17 December 1999

Ž .Chemical Physics Letters 315 1999 82–86www.elsevier.nlrlocatercplett

High-resolution Fourier transform infrared spectroscopy andanalysis of the n fundamental band of ethylene-d12 4

T.L. Tan a,), K.L. Goh b, P.P. Ong b, H.H. Teo b

a DiÕision of Physics, School of Science, Nanyang Technological UniÕersity, National Institute of Education, 469 Bukit Timah Road,Singapore 259756, Singapore

b Department of Physics, Faculty of Science, National UniÕersity of Singapore, Lower Kent Ridge Road, Singapore 119260, Singapore

Received 6 September 1999

Abstract

Ž . Ž .The Fourier transform infrared IR spectrum of the n fundamental band of ethylene-d C D has been measured12 4 2 4

with an unapodized resolution of 0.004 cmy1 in the frequency range of 1030–1130 cmy1. A total of 1340 assignedtransitions have been analyzed and fitted using a Watson’s A-reduced Hamiltonian in the I r representation to derive

Ž . y1rovibrational constants for the upper state Õ s1 up to five quartic terms with a standard deviation of 0.00042 cm .12

They represent the most accurate constants for the band thus far. The ground state rovibrational constants were also furtherimproved by a fit of combination–differences from the IR measurements. The relatively unperturbed band was found to bebasically A-type with a band centre at 1076.98492"0.00003 cmy1. q 1999 Elsevier Science B.V. All rights reserved.

1. Introduction

Ž .The infrared IR spectrum of some fundamentaland combination bands of gaseous ethylene-d4Ž .C D has been studied at a resolution up to 0.022 4

y1 w xcm by Duncan and co-workers since 1981 1–5 .The Raman spectrum of n and n bands has been3 6

w xfurther investigated by Mompean et al. 6 . In partic-ular, the n fundamental of ethylene-d was mea-12 4

w x y1sured 2 at a resolution of 0.05 cm and analyzedto obtain up to one quartic constant. In another IRmeasurement at 0.02 cmy1 resolution by Mose et al.w x7 , the rovibrational constants of the upper stateÕ s1 and those of the ground state were further12

) Corresponding author. Tel.: q65-460-5920; fax: q65-469-8952; e-mail: tlatan@nie.edu.sg

improved. So far, IR measurements of n of resolu-12

tion better than 0.02 cmy1 have not been reportedfor ethylene-d .4

A systematic study of the high-resolution IR spec-trum of some of the bands of ethylene-d will be4

useful for a more accurate understanding of thestructure of the molecule. In this work, we report theresults of the analysis of the n band which was12

measured with a resolution of 0.004 cmy1. From 821combination differences of the IR transitions, wehave improved the values for the rotational and allfive quartic centrifugal distortion constants of theground state. By fitting 1340 assigned transitions forthe n band, the constants of the Õ s1 state were12 12

further improved.All the rotational and quartic centrifugal distortion

constants were sufficient to give an accurate fit ofthe whole band. In the analysis of its rotational

0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 99 01200-2

( )T.L. Tan et al.rChemical Physics Letters 315 1999 82–86 83

Ž .structure, the root mean square rms deviation of thetransitions is found to be 0.00042 cmy1 which is anorder of magnitude more accurate than the reported

w xwork 7 . Since the rms deviation is close to theŽ y1 .estimated absolute accuracy 0.0004 cm of the

measured line, the n band appears to free of12

significant frequency perturbations.

2. Experiment

Ž .Samples of ethylene-d C D used in these4 2 4

measurements was purchased from Cambridge Iso-Ž .tope Laboratories Cambridge, MA . The sample of

gaseous C D has a chemical purity better than2 4

98%. Pyrex glass, stainless steel, Viton O-rings,CaF IR windows, and perfluorinated grease were2

used.For these measurements we used a single-pass

absorption cell which had a 20 cm absorption pathlength. The vapor pressure in the cell was measuredand adjusted to about 5 Torr and the cell was sealedfor the spectral measurements. The pressure mea-surements were made with a capacitance gauge. Allmeasurements were made at the ambient temperatureof about 296 K.

