t r i c f i e l d .
mm
The
asy n m etry d o u b le t w as t r e a t e d a s a tw o l e v e l sy stem an d a n a l y t i c e x p re s ­
s io n s w ere u se d t o d e te rm in e
1 .4 0 5 2 (1 3 ) D.
ji_
q
.
The v a lu e o f |i_ was d e te rm in e d t o be
a
The a component o f t h e d i p o le moment was a l s o m easured on
t h e 42 a sy n m etry d o u b le t w here an i d e n t i c a l v a lu e was fo u n d (1 .4 0 6 4 (6 9 )
D) w ith in
e x p e rim e n ta l u n c e r t a i n t i e s .
Hence t h e
a
component o f th e
d i p o le moment o f (S02 ) 2 i s s m a lle r t h a n t h e d i p o le moment o f t h e S02
monomer (1 .6 1 7 (1 6 ) D ) [ 1 6 ] .
The d e te r m in a tio n o f t h e a v e ra g e s t r u c t u r e o f S02 dim er from t h e
s p e c tr o s c o p ic c o n s ta n t s an d na i s d i f f i c u l t .
I n f a c t , t h e a v e ra g e d i s ­
ta n c e betw een t h e c e n te r o f m asses o f t h e S02 s u b u n it s . Rq j , i s t h e o i l y
s t r u c t u r a l p a ra m e te r w hich i s w e ll d e te rm in e d .
A.
I t s v a lu e i s 3 .8 2 5 (1 0 )
Rq j i s known w e ll b e c a u se B + C i s m easured p r e c i s e l y .
From Rq .,
B + C. a n d A j. a s t r e t c h i n g f o r c e c o n s ta n t . kg . f o r t h e v a n d e r U a a ls
bond, may b e c a l c u l a t e d
1 1 7 ].
The v a lu e o f kg o b ta in e d i s
0 .0 2 6 4 (4 )
m dynes/A.
The r e l a t i v e o r i e n t a t i o n o f t h e s u b u n its i s
d ista n c e
of
th e ir
s e p a r a ti o n .
l e s s c l e a r th a n t h e
A m u ltip a ra m e te r s e a r c h was a t t e n p te d
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
o v e r t h e f i v e o r i e n t a t i o n a l d e g re e s o f freedom i n a n a tte m p t t o f i n d
th o s e s t r u c t u r e s c o n s i s t e n t w ith t h e e x p e rim e n ta l r o t a t i o n a l c o n s ta n ts
a n d t h e m easured v a lu e o f na .
Only a h a n d fu l o f r e a s o n a b le s t r u c t u r e s
w ere fo u n d th o u g h s e v e r a l hundred th o is a n d w ere exam ined.
T hese s t r u c ­
t u r e s w ere n o t n e a r l y i d e n t i c a l and w ere n o t co n v e rg in g i n a n obvious
m anner t o
a u n iq u e c o n f i g u r a t io n .
The d e t a i l s o f t h e m u ltip a r a n e te r
s e a r c h and o f t h e s t r u c t u r e s p e r m itte d a r e g iv e n i n t h e a p p e n d ix ,
in
o rd e r t o r e p o r t a r n iq u e an d a c c u r a te s t r u c t u r e f o r f o r S02 d im e r, we
w ould n e e d m ore in fo r m a tio n a b o u t t h e
s p e c ie s .
d ip o le moment v e c to r
of th is
A good e s tim a te o f t h e in d u c e d d i p o le moment c o n tr i b u ti o n and
a m easurem ent o f t h e p e r p e n d ic u la r compone n t s o f t h e d ip o le moment would
e a c h b e v e ry h e l p f u l i n e l u c i d a t i n g t h e s t r u c t u r e o f S02 d im e r.
I t is
i n t e r e s t i n g t o n o t e , how ever, t h a t t h e s t r u c t u r e s d is c o v e r e d by th e mul­
tip a r a m e te r
s e a r c h te n d t o
in v o lv e o r i e n t a t i o n s i n w hich n e it h e r S02
s u b u n it h a s i t s a - a x i s p a r a l l e l o r even n e a r ly p a r a l l e l t o t h e l i n e con­
n e c tin g t h e s u b u n i t s ' c e n te r o f m a sse s.
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DISCUSSION
S in c e s o l i d s u l f u r d io x id e i s
t r u e m o le c u la r c r y s t a l ,
it
is
th o u g h t t o be a good e x a n p le o f a
i n t e r e s t i n g t o compare t h e s t r u c t u r e o f
t h e g a s p h a se S02 dim er complex w ith t h e
fo m d in
S02 c r y s t a l s
[2 ],
n e a re st
s tru c tu re
H ie d i s t a n c e betw een t h e c e n te r o f m asses
o f t h e n e a r e s t n e ig h b o r s i n t h e c r y s t a l , R ^ ,
is ,
n e ig h b o r
i s 4 .2 8 A .
T h is d is ta n o e
o f c o u r s e , much g r e a t e r th a n t h a t fo u n d i n t h e g a s p h a s e complex
(Rq j « 3 .8 2 5 (1 0 ) A ) .
F u rth e rm o re , t h e m o le c u le s i n t h e c r y s t a l a r e a ls o
o r i e n t e d d i f f e r e n t l y th a n i n t h e com plex.
The a component o f t h e d ip o le
moment w hich w ould b e e x p e c te d f o r t h e n e a r e s t n e ig h b o r c r y s t a l s t r u c ­
t u r e i s l e s s t h a n 0 .2 D ( n e g le c tin g t h e in c b c e d d i p o le moment c o n tib u t i c n ) , w hereas t h a t m easured i n t h e dim er w as 1 .4 0 5 2 (1 3 ) D.
F in a lly , in
t h e c r y s t a l t h e a i n e r t i a l a x i s o f one o f t h e S02 s u b u n its i s p a r a l l e l
t o t h e l i n e c o n n e c tin g t h e n e a r e s t n e ig h b o r s ' c e n t e r s o f m ass, w h ile th e
o th e r s u b u n it h a s i t s
lin e .
a i n e r t i a l a x i s o r i e n t e d p e r p e n d ic u la r t o t h a t
Our r e s u l t s s u g g e s t t h a t i n S02 d im e r, n e i t h e r
s u b u n it h a s i t s
a - a x i s a lig n e d p a r a l l e l o r n e a r l y p a r a l l e l w ith t h e l i n e c o n n e c tin g t h e
s u b u n i t s ' c e n t e r s o f m ass.
I t seem s, t h e n ,
t h a t t h e g a s p h a s e dim er
s t r u c t u r e and t h e n e a r e s t n e ig h b o r c r y s t a l s t r u c t u r e f o r SO,, a r e s t r i k ­
in g ly d i s s i m i l a r .
T h is i s d is a p p o in tin g , s i n c e , t h e d e m o n s tra tio n o f a
c l e a r r e l a t i o n s h i p ( i f i t e x i s t s ) betw een t h e g a s p h a s e s t r u c t u r e o f a
w eakly bound com plex a n d i t s
c o rre s p o n d in g
c ry s ta l
s tru c tu re ,
c o u ld
p ro v e v e ry h e l p f u l t o o u r u n d e rs ta n d in g o f t h e weak i n t e r a c t i o n s p r e s e n t
i n e a ch o f t h e s e s y s te m s .
E xam ination o f t h e s p l i t t i n g s i n t h e e n e rg y l e v e l diag ram o f S02
dim er i n d i c a t e s t h e e x is te n c e o f a lew fre q u e n c y in v e r s io n m o tio n .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
As
d is c u s s e d a b o v e , t h i s n o tio n in v o lv e s t h e c o n c e r te d in te r c h a n g e o f th e
tw o n o n e q u iv a le n t s u b u n its o f t h e com plex.
i n t e r e s t i n g b e c a u se i t i s so slo w .
l i n g i s 14 m ic ro se c o n d s.
T h is n o t io n i s p a r t i c u l a r l y
The p e r io d o f t h e exchange tu n n e l­
I t i s im p o rta n t t o n o te t h a t i t i s q u i t e po s­
s i b l e t h a t o th e r t m n e l l i n g n o tio n s o c c u r i n
f a s t e r tim e s c a l e , a s i n A r-S02 [ 1 3 ] ) .
