V. Braun et al- Infrared emission spectroscopy at 100-mu-m: Vibration-rotation spectrum of CsI

8/3/2019 V. Braun et al- Infrared emission spectroscopy at 100-mu-m: Vibration-rotation spectrum of CsI

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E L S E V I E R

14 October 1994

Chemical Physics Letters 228 (1994) 633-640

C H E M I C A L

P H Y S I C S

L E T T E R S

Infrared em ission spec troscopy at 100 tm.Vibration-rotation spectrum of CsI

V. Braun a, B. Guo a, K.-Q. Zha ng ~, M. Dulick a, P.F. Bern ath a, G.A. Mc Ra e b"Ce ntre for Molecular Beam s and Laser Chemistry, Department o f Chemistry, University of Waterloo,

Waterloo, Ontario, Canada N2 L 3 G Ib Ato mic Energ y of Canada Lim ited, Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada KOJ lJO

Received 3 May 1994; n final form 16 August 1994

Abstract

The vibratio n-rotation emission spectrum of CsI was recorded in the 110-130 cm -1 region o f the spectrum. Although indi-vidual rotational lines were not resolved, we measured the positions of 29 b and heads involving the vibrational bands from 1-0to 30-29. These vibrational data when com bined with previously measured microwave and millimeter-wave pure rotationaltransitions yielded impro ved Dun ha m constants. I n addition, an experimentally derived Born-O ppen heim er potential is alsoreported and compa red with the purely ionic internuclear potential of the R ittner model. The results reported here demonstratethat far-infrared em ission spectroscop y is a very sensitive tech nique fo r detecting high-temperature molecules, even at wave-

lengths aro und 100 ~tm.

1 . In t roduc t ion

Ces iu m iod ide , a c rys tal l ine so l id a t roo m tem per-a tu re , i s an ex t remely vo la t i l e subs tance a t e leva tedtempera tu res . Because o f it s vo lat i l ity, a t t en t ion re -cen t ly has been d i rec ted tow ard CsI as a p r ime can-d ida te in the t ranspor t o f rad ioac t ive iod ine f rom f i s -s ion p roduc t s p rodu ced in nuc lea r reac to rs [ 1 ] .

P rev ious spec t roscop ic work on the a lka l i ha l ideshas inc luded microwave absorp t ion exper iments. CsIi s an ion ic molecu le wi th a l a rge d ipo le moment o f11 .69 D [2] . Pure ro ta t iona l spec t ra have been ob-ta ined fo r mos t o f the d ia to mic a lka l i ha lides in thecen t imete r-wave reg ion [3 ,4 ] , and fo r a lka l i b ro-mides and iod ides in the mi l l imete r-wave reg ion [ 5 ] .T h e h y p e r t i n e s t r u c tu r e o f C sI w a s m e a s u r e d f o r t heJ = 2--, 3 rotat iona l t ran si t ion by Ho eft e t a l. [ 6 ] . Th emo s t recen t wo rk was ca r r i ed ou t by Honer j~ iger andTischer [ 7 ] , who ob t a ined the ro ta t iona l spec t ra o f

ces ium ha l ides in the 1 cm wave leng th reg ion andcom bin ed the i r resu lt s wi th the mi l l imete r-wave da tao f R u s k a n d G o r d y [ 5 ] t o y i e ld a n i m p r o v e d s et o fD u n h a m Y c o n s t a n t s .

Addi t iona l work inc luded e lec t ron d i ff rac t ionstudies on CsI in the gas pha se [ 8 ] . Olden berg et al .[ 9 ] ob ta ined the CsI u l t rav io le t chem i luminescen ces p e c t r u m f r o m t h e r e a c t io n C s2 + 12 . R o u n d i n g o u tthese type o f inves t iga tions o n CsI in the gas phaseare pho tod issoc ia t ion [ 10-1 2 ] , co l l i s ion- induceddissoc ia t ion [ 13-17 ] , and mass spec t romet r ic [ 18-20] s tudies .