The spectra were obtained with a BomemDA3.002 Fourier transform spectrophotometer at the

w xNational University of Singapore 8 . A KBr beamsplitter, a globar IR source, and a high-sensitivityliquid nitrogen-cooled Hg–Cd–Te detector were

Ž y1 .used. A low-pass band filter 0–1500 cm wasused to reduce background noise level.

The final spectrum was produced by coaddingthree runs of 50 scans each with the total scanningtime of about 14 h. All spectra collected were un-

Ž .apodized. The observed linewidth FWHM in thespectrum was about 0.0036 cmy1.

A spectrum of the evacuated cell, consisting of200 scans at a resolution 0.1 cmy1, was then mea-sured and transformed at 0.004 cmy1 with zero-fill-ing in order to obtain a background spectrum. Thisspectrum when ratioed with the sample spectrumgave a transmittance spectrum with an essentiallyflat baseline.

The spectrum of the n band was calibrated12

using the absorption lines in the range 1027–1150cmy1 of NH , which was recorded immediately3

before the scanning of the spectra of C D . The NH2 4 3

calibration frequencies were taken from Guelachviliw xand Rao 9 .

Corrections of about 0.00065–0.00071 cmy1 wererequired to bring the observed wavenumbers intoagreement with the calibrated frequencies. From theline fitting involving 31 frequency values, the rela-tive precision of the wavenumbers obtained was inthe order of 0.0002 cmy1. It seems reasonable toestimate the absolute accuracy of the measured linesto be approximately "0.0004 cmy1 given the possi-bility of small systematic errors.

3. Assignments and frequency analysis

Ž .Ethylene-d C D is an asymmetric top4 2 4Ž .molecule ksy0.818 with 12 fundamental modes

of vibrations. The n band which is IR active has12w xB symmetry 4 . The band has been analyzed to be3u

Ž .primarily A-type. A survey spectrum Fig. 1 showsthe presence of a prominent strong central Q branchat about 1077 cmy1, which is typically an A-typeband. Fig. 2 shows a region of the Q branch regionwhere the absorption lines are well resolved.

In the initial assignment of the A-type n band,12

several strong transitions were immediately notedy1 Ž .with a spacing of about 1.3 cm which is BqC

in the P and R branches. The strongest of these wasattributed to the resolved JsK and K s0 or 1 inc a

Fig. 1. A survey spectrum of the n band of C D .12 2 4

( )T.L. Tan et al.rChemical Physics Letters 315 1999 82–8684

Fig. 2. A detailed section of the Q branch region of C D .2 4

the P and R branches. For higher K values, thea

intensity of the transitions decreases. Fig. 3 illus-trates a region in the P branch for some transitionsof J X s7, 8, and 9.

From Fig. 3, asymmetry splittings were observedfor K (4 in the J X s7 and 8 clusters, while thea

transitions of K s5, 6, 7, 8 and 9 were not splita

and were unresolved doublets. As the J value in-creases the asymmetry splitting occurs for evenhigher K values. Fig. 4 illustrates the J X s14–17a

region in the R branch where K values up to 11 area

Fig. 3. A detailed section of the P branch region of C D .2 4

Fig. 4. A detailed section of the R branch region of C D .2 4

shown. The figure also shows that splitting starts tooccur for the J X s15, K s6 transition.a

Assignment of the transitions was relatively easyby using accurate ground state combination differ-ences which are calculated from the available ground

w xstate rotational constants 2,7 . The assignments wereinitially made for the transitions with low J values.Those low J transitions were fit to get preliminaryconstants that were used to predict the higher Jtransitions. These transitions were then assigned andthe process repeated to extend the assignments toeven higher quantum numbers. This bootstrap proce-dure allowed us to assign all the transitions withconfidence and to remove any wrong assignments inthe process.