(S02 ) 2 (p e rh a p s on a much
The e f f e c t s o f t h e s e h y p o th e ti­
c a l m o tio n s m ig h t o n ly be e v id e n t from t h e o b s e r v a tio n o f p e r p e n d ic u la r
tra n s itio n s .
P r e lim in a r y
b e e n , s o f a r , u n s u c c e s s f u l.
a tte m p ts t o
o b s e rv e t h e s e
t r a n s i t i o n s have
T h is m ig h t be e x p la in e d by t h e e x is t e n c e o f
l a r g e p e r t u r b a t i o n s i n t h e p e r p e n d ic u la r s p e c t r a due t o h ig h fre q u e n c y
i n t e r n a l m o tio n s .
A l t e r n a t i v e l y , s m a ll p e r p e n d ic u la r d i p o le moment com­
p o n e n ts o r p o o r e x p e rim e n ta l s i g n a l t o n o is e r a t i o , m ig h t be r e s p o n s ib le
f o r t h i s d i f f i c u l t y i n t h e s p e c tr o s c o p y o f S02 d im e r.
He h o p e , i n t h e
f u t u r e , t o m easure p e r p e n d ic u la r t r a n s i t i o n s o f S02 d im e r.
T hese t r a n ­
s i t i o n s w ould a i d i n t h e s t r u c t u r e d e te r m in a tio n f o r t h i s com plex by
p r o v id in g a
p r e c i s e m easure o f A a n d a l s o b y d e te rm in in g t h e d ip o le
moment com ponents a lo n g t h e b a n d c i n e r t i a l a x e s .
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The o r i e n t a t i o n o f e a ch S02 u n i t i s
o r d in a t e sy s te m .
d e s c r ib e d by a s e p a r a te co­
The z a x e s o f t h e tw o c o - o r d i n a t e sy ste m s a r e c o in ­
c i d e n t . b u t t h e o r i g i n o f fra m e 2 i s t r a n s l a t e d from t h a t o f fram e l in
t h e p o s i t i v e z d i r e c t i o n by E g j.
t h e c o - o r d i n a t e sy ste m s a r e
F u rth e rm o re , t h e x z a n d y z p la n e s of
c o in c id e n t.
Each S02 u n i t i s
in itia lly
a li g n e d w ith i t s a i n e r t i a l a x i s a lo n g t h e z a x i s , i t s b i n e r t i a l a x is
a lo n g t h e y a x i s a n d i t s c i n e r t i a l a x i s a lo n g t h e x a x i s .
o rie n ta tio n
of
t h e S02 u n i t i s
The d e s ir e d
s p e c i f i e d by t h e v a lu e o f t h e E u ler
a n g le s ( a , p . y ) w hich r o t a t e i t t o i t s p ro p e r p o s i t i o n .
We d e f in e our
E u le r a n g le s a c c o rd in g t o t h e c o n v e n tio n o f M essiah [ 1 8 ] .
A m u ltip a ra m e te r s e a r c h w as c o n d u c te d o v e r f i v e in d e p e n d e n t r o t a ­
tio n a l
d e g re e s
of
freed o m
w ith
a
7 .5 °
s te p
s iz e .
S t r u c t u r e s w ere
a c c e p te d w hich p o s s e s s e d b o th t h e r o t a t i o n a l c o n s ta n t s a n d t h e a com­
ponent o f
th e
d i p o le moment m easured i n
th e
com plex.
The c r i t e r i a
r e q u i r e d t o a c c e p t a s t r u c t u r e w ere c o n s id e r a b ly l e s s s t r i n g e n t t h a n t h e
u n c e r t a i n t i e s r e p o r t e d i n o u r m easured v a lu e s a n d r e f l e c t e d o u r e s tim a ­
t i o n o f t h e e r r o r s i n h e r e n t i n o u r m o d el.
MHz. i n
We a llo w e d e r r o r s i n A o f 2
2- C? o f 1 KHz. i n & -=- £ ) o f 1 MHz. a n d i n na o f 0 .2 5 D.
number o f c o n f i g u r a t io n s a c c e p te d w as 1 8 .
The E u le r a n g le s o f n in e o f
t h e a c c e p te d s t r u c t u r e s a r e p r e s e n te d i n T a b le IV .
The m ag n itu d e o f th e
d i p o le moment component a lo n g t h e a i n e r t i a l a x i s ,
( n e g le c tin g
The
u , i s a l s o g iv e n
in d u ce d d i p o le moment a n d v i b r a t i o n a l a v e ra g in g e f f e c t s ) .
An a d d i t i o n a l s t r u c t u r e may b e o b ta in e d from e a ch o f th o s e l i s t e d
T a b le IV by a d d in g 180® t o t h e l i s t e d v a lu e s o f b o th y 1 a n d y 2 .
in
The new
s t r u c t u r e h a s t h e same r o t a t i o n a l c o n s ta n t s a s t h e o r i g i n a l s t r u c t u r e .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
but its dipole moment vector is inverted.
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102
REFERENCES
1.
F . A. C o tto n a n d G. W ilk in so n , Advanced I n o r g a n ic C hem istry
( I n t e r s c i e n c e . New Y ork. 1 9 7 2 ).
2.
B. P o s t, R. S . S chw artz a n d I . F ankuchen, A cta C r y s t. 5 , 372 (1 9 5 2 ).
3.
I . 11. C a n p b e ll, E nergy an d t h e Atm osphere (W iley, London, 1977)
4.
J . R. Sodeau a n d E . K. C. L ee, J . Chem. P h y s. 84, 3358 (1 9 8 0 ).
5.
J . H e ik le n , A tm ospheric C h em istry (A cadem ic, New Y ork. 1 9 7 6 ).
6.
T . R . Dyke, B . J . Howard a n d W . K lem p erer. J . Chem. P h y s. 5 6 ,
2442 (1 9 7 2 ).
7.
N. O hashi an d A. S . P in e , J . Chem. P h y s. 8 1 , 73 (1 9 8 4 ).
8.
L . W. B uxton, E. J . C an p b ell an d W. H. F ly g a r e , Chem. P h y s. 5 6,
399 (1 9 8 1 ).
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9.
T . R. Dyke, K. H. Hack a n d J . S . H u e n te r, J . Chan. P h y s. 66
498 (1 9 7 7 ).
1 0 . G. T . F r a s e r , D. 0 . K e lso n , J r . , A. C. G ia ro an d U. K lem perer.
J . Cham. P h y s. ( t o be p u b l is h e d ) .
1 1 . P . A. Vanden B o u ten , J . H. S te e d . L . S . B e r n s te in a n d 17. .K lem perer,
Ap. J . 2 3 4 , 503 (1 9 7 9 ).
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S.
E . N ovick, H o le c . P h y s. 4 4 , 145 (1 9 8 1 ).
1 3 . R. L . DeLecn, A. Y okozeki a n d J . S . H u e n te r. J . Chem. P h y s.
7 3 . 2044 (1 9 8 0 ).
1 4 . K. H. Bowen, H arvard U n i v e r s i ty P h.D . T h e s is (1 9 7 7 ).
1 5 . J .K .G . W atson. J . Chem. P h y s. 4 6 . 1935 (1 9 6 7 ).
1 6 . R.D . Brown, F .R . B urden, an d G .II. Hohay. A u s t. J . Chem. 2 2 , 251 (1 9 6 9 ).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 7 . K.R. L eo p o ld , G .T . F r a s e r , an d T-7. K lem p erer, J . Chem. P h y s. 80,
103 9 (1 9 8 4 ).
N ote t h a t t h e r e i s a ty p o g r a p h ic a l e r r o r i n t h e
e x p r e s s io n f o r ks (e q u a tio n ( 1 3 ) ) .
The h i n t h e denom inator
o u g h t t o be
I S . A. M e ssia h , Q iantum M echanics (John W iley an d S e n s , New Y ork,
1 9 7 6 ).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 1.