In con t ras t , on ly a l imi ted a mo un t o f in f ra red spec-t roscop ic work has been repo r ted fo r CsI . The fa r- IRabsorp t ion spec t rum o f CsI i so la ted in so l id a rgon hasbeen repor ted [ 21 ] . R ice and Klem perer [ 22 ] mea-sured IR sp ectra of several l ighter a lkal i hal ides andper formed an ex t rapo la t ion to de te rmine the v ib ra -t iona l f req uen cy of CsI . Konin gs et a l . [ 1 ] record ed

0009-2614/94/$07.00 1994 Elsevier Science B.V. All fights reservedSSD10009-2614 ( 94 ) 0099 8-8


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634 V. Braun et aL / Chemical Physics Letters 228 (1994) 633-640

a 0.1 c m- t low-resolution IR absorption spectrum inthe gas phase. The y assigned the b road double-peakedfeature, centered at 113.9 cm-1, to the fundamenta lvibrational band of CsI but were unable to resolveany rotational structure.

In this Letter, we report on the analysis of the far-IR emission spectrum of CsI recorded with a Fouriertransform spectrometer. Band head positions weremeasured consecutively from 1-0 to 30-29, with theexception of the 17-16 band which was not mea-sured. The infrared data were then combined withpure rotational lines from the literature to yield im-proved spectroscopic cons tants for the X ~Y.+ grou ndstate.

2. Experimental

The experimental procedures followed were simi-lar to those described in a previous paper on A1CI[23 ]. A l0 g sample of CsI was gradually heated to900(2 in a carbon b oat pla ced in the center of a car-bon liner that was housed inside of a Mullite( 3A1203"2SIO2) tube. The tube was pressurized withl 0 Tort of argon gas to prevent condensation of CsIon the polyethylene windows. The central 50 cm por-tion of the Mullite tube, 1.2 m in length and with anoutside diameter o f 5 cm, was heated by a commer-

cial CM Rapid Temp furnace. The ends of the Mul-lite tube were water cooled and the window holderswere attach ed with O rings.

The infrared radiation from the furnace was di-rected through the emission port of a Bruker IFS 120HR Fourier transform spectrometer at the Univer-sity of Waterloo. The far-IR emission spectrum wasrecorded with a liquid-helium cooled Si bolometerfrom Infrared Laboratories and a 12 gm Mylarbeamsplitter.

At 900C where the vapor pressure of CsI is esti-mat ed to be 30 Torr [ 24 ], 90 scans were coadde d ata resolution o f 0.01 c m -~ in the 5 0-20 0 c m -t spec-tral range.

Fig. 1 shows a compressed view of the far-infrare demission spectrum of CsI. The sharp lines, labelledin Fig. 1 with leader lines, are actually rovibrat ionalband heads where rotational lines from each vibra-tional band form heads at J~ 300 in the R branch.The positions of 29 band heads were measured forthe 1-0 to 30-29 bands, with the exception of 17-16,which was not measured due to the presence of astrong H2 0 absorption band. Actual measurement o fband head positions was accomplished by usingBrault's computer program PC-DECOMP and pro-ceeded by calibration with respect to impurity" H20lines also present in the spectrum [ 25 ].

I Csl

121.0 123.0 125.0Wavenumber (cm I)

Fig. 1. A portion of the vibration-rotation emission spectrum of CsI with the band heads marked above.

113.0 t15.0 17.0 11g.0


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E Braun et al. / ChemicalPhysics Letters 228 (1994) 633-640 635

Table 1Pure rotational transitions of CsI (in e ra- ~

v J',,--J" Observed Obs. -ca lc.