Assignments of the Q branch lines could only beconfidently made after the P and R branch transi-tions had been assigned and fit. Band constantsobtained from the fitting of the R and P branchlines were used to calculate the Q branch transitionswith a high degree of accuracy. A total of 264well-resolved Q branch transitions were used in thefit. The strongest lines were all doublets with twopossible values of K . There were enough fairlyc

isolated lines in the strong Q branch to ensure theaccuracy of the present assignments. Fig. 2 showsthe assignments of the Q branch transitions belong-ing to the K s6, 7, and 8 clusters.a

( )T.L. Tan et al.rChemical Physics Letters 315 1999 82–86 85

4. Results and discussion

The assigned transitions were fitted using thesame non-linear least-squares program that was used

w xfor HCOOD 8 . That program for fitting asymmetricw xrotor spectra uses a Watson Hamiltonian 10 with an

I r representation in an A-reduction.The initial ground state constants were taken from

w xMose et al. 7 . In this work, we add combination–differences from the IR measurements as they wereassigned. The improved ground state constants werethen fixed in the fitting program to fit the upper stateŽ .n s1 constants. As more newly assigned IR12

transitions were gradually included in the fittingprocedure to expand the set of data, the ground stateconstants were systematically refined. In the least-squares analysis the measurements were weighted bythe inverse square of the estimated uncertainty. TheIR transitions were given an uncertainty of 0.0004cmy1 which is the absolute accuracy of the mea-sured line.

The best possible ground state constants wereneeded because they would be used as fixed valuesfor the analyses of the n band and other fundamen-12

tal bands of C D . A total of 821 combination–dif-2 4

ferences from the present IR transitions of the n12

band of C D was eventually used in the final2 4

refinement. By using combination–differences to fitthe ground state constants separately from the upper

Žstate constants, any perturbations known or un-.known of the upper states will not affect the ground

state constants.w xThe ground state constants from Ref. 7 and

those derived from this work are presented in Table1. We have also fitted the n s1 constants using12

Ž .both sets of ground state constants Table 1 . Inclu-sion of more sextic constants did not improve theaccuracy of the fit and are thus fixed at zero. A totalof 1340 IR transitions was used in the determinationof the upper state constants. The fitting program,although written in terms of prolate matrix elements,presented no difficulty in rapidly converging to thecorrect solution after several iterations. The rmsdeviation of the fit with all weighted lines was0.00042 cmy1. The transitions include values of Ka

ranging from 0 to 16. For the P branch, we have J X

and K X ranging from 0 to 38 and 0 to 37, respec-c

tively. For the R branch, we have J X and K X rang-c

ing from 2 to 38 and 1 to 38 respectively. The valuesof J and K range from 2 to 24 and 0 to 16,c

respectively, for the Q branch. The wide rangingvalues of J X, K X and K X used in the analysisa c

effectively cover the whole frequency range of1030–1130 cmy1 for the n band.12

w xIn an earlier work in 1981 by Harper et al. 2 , theŽ .rotational constants A, B,C , distortion constant D ,J

and band center for the upper state n s1 were12

obtained from the analysis of 375 IR transitions with

Table 1Ž y1 . Ž r .Rovibrational constants cm for the ground state and n of C D A-reduction, I representation12 2 4

Ground state Õ s1 Ground state Õ s112 12w x Ž .Ref. 7 present work

Ž . Ž . Ž . Ž .A 2.441 656 20 2.464 179 8 20 2.441 678 133 2.464 189 65 77Ž . Ž . Ž . Ž .B 0.734 913 9 0.739 788 03 47 0.734 933 4 33 0.739 810 27 34Ž . Ž . Ž . Ž .C 0.563 517 9 0.562 788 84 26 0.563 522 1 26 0.562 793 68 19

6 Ž . Ž . Ž . Ž .D =10 0.788 5 0.833 62 32 0.803 3 21 0.850 00 24J5 Ž . Ž . Ž . Ž .D =10 0.273 1 25 0.218 77 20 0.268 75 143 0.214 739 148JK