Observed zero-field transitions for (SOg)g
v 0bs (MHz)
J Kf K,
Vots'Veal (MHz)
221
0.1747(13)
-0.003
734
735
0.249(2)
-0.002
835
B36
0.3245(60)
-0.003
S21
322
1.3083(10)
-0.001
422
423
3.6483(20)
0.001
523
524
8.7430(25)
0.000
624
825
17.2758(23)
0.001
725
726
31.2815(25)
0.001
B27
92B
81.700(7)
-0.005
4 13
4 14
446.341(3)
0.004
5 14
5 15
669.670(3)
0.004
615
6 16
937.3245(23)
CD
r4
a-
7 17
1249.842(5)
-0.005
441
542
9245.088(9)
0.006
440
541
9245.225(6)
0.003
cm
533
9252.336(6)
-0.001
431
532
9252.488(6)
-0.007
541
642
11093.724(35)
0.002
542
643
11093.859(15)
-0.002
532
833
11102.626(10)
0.004
533
634
11102.715(11)
0.002
843
744
12942.151(3)
0.001
842
743
12942.281(6)
-0.009
834
735
12952.687(18)
0.016
833
734
12952.936(20)
0.017
i
220
-0.001
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Table II.
Spectroscopic constants of (SOg)g
^ -^ -(M H z)
92 6 .1 6 0 (2 )
2 2 .3 2 0 7 (1 )
A {MHz)
695B.5(6)
Lj{MHz )
0.00217(2)
H rA M H z)
0.0995(1)
6 ^ (MHz)
0.070(1)
M a&)
1.4052(13)
U ncertainties are two standard erro rs as determ ined from the
le ast squares fit.
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Table 111.
Observed non-zero field transitions of (S0g)2
Transition
321(A/,=2) - 322(AO=2)
422(M/=2) - 422(Af/=2)
E (V/cm)e
frequency(MHz)
0.00
1.3083(10)
1.0158
1.3945(10)
2.501
1.7625(50)
5.022
2.710(7)
9.BB5
4.B873(10)
0.00
3.8483(20)
9.993
4.617(6)
a) Electric field known to b e tte r th an 0.1%.
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Table IV.
P o ssib le s tr u c tu r a l param eters fo r (S O j^ *
(deg)
Yj (deg)
<*2
(deg)
iB2 (deg)
Y2 (deg)
(D)
60.0
-2 2 .5
67.5
45.0
45.0
1
52.5
-37.5
67.5
52.5
30.0
1
52.5
30.0
67.5
52.5
37.5
1
67.5
15.0
75.0
37.5
45.0
1
67.5
-1 5 .0
75.0
37.5
52.5
1
67.5
30.0
82.5
37.5
0 .0
0
67.5
30.0
82.5
37.5
7.5
0
67.5
-22.5
105.0
37.5
52.5
1
75.0
15.0
112.5
30.0
37.5
0
* The s tr u c tu r a l param eters In th e ta b le a re defined in th e appendix
a . i s s e t equal to zero fo r each of the s tr u c tu r e s .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
e is s b e
c& m o ss
F ig u re 1 .
A p o r ti o n o f t h e e n e rg y l e v e l d iag ra m o f SO^ d im e r.
\)Q
i s t h e fre q u e n c y o f t h e u n p e rtu rb e d r i g i d r o t o r t r a n s i t i o n an d
6in v ^
t *ie fre q u e n c y o f t h e i n v e r s io n m o tio n . The p a r i t y
o f e a c h s t a t e under t h e in v e r s io n m otion i s i n d i c a t e d .
d a sh ed e n e rg y l e v e l s a r e n o t o b s e rv e d e x p e r im e n ta lly .
The
The
o b se rv e d t r a n s i t i o n o c c u rs a t »0 + 6i n v *
F ig u re 2 .
The " p u re " i n v e r s io n t r a n s i t i o n f o r t h e a moment r e v e r s a l
o f S02 d im e r.
T h is t r a n s i t i o n i s a c t u a l l y t h e s u p e r­
p o s i t i o n o f a l l t h e r o t a t i o n - i n v e r s i c n t r a n s i t i o n s f o r v/hich
t h e r o t a t i o n a l s e p a r a ti o n i s v e ry s m a ll com pared t o th e
i n v e r s io n s p l i t t i n g ( 70(1) k H z ).
The l a r g e f e a t u r e in c lu d e s
t h e asy n m etry d o u b le t t r a n s i t i o n s f o r K 2. 4 and f o r K=3,
J » 3 .4 .
The s m a ll f e a t u r e i s t h e 53 d o u b le t.
u
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/
\
\
\
/
/
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
R e p ro d u c e d with perm ission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 6
ELECTRIC DIPOLE MOMENT OF X % OH AND OD IN SEVERAL
VIBRATIONAL STATES
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
IH
1502
Electric dipole moment of A"211 OH and OD in several vibrational states'
K. 1.
P e te rs o n .
G. T.
F ra se r, an d
W.
K le m p e re r
D ep a rtm en t o f C he m istry . H a rva rd U niversity. C am bridge. M A 0 2 13 8 U .S .A .
R eceived July 19. 1984
D ipole m om ents arc m easured fo r O H ("11 ) in the v = 0 . 1. and 2 vibrational states and f o r O D in the v = 0 and 1 states
using the m olecular beam electric reso n an c e technique. T hese arc listed in the table below .
OH
OD
ft
J
V
|i( D )
1/2
3 /2
3 /2
3 /2
3 /2
3 /2
1 /2
3 /2
3 /2
3 /2
3 /2
3 /2
0
0
1
2
1.6549(13)
1.65520(10)
1.66257(16)
1.6648(10)
1.65283(16)
1.6550(27)
0
1
A very accurate value o f 0 .0 0 7 3 5 (7 ) D is obtained fo r the d ifference in dipole m om ents betw een the v = 0 and 1 vibrational
states o f O H . T h is is w ithin 209c o f the best theoretical results. T he dependence on vibrational state is very n o n lin ear, w hich
is also in agreem ent w ith theoretical resu lts. F in ally , the difference betw een the v = 0 dipole m om ents o f O H and O D is close
to the ex p ected value.
O n a m esure les m om ents d ip o laires p o u r O H ( “111 dans les etats vibrationncls v = 0 . 1, et 2 . ainsi que po u r O D d a n s les
6tats v = 0 et 1. en utilisant la tech n iq u e dc resonance electroniquc de faisceau m oleculaire. Le tableau suivant d o n n e les
resu ltats o b ten u s.
OH
OD
ft
J
V
p.(D )
1 /2
3 /2
3 /2
3 /2
3 /2
3 /2
1/2
3 /2
3 /2
3 /2
3 /2
3 /2
0
0
1
2
0
1
1.6549(13)
1,65520(10)
1.66257(16)
1.6648(10)
1.65283(16)
1.6550(27)
U ne v aleu r tres p recise de 0 .0 0 7 3 5 (7 ) D est obtenue po u r la d ifference des m om ents d ip o laires entre les etats v ib ratio n n cls
v = 0 et v = 1 de O H . C ette v aleu r est en accord a m ieux de 2 0 9c avec les m eilleurs resultats th eoriques. L a dep en d en ce
d e P etat vibrationnel est fo rtem en t non lin eaire. ce qui est aussi en accord avec les resultats th eoriques. E nfin, la difference
en tre les m om ents d ipolaires de O H et de O D . p our v = 0 est proche dc la v aleu r attendue.
[T raduit p ar le jo u rn a l]
Cun. J. Phyv 62. 1502 (19841
Introduction
The hydroxyl radical has been the subject of a consid­
erable amount of research since the beginning of this
century (I). This interest has been stimulated in part
from the detection of OH in a large number of natural
sources, such as flames (2). interstellar space (3). and
the atmosphere of the earth (4). In addition, it was one
of the first radicals produced and studied in the labora­
tory and. in the last 30 years, an extensive amount of
spectroscopic data has been obtained (1, 18). The sim'S u p p o rted by the N ational S cience F oundation.
plicity and importance of OH has also encouraged care­
ful theoretical studies. It is a nine-electron system
that is manageable enough that ah initio, quantummechanical calculations can be expected to accurately
predict the molecular properties. In the case of the vi­
brational transition probabilities, experimentally de­
rived results are very difficult to obtain and researchers
have depended heavily on the theoretical results. For
the OH radical, the difficulty of performing absolute
absorption measurements is severe (5). and stems pri­
marily from the difficulty of obtaining precisely known
column densities of reactive species. Therefore, the­
oretical transition probabilities are very important for
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1503
PETERSON ET AL.
determining OH concentrations in astrophysical and at­
mospheric systems.