( x l O - ~)

0 3~2 0.1415587" -90 16~ 15 0.7549309 b 520 17~ 16 0.8021016 b 130 18~1 7 0.8492719 b -1 40 20~ 19 0.9436108 c -3 60 104~ 103 4.8906551 a - 60 111~110 5.2173437d --100 128~ 127 6.0086465 n I00 135~-134 6.3335389 d 90 139~ 138 6.5189272 d 131 3~ 2 0.1411499 a --71 16 ~1 5 0.7527548 b 106

1 17~ 16 0.7997853 b 301 18~ 17 0.8468205 U 161 20 `-1 9 0.9408855 ~ -- 171 111.-1 10 5.2021936 d --521 128~ 127 5.9911771 d 141 129---128 6.0374874 d 21 13 9- --1 38 6.4999507 a --192 3*-2 0.1407419 a --32 17-- 16 0.7974750 b 742 18,--17 0.8443728 b 472 20---19 0.9381615 --272 111,--110 5.1870788 d 392 12 8~ 127 5.9737340 d 272 139,-- 138 6.4810056 a -- 23 3,-2 0.1403339" -43 17~ 16 0.7951658 b 933 20,--19 0.9354428 c --233 128,--127 5.9563113 d --123 140~ 139 6.5079926 a - 64 3~ 2 0.1399250 " -2 04 20~ 19 0.9327278 -2 25 20~ 19 0.9300161 -2 96 20,--19 0.9273111 ~ - 97 20 ~1 9 0.9246076 * - 168 20`- 19 0.9219096 c - 99 20,--19 0.9192160 1

10 20,--19 0.9165264 c 8"11 20 ~1 9 0.9138398 312 20,--19 0.9111574 c -- 413 20 ~1 9 0.9084881 c 714 20,--19 0.9058086 c 1515 20 ~1 9 0.9031394 * 1216 20 ~1 9 0.9004728 - 917 20 `-1 9 0.8978143 ~ 618 20,--19 0.8954561 ~ --2 019 20 ~1 9 0.8925062 - 820 20 ~1 9 0.8898625 ~ 2121 20,--19 0.8872187 423 20 ~1 9 0.8819450 * --2824 20. -19 0.8793212 c 17

"Se etext, Ref. [61. bRef. [31.See text, Ref. [ 7 ]. a Ref. [ 5 ].

3. Resul t s and d iscuss ion

3.1. Dunh am fi ts

A l l o f t h e a v a il a b le m i c r o w a v e a n d m i l l i m e t e r - w a v e

a b s o r p t i o n d a t a p u b l i s h e d s o f a r o n C s I [ 3 , 5 - 7 ] a r ed i s p l a y e d i n Ta b l e 1. Wi t h t h e e x c e p t i o n o f th e H o e f te t a l. d a t a [ 6 ] , a ll o f t h e r e p o r t e d d a t a c o r r e s p o n d st o p u r e r o t a t i o n a l l i n e f r e q u e n c i es w i t h n o r e s o l v e d

h y p e r f i n e s t r u c tu r e . I n o r d e r t o i n c o r p o r a t e t h e H o e f te t al . d a t a s e t i n t o o u r f i t s ( w h e r e i n d i v i d u a l h y p e r -

f i n e li n e s f o r t h e J = 2 ~ 3 t r a n s i ti o n s o f v = 0 - 3 w e r er e p o r t e d i n s t e a d ) l i n e c e n t e r s f o r t h e s e p u r e r o t a -t i o n a l t r a n s i t i o n s w e r e c a l c u l a t e d u s i n g t h e i r r e -p o r t e d eqQ c o n s ta n t s . A f i t o f t h e c o m b i n e d m i c r o -w a v e a n d m i l l im e t e r - w a v e da t a t o th e D u n h a m e n e rg y

l e v e l s y i e l d e d a s t a n d a r d d e v i a t i o n o f 0. 6 7 5 w i t h r e-

s i d u a l s g i v e n i n Ta b l e 1.T h e D u n h a m ITS o b t a i n e d f r o m t h i s p r e l i m i n a r y f i t

w e r e t h e n u s e d i n c o n j u n c t i o n w i t h t h e s o l u ti o n s o f

_a 2J q ( Ye ( v + ) ' { [ ( J + 1 ) ( J + 2 ) l J

- [ J ( J + 1 )1 j } ) = 0 , ( 1 )

t o o b t a i n R ( J ) a s s i g n m e n t s f o r t h e b a n d h e a d s .