4 Ž . Ž . Ž . Ž .D =10 0.209 9 8 0.251 13 24 0.225 29 0.264 331 34K6 Ž . Ž . Ž . Ž .d =10 0.212 3 0.235 07 19 0.214 38 105 0.238 231 139J5 Ž . Ž . Ž . Ž .d =10 0.378 11 0.463 80 54 0.383 5 66 0.468 85 40K9 Ž . Ž .H =10 0.89 9 1.406 71 0 0K

Ž . Ž .n – 1076.984 847 47 – 1076.984 919 320aNumber of IR transitions 1340 821 1340

y1Ž .rms deviation cm 0.000 57 0.000 68 0.000 422Ž . Ž . Ž .D mA 0.325 6 5 0.326 01 812

a For the ground state the number of IR transitions is actually the number of combination differences used in the fit.

( )T.L. Tan et al.rChemical Physics Letters 315 1999 82–8686

rms deviation of 0.0101 cmy1 using a full asymmet-ric rotor model. Although the accuracy of their re-sults is limited mainly by the small number oftransitions, lower J and K values used in thea

analysis, there is generally good agreement betweentheir constants and those from the present work asgiven in Table 1. The band center derived from thiswork falls between the two values given by Harper

w xet al. 2 in their two different methods of analysis.˚2The inertial defect D of 0.326 mA from the12

present analysis is slightly higher than that of Ref.˚2w x2 which is 0.320 mA .

Table 1 shows that the all ground state constantsw xtaken from Ref. 7 and those from the present IR

combination–differences analysis are in good agree-ment. Except for constants A and D , the otherK

ground state constants from the present work aremore accurately determined using 821 combinationdifference transitions which were fitted with a rmsdeviation of 0.00068 cmy1. These ground state con-stants represent the latest improved values for C D .2 4

The upper state n s1 constants especially the band12

center and rotational constants, derived using twodifferent sets of ground state constants show goodagreement. The rms deviation from both sets ofanalysis is found to be close to the absolute lineaccuracy of 0.0004 cmy1. The investigation on the

w xn band by Mose et al. 7 in 1989 from a spectrum12

collected with the resolution of 0.03 cmy1, gaveaccurate band constants which are closer to theirrespective ground state constants. This is because then , n , and n bands were analyzed simultane-12 7 10

ously taking into account all first-order Coriolis reso-nances within the tetrad n , n , n , n . The rms12 4 7 10

w x y1deviation of the fit in Ref. 7 was 0.0070 cm . Theaccuracy of their results is mainly limited by the lowresolution of the spectrum which does not allow acomplete analysis of the Q branch lines which arevery dense. From our analysis and those of Harper et

w xal. 2 , the n band is observed to be free from local12

perturbations. Therefore the rovibrational constantsfor n can be accurately derived from a straightfor-12

ward analysis using a set of accurate ground stateconstants. The constants obtained from the presentinvestigation can be used to reproduce the absorptionlines with a rms deviation of 0.00042 cmy1. Theyrepresent the latest improved values for the n band12

of C D .2 4

References

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w x2 J. Harper, A.R. Morrisson, J.L. Duncan, Chem. Phys. Lett.Ž .83 1981 32.

w x Ž .3 J. Harper, J.L. Duncan, Mol. Phys. 46 1982 139.w x Ž .4 J.L. Duncan, A.M. Ferguson, J. Chem. Phys. 89 1988 4216.w x Ž .5 J.L. Duncan, Mol. Phys. 83 1994 159.w x6 F.J. Mompean, R. Escribano, S. Montero, J. Mol. Spectrosc.

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Ž .Mol. Spectrosc. 191 1998 343.w x9 G. Guelachvili, K. Narahari Rao, Handbook of Infrared

Standards, Academic Press, Orlando, FL, 1986.w x Ž .10 J.K.G. Watson, in: J.R. Durig Ed. , Vibrational Spectra and

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