The importance of determining the dipole moment
function of OH was recognized 30 years ago by Heaps
and Herzberg (6) in their analysis of the intensity distri­
bution of the Meinel bands (7). It was clear to these
authors that the dipole moment function of OH must be
highly nonlinear near the equilibrium intemuclear sepa­
ration. More recently, Murphy (8) has also found that
experimental measurements of relative transition proba­
bilities could only be explained by a nonlinear dipole
moment function; infrared emission of the first overtone
bands were much stronger than expected. Later ab
initio calculations by Stevens et al. (9) showed that the
dipole moment function has its maximum very close to
the equilibrium bond length, and this results in a weak
infrared fundamental. Mies (10) used this dipole mo­
ment function to obtain calculated vibrational transition
probabilities of OH that qualitatively reproduce the ex­
perimental results. Since then a number of papers have
given theoretically derived dipole moment functions,
the most recent being that of Wemer et al. (11). in
which a number of results are compared.
The utility of highly accurate diagonal vibrational,
dipole-moment matrix elements has been discussed by
Kaiser (12). In cases where vibrationally averaged di­
pole moments are calculated, a direct comparison can
be made with the vibrational dependence of the dipole
moment obtained experimentally. The most accurately
measured dipole moment for the ground vibrational
state of OH is that of Meerts and Dymanus (13), who
also obtained a dipole moment for OD. Dipole mo­
ments for upper vibrational states were not determined.
The OH and OD results imply a much steeper dipole
moment function than that obtained by any of the the­
oretical calculations and, excluding a severe failure of
the Bom-Oppenheimer approximation, the discrep­
ancy could not be explained. In this paper, we report
dipole moments for the v = 0, 1, and 2 vibrational
states of OH and the v = 0 and 1 states of OD.
radicals to be immediately cooled by expansion. The
rotational and vibrational temperatures of the radical
were measured by Droege and Engelking to be II and
3400 K, respectively; their source utilized He as a
buffer. In our source, the vibrational temperature ap­
peared to be lower. OH radicals were detected in the
v = 0, 1, and 2 states, although transitions within the
latter states were extremely weak. OD radicals were
detected in the v = 0 and 1 states.
A molecular-beam. electric resonance apparatus with
mass spectrometric detection (15) was used to measure
the Stark effects of the A-doublet transitions and sub­
sequently determine the dipole moments for different
states. Evidence for formation of the radical was
initially obtained by noting the focusing pattern of mol­
ecules by the first quadrupolar field while monitoring
th e m /e = 17 ion peak. Water focuses at relatively high
voltages (greater than 8 kV), whereas OH focuses at
less than 1 kV. Most of the radical population resided
in the 2I1.v2, J = 3/2 state. For OH, some population
was observed in the 2F1 J = 1/2 and 2n ,:. J = 5/2
states and a dipole moment was obtained for the former.
The signal-averaging time for the OH measurements
was approximately 15 min for the v = 0 state and
60—90 min for the v = I state. For v = 2, 120 min of
signal averaging with a slightly broadened oscillator
was used. The signal strength of different vibrational
states having similar rotational structure is expected to
scale with population in a flop-out resonance experi­
ment as performed here. The low vibrational tem­
perature (less than 3400 K) of the beam made the
signal-to-noise ratio of the v = 2 measurements much
poorer than those of v = 0 or 1. Thus, a larger experi­
mental uncertainty is reported for the dipole moment of
the v = 2 state.
The electric field was measured using OCS as a stan­
dard. For fields larger than 500 V/cm. the J = 1,
M j — 0 1 transition was monitored (16). and for lower
fields the v = I / doublet was monitored (17).
Analysis
Experimental
The OH and OD radicals were formed within a super­
sonic expansion. The source was of the type designed
by Droege and Engelking (14) and was made by
sanding down the closed end of a 0.635-cm, outsidediameter glass tube until a nozzle opening of 75-100
pm was formed. A gas mixture consisting of Ar satur­
ated with water was expanded through the nozzle at a
stagnation pressure of about 0.7 atm (1 atm =
101.3 kPa). A voltage of 6-15 kV was applied to an
electrode, current limited with a 200 Mfi resistor,
which was located just inside the high-pressure side of
the nozzle, producing a discharge through the nozzle to
the chamber wall. This design allows the newly formed
The Hamiltonian used in the data analysis was
Hy = H" - Ji.E
where H°v is the zero-field Hamiltonian as described by
Amano (18). fi, is the dipole moment for vibrational
level v, and E is the electric field. / / “ is diagonal in the
basis
= a ^ T l ^ J l F M r ) + br \2n i 2JI FMf )
+
± 1)IFMf )
+
d 'fn '^ y ±
i)if
m
f)
where p is the parity label for the A doublet. For our
purposes, the last two terms involving contributions off
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Ilk
1504
CAN. J. PHYS. VOL. 62. 1984
imfi
“ ises
53
o
—0
I
400
ELECTRIC
600
F IE L D
800
IV /em )
Fig. 1. Electric field effect on the J = 3/2 lambda-doublet
transition in the
state of OH.
diagonal in J are negligible and therefore do not need to
be included in the evaluation of the dipole moment
matrix elements. The matrix elements of | f E are given
by Meerts and Dymanus (13) in the \2Ylrn J 1FMf )
Hund’s (a) basis and were reevaluated in the [4*p) basis.
For each A doublet, H v was set up in the |tK> basis and
diagonalized to obtain the energy levels and thus the
electric field perturbed spectrum. Note that in the spe­
cial case where M F = F = J + /, the doublet can be
treated as a two-level system as long as terms offdiagonal in J can be neglected. The dipole moment
matrix elements then reduce to
_ p-lfllcffM/
^ “ J ( J + 1)
where,
liiu = <r\J:lr>
The eigenfunctions required to calculate |ft|crr were
supplied by T. Amano (private communication) for the
v = 0 and 1 states of OH and the v = 0 state of OD.
In the other cases ( v = 2, OH and v = 1, OD), |0 |cff
was calculated using the formula given by Dousmanis
et al. (19), which gives pi; as a function of X = A / B ,
the ratio of the spin orbit constant and the rotational
constant. For v = 2, OH, A and B were taken from the
results of Coxon et al. (20) and those for v = 1, OD,
were taken from the results of Amano (18). All values
of |0 |c(f used in this work are listed in Table 3. The
effects of nearby levels to the Stark shift were checked
and found to be less than 1 kHz for the voltages used.
This is as expected since the energy level nearest that of
the :n M, J = 3/2 state is 84 cm '1away.
Figure 1 is a representation of the electric field effect
on the :n„ 2 , J = 3/2 A doublet of OH. The \Mf j =
2 -2 transition can be treated as a two-level system, as
described above. In addition, the effect of the earth's
magnetic field on this transition is minimal. The paral­
lel component of the magnetic field (relative to the
applied electric field) affects the upper and lower levels
equally and, therefore, has no effect on the position of
the transition. The perpendicular component affects
each level differently, but since the contribution is sec­
ond order and the field is very weak, the transition is
shifted by only a small amount. An estimate of the
magnitude of the magnetic field present in the lab­
oratory can be obtained by resolving the structure of the
F = 2 -2 transition at zero electric field. Three lines are
resolved; the center one is at the zero-field position and
the other two are 420 kHz on each side of this. Neg­
lecting the coupling of the field to the nuclear spin, the
magnetic field is calculated to be 0.43 G (19).
The direction of the magnetic field relative to the
electric field is not known precisely, but is expected to
be approximately perpendicular. A perpendicular mag­
netic field of 0.43 G shifts the \MF\ - 2 -2 transition by
10 kHz when the electric field is 1000 V/cm. This is an
upper estimate of the actual effect experienced in the
laboratory and, in any case, is well within the reported
experimental eiTor.