Tw o s e p a r a te f i ts w e r e t h e n p e r f o r m e d w i t h a d a t as e t t h a t c o m b i n e d t h e b a n d h e a d d a t a w i t h t h e m i c r o -w a v e a n d m i l l i m e t e r - w a v e d a t a . I n t h e f i r s t f i t, d es -i g n a t e d u n c o n s t r ai n e d , a ll D u n h a m Y s w e r e t re a t e d

a s a d j u s t a b l e p a r a m e t e r s . T h e s e c o n d f i t, d e s i g n a t e dc o n s t r a i n e d , i n v o l v e d t r e a t i n g t h e Y ~ a n d Yi~ a s a d -j u s t a b l e p a r a m e t e r s a n d f i x in g al l r e m a i n i n g Ye f o rj > 1 t o c o n s t r a in t s i m p o s e d b y t h e D u n h a m m o d e l[ 2 3 , 2 6 ] . T h e s t a n d a r d d e v i a t i o n s f o r t h e u n c o n -

s t r a i n e d a n d c o n s t r a i n e d f i ts w e r e 0 . 6 7 4 a n d 0 . 8 0 2 ,r e s p e c t i v e l y. O t h e r p e r t i n e n t r e s u l t s f r o m t h e s e f i t sr e p o r t e d h e r e a r e th e b a n d h e a d r e s id u a l s f r o m t h ec o n s t r a i n e d f i t ( Ta b l e 2 ) a n d t h e D u n h a m Y v a l u e sa l o n g w i t h t h e i r u n c e r t a i n t i e s q u o t e d t o 1 s t a n d a r d

d e v i a t i o n ( Ta b l e 3 ).P r e v i o u s D u n h a m c o n s t a n t s r e p o r t e d b y Ho n er j~ i -

g e r a n d Ti s c h e r a r e a l s o l i s t ed i n Ta b l e 3 f o r c o m p a r -i s o n p u rp o s e s . N o t e t h a t t h e y a ls o u s e d D u n h a m r e-l a t i o n s s i m i l a r t o o u r s i n d e t e r m i n i n g t h e c o n s t a n t s

Y~o, Y2o, Yo3, an d Yo4. S t r i c t ly sp eak i ng , the D un ha mr e l a t i o n c o n s t r a i n t s a r e v a l i d f o r o n l y is o t o p i c a l l y i n -v a r i a n t D u n h a m U c o n s t a n t s , i .e . c o n s t a n t s t h a t c o n -


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636 V. Braun et al. / Chemical Phj, ics Letters 228 (1994) 633- 640

Table 2Band head position in c m- 1

Band Band origin Band head Obs. -ca lc.

1-0 118.6587 126.2504 -0 .0 01 62-1 118.1630 125.7216 0.00073-2 117.6672 125.1928 0.00114- 3 117.1711 124.6640 -0 .0 00 45-4 116.6827 124.1430 0.00416-5 116.1878 123.6157 0.00047-6 115.6975 123.0932 -0 .0 00 48-7 115.2109 122.5745 0.00079-8 114.7234 122.0551 -0 .0 00 7

10-9 114.2380 121.5380 -0 .0 01 811-10 113.7563 121.0248 -0.00 0812-11 113.2686 120.5057 -0. 00 7513-12 112.7968 120.0027 -0. 000114-13 11 2. 31 95 119.4943 0.000115-14 111 .84 35 118.9874 -0.000 116-15 111.3706 118.4838 0.001118-17 11 0. 42 66 117.4788 0.000219-18 10 9. 95 52 116.9772 -0. 002 220-19 109.4915 116.4834 0.001421-20 109 .02 38 115.9858 -0.0 00822-21 10 8. 56 06 115.4929 -0.00 0123-22 108.0994 115.0021 0.000824-23 10 7. 63 89 114.5122 0.000825-24 10 7. 17 98 114.0239 0.000526-25 10 6. 72 47 113.5397 0.002427-2 6 106.2679 113.0540 0.000928-27 105 .81 07 112.5681 -0.0 026