Results
The experimental results are given in Table 1. Listed
are the measurements from which the electric dipole
moments were obtained. The assignments of the ob­
served transitions were first checked by measuring the
transitions at several applied voltages. As an additional
check, the |A/f | = 2-1 transition of OH and the
\Mf \ = 5/2—3/2 transition of OD were measured at
various voltages. In the case of v = 1, OD, the zerofield, A-doublet transitions in the :n ,:. J = 3/2 state
were not previously measured, although an unassigned
transition at 292.28(22) MHz was observed (25). Our
zero-field measurement was made on the F =
5 /2 -5 /2 , A M f = 0 transition, which is negligibly
affected by the magnetic field of the earth.
When calculating vibrational transition probabilities,
the accuracy of the difference in dipole moment be­
tween various vibrational states is more important than
the magnitude of the values. In our experiments, A p.
can be determined more accurately than p because in­
strumental errors such as inhomogeneities in the electric
field are cancelled. Measurements of the Stark-shifted
transitions for the v = 0 and 1 states were taken within
r.
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Ill
PETERSON ET AL.
1505
T a b l e I . O bserved transitions o f OH and O D . In all cases, |A /f | = F = J + I
\M r\
2n „2u =
2n u =
2n „2( J =
2n,,2(7 =
2n«(7 =
2n,,2(7 =
OH:
„2
OD:
"Reference
“Reference
' Reference
"Reference
1
i / 2.
3/ 2 ,
V = 0)
V = 0)
3 / 2 . V = 1)
3 / 2 , V = 2)
3 / 2 , V = 0)
2
2
2
5 /2
5 /2
3 /2 , v = 0)
(M H z)
\M'r \
1
2
2
2
5 /2
5 /2
47 5 0 .6 5 6 (3 )"
1667.3590(2)“
1538.702(3)'
1414.424(3)'
31 0 .3 6 2 7 (1 0 )''
291.130(125)
vf. (M H z)
E (V /c m )
4766.038(25)
1925.545(30)
1818.171(50)
1530.000(125)
4 9 8.413(30)
413.107(250)
688.878
983.137
983 .1 3 4
590.595
393.622
295.255
21.
22.
23.
24.
T a b l e 2 . O b serv ed transition frequencies and dipole m om ents o f OH v =
0 and 1“
<
II
o
F requencies (M H z)
-------------------------------v = 1
1925.551
1925.569
1925.539
1925.564
1925.538
1925.524
1818.18
1818.178
1818.123
1818.189
1818.173
1818.184
E lectric
field
(V /c m )
9 8 3 .2 0 9
9 8 3 .1 7 5
9 8 3 .2 0 9
9 8 3 .1 2 0
9 8 3 .0 1 2
983.081
D ipole m om ents (D)
-----------------------------------------|Ao
Hi
1.65512
1.65523
1.65507
1.65531
1.65540
1.65524
1.66249
1.66254
1.66230
1.66266
1.66279
1.66271
An
0.00737
0.0 0 7 3 0
0.00723
0.00735
0.0 0 7 3 9
0.0 0 7 4 8
“Each set of dipole moments contains measurements taken within 2 h of each other.
T a b l e 3. D ipole m om ents o f O H an d O D in the 2I1 electro n ­
ic state
OH
OD
fl
J
V
|f l|e tr
1 /2
1 /2
3 /2
3 /2
3 /2
1 /2
3 /2
3 /2
1 /2
9 /2
3 /2
3 /2
3 /2
1 /2
3 /2
3 /2
0
0
0
1
2
0
0
1
0 .5
0 .6 5 1 5 9 6
1.469656
1.471409
1.473243
0 .5
1.488724
1.489338
MD)
1.6549(13)
1 .6 6 5 7 2 (1 0 )" “
1.65520(10)
1.66257(16)
1.6648(10)
1.65312(14)"
1.65283(16)
1.6550(27)
“Meerts and Dymanus (13).
“Reevaluated using the data o f Meerts and Dymanus. Their original
value was 1.6676(9) D. The error given in the table assumes no error
in the analysis.
a few hours of each other on four different days. This
set of measurements, given in Table 2, resulted in a
value for the dipole moment difference between the first
two vibrational states of Ap. = 0.00735(7). One reason
for the large amount of effort in obtaining this result
was caused by our initial concern that the difference we
obtained was much smaller than that which was implied
in the work of Meerts and Dymanus (13).
Electric dipole moments are listed in Table 3. The
results of Meerts and Dymanus are also listed in this
table. Within experimental error, the dipole moments of
OD are the same. In the case of OH, our results differ
markedly. This difference cannot be attributed to a vari­
ation in dipole moment for the 2Il|n and :I112 states.
Not only do our OD results agree, but the dipole mo­
ments we obtained for the 2ni,:, J = 1/2 and :n ?:.
J = 3/2 states of OH are also the same within experi­
mental error. Since Meerts and Dymanus indicated
some difficulties in the OH analysis, we reevaluated
their results using the more recent OH analysis of
Amano. The dipole moment obtained in the reevalu­
ation was 1.66572(10) D. This is still considerably
higher than our result. It is clear that this dipole moment
is incorrect, not only because it is inconsistent with our
results, but also because it is inconsistent with the ob­
servation of a weak fundamental vibration-rotation
band for OH (9). At this point, we have not been able
to determine the cause of the discrepancy.
Discussion
The history of OH vibration-rotation intensity deter­
minations is a lengthy one. Attempts have been made to
measure absolute intensities, but it is unlikely that the
accuracy is better than a factor of two (5). Even ob­
taining relative intensities is beset with difficulties be­
cause of the presence of strong vibration-rotation
interactions in OH. This last problem leads to a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1506
CAN. J. PHYS. VOL. 62. I1K4
5 1.84
Fig. 2. Experimental and vibrationally averaged the­
oretical dipole moments of OH plotted as a function o f vi­
brational state, (a) Meyers (26). (6) Mies (10), (r) this work.
The error in the v = 2 measurement is shown. Errors in v =
0 and I are about the size o f the drawn closed circle. (d)
W erner et al. (11).
dependence of the relative, Einstein-A, transition
probability coefficients, AI*1/ A
on rotational state
and is generally not treated adequately. As discussed
most clearly by Mies (10), the problem is quite com­
plex, and it is evident that careful theoretical calcu­
lations are necessary, both to interpret the experimental
results and to obtain reliable absolute intensities.
Theoretical calculations of Einstein A coefficients are
directly dependent on the accuracy of the dipole mo­
ment function used. This can be seen in the paper by
Werner et al. (11), in which a comparison is made of
relative rotationless Einstein A coefficients derived
from various dipole moment functions. The values ob­
tained are found to differ by 10-30%. It is important to
test the accuracy of the theoretical dipole-moment func­
tion by comparing vibrational-averaged, theoretical
dipole moments with experimental dipole moments. In
Fig. 2, experimental and theoretical dipole moments are
plotted as a function of vibrational state. The agreement
appears to be quite good, but it should be noted that the
important parameter is the difference in the dipole
moments of the vibrational states, Ap.,.vs and here the
discrepancies are much larger—between 10 and 40%
for Aiio. i- Empirical perturbative corrections can per­
haps be applied to obtain good (1%) agreement with the
present reliable value of A(Xu. t. Because of the severe
nonlinearity of the dipole moment function in this re­
gion of interest, more experimental data are necessary
to describe the complete vibrational dependence of the
dipole moment.
The OD results are potentially useful as additional
input in describing the curvature of p.,., but the present
data for v = 1, OD is too imprecise to allow such an
evaluation, especially considering the strong curvature
present. On the other hand, it is worthwhile to compare
the v = 0 dipole moments of OH and OD. The differ­
ence in the two values is due to two reasons. Werner et
al. (11) found a difference of 0.001 D between the
dipole moments of OD and OH in the v = 0 state upon
vibrational averaging of their dipole moment function.
Since the vibrational dependence of their dipole mo­
ments is within 20% of our experimental results, it is
reasonable to use their value as an estimate of the effect
of a vibrational difference for the two isotopic species.
Another cause of a difference in dipole moments for
OH and OD is a breakdown of the Bom—Oppenheimer
approximation. Kaiser (12) has shown in his study of
HC1—DC1 that this leads to a constant, vibrationally
independent displacement of dipole moments. We can
estimate this effect for the hydroxyl radical by sub­
tracting the contribution described in the previous para­
graph, 0.001 D, from the experimental difference of
0.0024 D. It is noteworthy that the result of 0.0014 D
is equal in sign and magnitude to that observed for
HC1-DC1. Since the direction of the dipole moments of
OH and HC1 are the same, we would expect the effect
of the Bom-Oppenheimer breakdown to be the same.
Therefore, we believe that the presently observed di­
pole moment of OH is completely in accord with that of
OD.
The results presented in this paper give the first re­
liable dipole moments for OH as a function of
vibrational state. Particularly important is the 1% accu­
racy of the dipole moment difference between the
ground and first excited vibrational state. This result is
useful as a critical gauge of the accuracy of theoretical
dipole moment functions. Because of the general form
of the dipole moment function and the relatively large
error in the experiment dipole moment obtained for v =
2, OH, the three experimental points shown in Fig. 1
are not sufficient to predict dipole moments for states
higher than v = 2. It is clear that higher vibrational
states must be characterized in order to adequately test
the theoretical calculations. The importance of dipole
moment determinations in a direct comparison between
theory and experiment encourages an extension of our
measurements to higher vibrational states.
Acknowledgment
We wish to thank Dr. Takayoshi Amano for sending
us some of his unpublished results on OH.
1. R. A. BEAUDETand R. L. P o y n t e r . J. Phys. Chem. Ref.
Data, 7.311 (1978).
2. A. G. G a y d o n . The spectroscopy of flames. 2nd ed.
Chapman and Hall Ltd.. London. England. 1974.
3. D. M. R a n k . C. H. T o w n e s , and W. J. W e l c h .
Sciences. 174.1083 (1971): R. M. C r u t c h e r and W. D.
W a t s o n . Astrophys. J. 203. L123 (1976).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PET ER SO N ET AL.
4. B. A. THRl'SH. A c c . Chem. Res. 14. 116 (1981).
5. J. R. P o d o l s k e and H. S. J o h n s t o n . J. Chem. Phvs. 79.
3633(1983).
6. H. S. H e a p s and G. H e r z b e r g . Z. Phvs. 133.48 (1952).
7. A. B. M e i n e l . Astrophvs. J. 111. 555:112. 120(1950).
8. R. E. M u r p h y . J. Chem. Phys. 54. 4852 (1971).
9. W. J. S t e v e n s . G. D a s . A. C. W a h l . M. K r a u s s . and
D. N e u m a n n . J. Chem. Phvs. 61. 3686 (1974).
10. F. H. M i e s . J. Mol. Spectrose. 53. 150 (1974).
11. H .-J. W e r n e r . P. R o s m u s . and E.-A. R e i n s c h . J.
Chem. Phys. 79. 905 (1983).
12. E. W'. K a i s e r . J. Chem. Phys. 53. 1686 (1970).
13. W . L. M e e r t s and A. D y m a n u s . Chem. Phys. Lett. 23.
45 (1973).
14. A. T. D r o e g e and P. C. E n g l e k i n g . Chem. Phys. Lett.
96. 316 (1983).
15. T . R. D yke. G. R. T o m asev ich . and W . K le m p e re r. J.
Chem. Phys. 57. 2277 (1972).
1507
16. J. S. M u e n te r. J. Chem. Phys. 48. 4544 (1968).
17. J. M. L. J. R e in a rtz and A. D ym anus. Chem. Phys.
Lett. 24. 346 (1974).
18. T . A m ano. J . Mol. Spectrose. 103. 436 (1984).
19. G. C. D ousm anis. T. M. S a n d e rs. J r . . and C. H.
T ow nes. Phys. Rev. 100. 1735 (1955).
20. J. A. C o xon . K. V. L. N. S astry . J. A. A ustin , and
D. H. Lev y . Can. J. Phys. 57. 619 (1979).
21. H. E. R a d fo r d . Rev. Sci. Instrum. 39. 1687 (1968).
22. J. J. t e r M e u len and A. D ym anus. Astrophys. J. 172.
L2I (1972).
23. W. L. M e e rts . J. P. B ekooy. and A. D ym anus.
Astrophys. J. 224. 177 (1978).
24. W.L. M e e rts and A. D ym anus. Astrophys. J. 180. L93
(1973).
25. M. H. R a sh id . K. P. Lee. and K. V. L. N. S a s tr y . J.
Mol. Spectrose. 68 . 299 (1977).
26. W. M e y e r. Theor. Chim. Acta. 35. 277 (1974).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 7
ABSORBER SPEED DEPENDENCE OF THE COHERENCE RELAXATION RATE
OF THE J=0-1 TRANSITION OF
1 5
N20
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12.1
Absorber sp eed d ep en d en ce of th e coherence relaxation
rate of th e J=0-1 tran sition of NgO
Gerald T. F raser and Stephen L. Coy
D epartm ent of Chemistry
Harvard University
Cambridge, MA 02138
* Supported by the National Science Foundation
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT
The coherence r e la x a t io n r a te
( T^ ) o f th e J=0-1 t r a n s it io n o f
has been examined u sin g microwave tr a n s ie n t te c h n iq u e s.
The tra n ­
s ie n t decays were analyzed by a model which c o n s id e r s th e absorber speed
dependence o f the c o l l i s i o n a l r e la x a tio n p rocess [S.L . Coy, J.Chem .Phys.
7 3 , 5531 ( 1 9 8 0 )] .
The decays were a ls o analyzed by th e standard speed
independent m odel.
speed
dependence
Boltzmann average
i
_
i
mTorr
In th e speed dependent a n a ly s is , a lin e a r _ a b so r b e r
of
the
form:
sp eed ,
k (v)= k Q + k ^ ( v - ' v ) ,
was assumed.
and k^v = 0 .0 0 9 9 (4 ) (is
mTorr
_i
where
is
th e
Values o f kQ = 0 .0 3 0 0 (1 )
(is~
were determ ined.
independent a n a ly s is a r e la x a tio n r a t e , k = 0 .0 2 9 2 2 (6 ) (is
found.
T his corresponds
to
a p ressu re
v
In th e speed
—1
mTorr
broadening parameter
—1
, was
t-4 t-
of
2
4 .6 5 (1 )
MHz/Torr.
dependent
A zero
frequency
s h ift
p ressu re t r a n s it io n frequ en cy and p ressu re
parameter were
a ls o
determ ined.
They
are
24274.7865(1) MHz and +30(4) kHz/Torr r e s p e c t iv e ly .
IHTRODUCIOM
T ransient tec h n iq u es in microwave sp ectro sco p y have r e c e iv e d
s id e r a b le a t te n t io n
in th e l a s t
15 y e a r s
[1 ].
Time domain microwave
sp ectro sco p y a llo w s th e measurement o f T^ and T
2
r o t a t io n a l
t r a n s it io n
r e la x a t io n
tim e
of
a s a fu n c tio n
the
in itia lly
of
r e la x a t io n tim e s o f a
sample p r e s su r e .
prepared
con­
non-Boltzmann
Tj
is
th e
p o p u la tio n
d iff e r e n c e between th e two r o t a t io n a l l e v e l s w h ile T^ i s th e decay tim e
o f th e induced m acroscopic p o la r iz a t io n .
Thus measurements o f T^ and T
r e la x a t io n
be
energy
tim es
tr a n sfe r
a llo w
in form ation
p r o c e sse s
and
to
2
u ltim a te ly
ob tain ed
about
about r o t a t io n a l
th e
in te r m o le c u la r
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
p o t e n t ia l.
S in ce th e r e are many decay mechanisms in th e t r a n s ie n t experim en ts
which are not d ir e c t ly r e la t e d to the phenom enological
and T
2
r e la x a ­
t io n tim e s, care must be taken in th e in t e r p r e t a t io n o f th e se measure­
m ents.