29-28 105.3587 112.0875 -0 .00 2730-29 10 4. 91 27 111.6131 0.0016

The observed-calculated values correspond to residuals ob-tained from the combined fit of ban d heads, microwave, and mil-limeter-wave data to the Dunham model with eonstraims. Esti-mates of band origins are based on the parameters listed in thesecond column o f Table 3.

vey in format ion so le ly about the mechanica l e ffec tsof nuc lear mot ion w i th the reduced mass exp l ici t lyfactored out . Howe ver, s ince

2Belog, ~ 0 . 0 0 0 4 , ( 2 )

i t can be sa fe ly assumed tha t B orn-O ppen he im erbreakdo wn, im plici t ly absorbed in the Ys and of or-d er 2Bdo , , is 'negl igible . Th erefore, applying theserelation s to the Ys is justified .

Final ly, with the Yol value obta ined fro m the con -strained f i t a long with the a tom ic masses taken fro mMills e t a l . [ 27 ], we c alculated the eq ui l ibr ium inter-nuclear separat ion Re to be 3.31519042 (40) A.

3. 2 . Born-Op penheim er potent ia l

The resul ts in Tables 2 and 3 are qui te astonishingin view o f the fac t that the v ibrat ional constants , Y~o,Y2o, and Y3o, were d eterm ined to such high degreesof p rec i s ion f rom f i t s con ta in ing band head da ta .Moreover, the agreement be tween observed and ca l-culated band hea d posi t ions is in mo st cases consid-erably bet ter than the assigned s tat is t ical weight of0 .002 cm-1 . Clearly the incorpo ra t ion of microwaveand mil l imeter-wave l ines to the da ta set together withDu nha m cons t ra in t s enhance the prec i s ion of theseconstants . But the que st ion remains as to whether thiss tat is t ical information is providing a real is t ic est i -mate as to how accura te one can expec t to p red ic t

A v = + l ro ta t iona l l ine f requenc ies wi th theseconstants .

In con t ras t to the f l ex ib il i ty o f the Du nha m model ,a m ore r igid mode l was also t ried, s imilar to the oneused in the analysis of AIF and A1C1 [23 ] . Specif i-cal ly, this involv ed f i t ting the da ta dire ct ly to the ei-genvalues of the radial SchrSdinger equat io n,

~ - u~ (R) +E(v, J )

)2--# [ 1 + q( R ) ] J ( J + 1 ) / R 2xv/(r, v, J ) = 0 , (3)

with the parameter ized Born-O ppenh e imer po ten t ia l ,

UBO=De {1 - e x p [ - f l ( R ) ]}2 ( 4 ){ 1 - e x p [ - f l ( o o ) ]} 2 '

where

# ( R ) = z Y. E z i , ( 5 )i=0

a n d

z = ( R - R e ) / ( R + R e ) . ( 6 )

Poten t ia l parameters ob ta ined f rom th i s f i t a re d i s -played in Ta ble 4 where the dissociat ion energy Dewas f ixed to the value given in Ref . [28] . The s tan-dard deviat ion was now signif icant ly higher, 60.4,with the largest increase in the residuals contr ib utedby the band h ead da ta wi th a roo t -mean-square de-v ia t ion of 0 .197 cm -1 . I t i s a lso impor ta n t to no tethat the s tat is tical weights used in the Dun ha m Yfi ts ,


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K Braun et aL / ChemicalPhysics Letters 228 (1994) 633-640

Table 3Dunham Y constants for CsI (in cm- t )

637

Constant This work

unconstrained constrained"

Re [7]