C areful c o n s id e r a tio n o f th e v a r io u s n o n -ex p o n en tia l decay path­
ways which are in v o lv e d has a llo w ed , fo r in s ta n c e , th e e x tr a c tio n o f the
speed
dependence o f th e coherence r e la x a t io n tim e, T
[2 ],
speed
dependence in th e coherence r e la x a t io n tim e i s
p r e d ic te d i n most
2
t h e o r ie s o f r o t a t io n a l r e la x t io n
[2 ].
An absorber
C areful measurements o f T
2
decay
tim e in tim e-dom ain measurements i n th e microwave r e g io n h as been shown
to be a u s e fu l method to e x t r a c t t h i s speed dependence [ 2 ] .
speed
dependence o f th e coherence decay tim e has on ly
a few
sy stem s, fu r th e r measurements are needed.
S in ce th e
been rep orted fo r
In t h i s paper we re p o r t
th e speed dependence o f the
r e la x a t io n fo r th e J=0-1 t r a n s it io n
H 0.
from
2
To avoid
s tr u c tu r e i n
14
co m p lic a tio n s
M
2 0
the
n u clea r
quadrupole
th e measurements were made u sin g a sample o f
of
h yp erfin e
15
N
2 0
.
EXPERIMENTAL
The apparatus used in th e s e experim en ts have been d escrib ed p r e v i­
o u sly by Coy [ 2 ] .
Measurements were made w ith the sample p ressu re vary­
in g between 5 .7 and 4 6 .8 mTorr.
The p o la r iz in g r a d ia tio n came from an
OKI 24V11 K-Band K lystron which was frequ en cy s t a b i l i z e d a t 24,2 7 2 ,9 4 3 7
MHz.
In th e s e exp erim en ts a bridged K-band waveguide c i r c u i t was used
fo llo w e d
a d m itted .
by an empty 1 0 .4 meter X-band c e l l
A n /2 p o la r iz in g microwave p u lse
to which th e sample was
was se n t through one arm o f
the bridged c i r c u i t and through the sample c e l l .
The oth er arm allow ed
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IZH
f o r tra n sm issio n o f the o ff-r e s o n a n t r a d ia tio n fo r b ia s in g th e c r y s t a l
d e te c to r and fo r g e n e r a tin g a heterodyne
output s i g n a l .
Depending on
th e sample p r e ssu r e , th e heterodyne output s ig n a l was sam pled, a f t e r a
0 .2 3 5 ps d e la y , in e it h e r 5 or 10 ns i n t e r v a l s fo r a t o t a l o f 1024 sam­
p le
p o in t s .
The
d e te c tio n
and
s ig n a l
averagin g
system
has
been
d e sc rib e d by Coy [2]
The * N ° san P le Mas o b tain ed from S to h le r and was se n t through a
5
2
f r e e z e thaw c y c le a t l iq u id n itr o g e n tem perature to remove any v o l a t i l e
im p u r it ie s .
and 2 0 .7
A ll th e measurements were made a t tem peratu res between 1 9 .7
C.
0
RESULTS
The d i g i t i z e d , t r a n s ie n t em issio n s ig n a ls were f i t to two d if f e r e n t
m od els.
The f i r s t
independent
of
th e
model assumes a coherence r e la x a t io n r a te which i s
absorber
sp eed .
The second
model
c o n s id e r s
r e la x a t io n r a te to be a lin e a r fu n c tio n o f th e absorber sp e e d .
speed independent a n a ly s is ,
th e model used fo r
th e
observed
th e
For the
e m issio n
s ig n a l, S ( t ) , is :
S (t)= C jP (t)e x p (-k t)sin (< o t + 0 ) + C - C ^N (t).
2
In t h i s e x p r e ssio n
i s th e beat freq u en cy between th e m olecu lar em is­
s io n and th e l o c a l o s c i l l a t o r , P ( t ) d e s c r ib e s th e n on -ex p o n en tia l decay
mechanisms due to w a ll c o l l i s i o n s and th e Doppler e f f e c t , H (t) i s a s i g ­
n a l tr a c e taken w ith ou t a sample p laced in th e c e l l , and k =
p r essu re dependent, speed in d ep en d en t, coherence r e la x a t io n
1
/T
2
i s th e
r a te .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
MS'
* 5N m agnetic
h yp erfin e
str u c tu r e
was n e g le c te d
in
th is
m odel.
The
h y p e r fin e s p l i t t i n g o f th e J=1 l e v e l i s exp ected to be approxim ately 10
kHz.
C j,
C2 ,
squ ares f i t t i n g
e x p r e s s io n .
su re fo r
C3> <i)Q,
9, and k were determ ined by n o n lin ea r l e a s t
o f th e observed d i g it i z e d
s ig n a l tr a c e s to
th e above
F igure 1 shows a p lo t o f r e la x a tio n r a t e , k, v e r s e s p res­
th e J=0-1 t r a n s it io n o f ^N^O.
The r e la x a t io n r a te d erived
from the data in F igure 1 i s 0 .0 2 9 2 2 (6 ) ps
—1
mTorr
-1
and corresponds to a
p ressu re broadening c o e f f i c i e n t l/( 2 n T 2 ) o f 4 .6 5 (1 ) MHz/Torr.
The l in e
c e n te r , determ ined from th e p ressu re dependence o f toQ, i s 24274.7865(1)
MHz.
The p ressu re
dependence
of
th e
t r a n s it io n
frequency
is
+30(4)
kH z/Torr.
The speed dependent model assumed a lin e a r speed dependence o f the
form:
k (v ) = kQ+k1(v - v)
where v” i s th e Boltzmann average sp eed .
The f i t t i n g procedure i s id e n t ­
i c a l to th a t o f th e speed independent model ex cep t th a t P ( t) i s m u lti­
p lie d by F (t,k ^ ) and k i s
e x p o n e n tia l
decay
behavior
dependence in th e m odel.
p lo tt e d
in
F igu re
1.
0 .0 3 0 0 (1 ) (is- mTorr
1
r e p la c e d by kQ.
_ 1
due
to
th e
F U .k j )
a d d itio n
of
c o n ta in s th e non­
the
lin e a r
speed
The r e s u lt in g v a lu e s o f kQ and k j 7 are a lso
A lin e a r
fit
to
th e se
r e s u lts
and k^v = 0 .0 0 9 9 (4 ) ps^mTorr*"1 .
g iv e s
kQ =
In t h i s ca se the
z e r o p ressu re frequ en cy o f th e l i n e i s 242 7 4 .7 8 6 4 (1 ) and th e pressu re
dependence o f th e t r a n s it io n frequ en cy i s + 34(4) kH z/Torr.
The lin e a r
l e a s t squares f i t s o f th e r e la x a tio n r a t e s or the t r a n s it io n fr e q u e n c ie s
to
th e
sample
p r e ssu r e ,
fo r
both
th e
speed
independent
and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
speed
U4.
dependent m odels,
are summarized in Table 1 .
The experim en tal uncer­
t a i n t i e s rep orted in Table 1 r e f l e c t two standard e r r o r s from th e l e a s t
squares f i t s .
Sin ce th e a b so lu te p ressu re c a lib r a t io n i s estim a te d to
be known only to
1
ft, the experim en tal u n c e r ta in t ie s o f th e s lo p e s must
be in c re a se d by a corresponding 1 ft.
The r e l a t i v e
p r e s c is io n o f the
pressu re measurements though are q u ite high a s seen by exam ination o f
th e q u a lity o f the l e a s t squares f i t s .
DISSCUSSIOH
Measurements o f
t r a n s it io n s
have
the
been o f
s e lf - p r e s s u r e
in te r e st
broadening
due
to
th e
of
N20
sm all
r o ta t io n a l
e le c tr ic
d ip o le
moment (0 .1 6 0 8 3 0 (1 6 ) D [3 ]) and la r g e e l e c t r i c quadrupole moment o f b'20
( -3 .6 5 ( 2 5 ) D A
[4 ]).