Yio 119. 1600 2(14 4) 119.16 5242(9 75)Y2o -0.250285(116) -0.2505696(750)10aY3o 0.28453(293) 0.28573(197)1 0 2 y o l 2.36274612(245) 2.36273842(58)1 0 S YH --0.06827322(967) --0.06826443(377)106Y21 0.048969(991 ) 0.048780(533)109Y31 0.1255(281) 0.1224(187)109 Yo 2 --3.72237(141) -3.7154183210 12 y~ 2 --2.028(196) --2.308810291013]:22 -- 0.2533536101 0 1 S Yo s -0.0714(321) -0.250428337

1019yi3 - --0.98150274610~Y23 - 0.7980648411022y~ - - 0.8892158271024y14 - 0.152376355I028 os - -0.2570415661031Yts - 0.820852269103sY~ - -0.8758004011041 I"o7 - - 0.315840421

119.1776(76)-0.2505(7)

2.3627357(15)-0.0682626(70)

0.04893(80)0.114(25)

-3.71464(47)-2.30(50)

-0.25043(13)

-0.8876(17)

"See text.

Table 4Born--Oppenheimer potential parameters

D~(cm -1) 28710Re(A) 3.3150949(177),8o 4.404121(304)

Pl -1.0409(190)

3 10 -6 cm -~ for the microwave and mill imeter-wave l ines and 0.002 cm- 1 for the band head posi-tions, were also used in this fit. Therefore, a fit of thedata to this more rigid model places a conservativeupper l imit of 0.2 cm - ~ on the accuracy of predictedAv= + 1 rotational l ine posit ions.

In addi t ion to representing the Born-Op penhei -mer potential by Eq. ( 4), we also obtain ed the Dun-ham form by expanding Eq. ( 4) in a power seriesabout R=Re . The Dun ham potent ia l cons tants de-rived in this manner are given in Table 5. For thepurpose of comparison, the as derived fro m the Ys ofthe co nstr aine d fit are also listed.

Table 5Dunham potential constants

BO potential Dunham Ys

ao(cm -I ) 149382(2 67) 150253(477)a~ -3.43841(452) -3.4286(154)a2 8.0309(220) 7.624(110)as - 15.5029(657) - 12.960(514)a4 26.508(153) 17.42(206)as -41.552(306) - 18.61(790)

3.3. Rittne r model

One ad dit ional model that we used in analyzing the

data was the Rittner potential ,

U(R) =-e ~+ 2R 4 + - - - -

c ,- R---g +A e x p ( - R / p ) + Uo. (7)

In Eq. (7) a+ and oz_ are the atomic polarizabil i t iesfor Cs and I- , C6 is a meas ure o f the va n der Waalsattraction between ions, A and p are co nstants that


6/8

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7/8

v. Braun et al. / Chemical Physics Letters 228 (1994) 633- 640 639

d i c a t e s ex c e l l e n t a g r e e m e n t b e t w e e n t h e r ; a n d a t o b -t a i n e d f r o m t h e D u n h a m Y s. O n t h e o t h e r h a n d , f o ra i f r o m t h e p o t e n t i a l f i t, g o o d a g r e e m e n t i s e x h i b i t e d

o n l y b e t w e e n t h e l o w e s t rt a n d a i a n d b e c o m e s p r o -g r e s s i v e l y w o r s e f o r t h e h i g h e r r t a n d a t .T h e f a c t t h a t a t fr o m t h e D u n h a m Y s r a t h e r t h a n

a t f r o m t h e p o t e n t i a l f i t ag r e e w i t h t h e R i t t n e r r~ t o5 % s e e m s t o s i g n i f y t h a t t h e R i t t n e r m o d e l i s ca -

p a b l e o f p r e d i c t i n g t h e s p e c t r u m m u c h m o r e a c c u -r a te l y t h a n t h e B o r n - O p p e n h e i m e r p o t e n t i al g i v en b yE q . ( 4 ) . To d e m o n s t r a t e t h a t t h i s w a s n o t t h e ca s e , as e t o f Y s w a s c o m p u t e d b y a v e r a g i n g t h e R i t t n e r r ;a p p e a r i n g i n t h e la s t t w o c o l u m n s o f Ta b l e 6 . G e n e r -a t i n g a s p e c t r u m w i t h t h e s e R i t t n e r Y s ( Ta b l e 7 ) g a v ea r o o t - m e a n - s q u a r e d e v i a t i o n o f 1 . 2 c m - 1 f o r th e o b -

s e r v e d - c a l c u l a t e d b a n d - h e a d p o s i t io n s ( 0 .0 0 2 c m - ~f o r p u r e r o t a t i o n t r a n s i t i o n s ) a s c o m p a r e d t o 0 .2c m - ~ f o r th e B o r n - O p p e n h e i m e r p o t e n t i a l f it . T h u s ,i t a p p e a r s t h a t t h e R i t t n e r m o d e l i s c a p ab l e o f p re -d i c t in g t h e r o v i b r a t i o n a l s p e c t r u m t o n o b e t t e r t h a n

1 c m - !. O b v i o u s l y, a m o r e r e f i n e d t r e a t m e n t m u s ta w a i t t h e a n a l y s i s o f r e s o l v e d r o t a t i o n a l s t r u c t u r e i nt h e f a r - I R s p e c t r u m b e f o r e a n y f i n a l c o n c l u s i o n c a nb e r e a c h e d .

4. Conclusion

I n f r a r e d e m i s s i o n s p e c t r o s c o p y i s a r e m a r k a b l ys e n s i t iv e t e c h n i q u e f o r t h e d e t e c t i o n o f h i g h - t e m p e r -a t u r e m o l e c u l e s , e v e n a t t h e l o n g e r w a v e l e n g t h e n do f t h e s p e c t r u m ( 1 0 0 ~ t m ). A l t h o u g h i n d i v i d u a l r o -t a t i o n a l l i n es c o u l d n o t b e r e s o l v e d b e ca u s e o f t h es m a l l r o t a t i o n a l c o n s t a n t , B ~ . 0 . 0 2 c m -~ , i t w a s s t i llp o s s i b l e t o i m p r o v e t h e v i b r a t i o n a l c o n s t an t s b y u s -i n g b a n d - h e a d p o s i t io n s . T h e a v a i l a b i l i t y o f h i g h - p r e-c i s i on m i c r o w a v e a n d m i l l i m e t e r - w a v e d a t a a l l o w e dt h e s e p a r a t i o n b e tw e e n t h e b a n d h e a d s a n d b a n do r i g i n s t o b e c a l c u l a t e d r e l i a b l y fo r t h e f i r s t t i m e .E m i s s i o n s p e c t r o s c o p y a t v e r y l o n g w a v e le n g t h s i s n o to n l y f e a s i b l e b u t i s al s o a u s e f u l t e c h n i q u e f o r e l u c i-d a t i n g m o l e c u l a r s t r u ct u r e a n d m o n i t o r i n g t h e c o n -c e n t r a t i o n s o f m o l e c u l e s a t h i g h t e m p e r a t u r e s .

Acknowledgement

We w i s h t o t h a n k R . H o n e r j~ i g er a n d T. T 6 r r i n g f o r

p r o v i d i n g t h e m e a s u r e d l i ne p o s i t i o n s u s e d i n R e f.[ 7 ] . We a l s o w i s h t o t h a n k J . O g i l v i e f o r k i n d l y p r o -v i d i n g u s w i t h t h e D u n h a m r e l a ti o n s i n a d v a n c e o fp u b l i c a t i o n . T h i s w o r k w a s s u p p o r t e d b y C A N D UO w n e r s G r o u p R e s ea r ch a n d D e v e l o p m e n t P r o g r am( W P 8 W P I R 1 80 7 ) , A E C L , a n d t h e N a t u r a l S c i e n c ea n d E n g i n e e r in g R e s e a r c h C o u n c i l o f C a n a d a .

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