P reviou s measurements by B erendts and Dymanus [5]
and by Wensink, Moorman, and Dijkerman [ ] gave s e lf-b r o a d e n in g c o e f f i ­
6
c ie n t s o f 4 .5 0 (2 0 ) MHz/Torr (room tem perature) [7] and 4 .4 4 (8 ) MHz/Torr
(2 9 2 .7 K) fo r ^N^O.
These r e s u lt s are reason ab ly c o n s is t e n t w ith th e
v a lu e o f 4 .6 5 (1 ) MHz/Torr ob tain ed i n t h i s stu d y .
W ithin t h e ir e x p e r i­
mental e r r o r , U ensink, Moorman and Dijkerman were not a b le to ob serve
any p ressu re dependent s h i f t o f th e frequ en cy o f th e J=0-1 t r a n s it io n o f
^N^O.
T his i s not unexpected s in c e
th e frequency o f t h i s t r a n s it io n
h as a sm all p ressu re dependence o f 3 0 (4 ) kH z/Torr.
B elov e t . a l .
[ ]
8
have shown t h a t, e m p ir ic a lly , the magnitude o f th e s e l f - s h i f t i n g parame­
t e r i s n ea rly p ro p o rtio n a l to the square o f th e e l e c t r i c d ip o le moment
o f the m o lecu le.
It is
thus not unexpected to ob serve such a
p ressu re dependence o f the t r a n s it io n frequency in
it
would a ls o
appear
th a t
th e
magnitude
of
th e
1 5
H 0.
2
sm all
Furthermore,
e le c tr ic
quadrupole
moment i s o f l i t t l e im portance fo r s e l f - s h i f t i n g when th e m olecule has a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ill
small e l e c t r i c d ip o le moment.
The absorber speed dependence o f the s e lf - r e la x a t i o n r a te has been
r ep o rted fo r only a few m olecular t r a n s it io n s [ ] : th e 2jl2 ~^h
2
d ou b let t r a n s it io n o f CH20 ; the J=0-1 and J = l-2 t r a n s it io n s o f OCS; the
J=3,K=2 in v e r s io n in v e r s io n t r a n s it io n
metry doub let t r a n s it io n o f C H 0 .
2
t r a n s it io n
4
o f KH^ ; and th e
asym­
The r e s u l t s are v a r ie d , w ith th e MKg
showing alm ost no speed dependence w h ile th e H.CO 2
**
1 0
1Z
-2 --
11
t r a n s it io n shows a speed dependence g r e a te r than th a t p r e d ic te d by th e
L an d a u -L ifsh itz
model
fo r
a hard-sphere
c o llis io n
in t e r a c t io n .
When
d is s c u s s in g th e absorber speed dependence o f c o l l i s i o n a l r e la x a t io n , the
r a t i o kj^v/k
0
is
a con ven ien t param eter.
For the J=0-1 t r a n s it io n
of
15 .,
NjO t h i s r a t i o i s 0 .33 and i s n ea rly i d e n t ic a l to th a t found fo r the
J=0-1 t r a n s it io n o f OCS, k^v/kQ = 0 .3 5 [ 2 ] ,
Coy [2] has shown th a t in
th e L a n d a u -L ifsh itz c o l l i s i o n model th e se v a lu e s o f k jv /k Q imply th a t
th e " e ff e c tiv e "
in t e r a c t io n
i
p o t e n t ia l has a — form.
r
T h is s im ila r it y
7
between OCS and 1<20 i s somewhat s u r p r is in g s in c e OCS and N20 have very
d if f e r e n t e l e c t r i c m u ltip o la r moments ( OCS n=0.71519(3) D [ 9 ] , Q jj=_
0 .7 8 6 (1 4 ) DA
[ 1 0 ]j N20 |i= 0 .160830(16) D [ 3 ] , Q |j= - 3 .6 5 (2 5 ) D A [4]
)
S in ce th e m asses and r o t a t io n a l l e v e l sp a cin g s o f th e se two m o lecu les
are d is s im ila r a more d e t a ile d
comparison
is
d iffic u lt
to
make.
To
o b ta in fu r th e r in s ig h t in to th e absorber speed dependence o f coherence
r e la x a t io n i t would be w orthw hile to examine t r a n s it io n s
w ith s im ila r r o ta t io n a l c o n s ta n ts and m asses.
in m o le c u les
One p o s s ib le can d id ate
f o r such a study i s th e J=0-1 t r a n s it io n o f C1CN.
C1CN has a r o ta t io n a l
co n sta n t and mass near th a t o f OCS y e t i t
has a la r g e e l e c t r i c
d ip o le moment (2 .8 D ).
a ls o
A study o f C1CN would a llo w
com parisons to
be
made between two system s whose c o l l i s i o n dynamics are s im ila r and whose
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
in t e r a c t io n p o t e n t ia ls are very d i f f e r e n t .
S tu d ie s such a s th e s e should
e n a b le us to g a in fu r th e r i n s ig h t in t o th e absorber speed dependence o f
r o t a t io n a l r e la x a t io n .
ACKNOWLEDGMENTS
We would l i k e to thank P r o fe sso r E. B. W ilson fo r a d v ic e and sup­
p ort o f t h i s work.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
FIGURE CAPTIOU
F igure 1 . P lo ts o f coherence r e la x a t io n r a te s v e r s e s p ressu re
fo r th e J=0-1 t r a n s it io n o f
(k —
; kQ
; k1
1 5
U °*
2
)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
130
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P R E S S U R E
V
0
REFERENCES
1.
R.H. Schw endem an, Ann.Rev.Phys.Chem. 29, 537 (1978).
2.
S.L. Coy, J.Chem.Phys. 73, 5531 (1980).
3.
L.H. ScharpeftjJ.S. M uenter, V.W. Laurie, J.Chem.Phys.
53. 2513 (1970).
4.
•
W.H. Flygare, R.L. Shoem aker, W. H uttner, J.Chem.Phys.
50. 2414, (1969).
5.
B.Th.Berendts and A. Dym anus, J.Chem .Phys. 48, 1361, (1968).
6.
W.A. Wensink, C. Noorm an, and H.A. Dijkerman, J.Phys.B
12, 1687 (1979).
7.
Wensink, Noorm an, and Dijerm an (referen ce 6) reca lcu la ted
the self-broadening coefficien t obtained by B eren d ts and
Dym anus (refe re n c e 5) by using a m ore r e ce n t and m ore
a ccu ra te value for the e le c tr ic dipole m om en t of NgO.
B.
S.P. Belov, V.P. Kazakov, A.F. Krupnov. V.N. Markov,
A.A. Mel'nikov, V.A. Skvortsov, and M.Yu. TYeCyakov,
J.M ol.Spec. 94, 264 (1982).
9.
J.S. M uenter. J.Chem .Phys. 56, 5409 (1972).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
10.
F.H. De Leeuw and A. Dymanus, Chem .Phys.Lett. 7, 288 (1970).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13 3
Table I.
Sum m ary of linear fits of relaxation ra te s, k , k 0 , k i , and
transitions frequencies, v, to sam ple p ressu re, P , for th e J =0-1
transition of *®NgO.
A bsorber speed independent model.
slope
in te rc ep t
kvs.P
0.02922(6)//s_1mTorr-1
0.006(l) / is ' 1
v v s. P
30(4) kH z/Torr
24274.7865(1) MHz
~ = - vs. P
4.65(1) MHz/Torr
1.0(2) kHz
C 7T i 2
A bsorber speed dependent model, fc(v) = k0 + fci(v —v).
k 0 vs. P
vs.
P
fcjiTvs. P
fiTT
vs. P
v vs. P
slope
in te rc ep t
0.0300(1) /is’1mTorr"1
0.010(3) / i s ' 1
4.78(2) MHz/Torr
1.6(4) kHz
0.0099(4) /is‘*mTorr“*
-0.007(6) / is '1
1.58(7) MHz/Torr
-1.0(8) kHz
34(4) kH z/Torr
24274.7864(1) MHz
U ncertainties a re statistical and reflect two stan d ard e rro rs from
th e le ast squares fits. The experim ental u n certain ty in the p ressure
m easurem ents contribu tes an additional 1 % e rro r in th e slopes.
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