Journal of Molecular Spectroscopy 261 (2010) 63–67

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Journal of Molecular Spectroscopy

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The m12 band of ethylene-1-13C (13C12CH4) by high-resolution FTIR spectroscopy

T.L. Tan *, G.B. LebronNatural Sciences and Science Education, National Institute of Education, Nanyang Technological University, 1, Nanyang Walk, Singapore 637616, Singapore

a r t i c l e i n f o

Article history:Received 9 February 2010In revised form 24 February 2010Available online 6 March 2010

Keywords:Ethylene-1-13C13C12CH4

High-resolution infrared spectrumRovibrational constantsFTIR study

0022-2852/$ - see front matter � 2010 Elsevier Inc. Adoi:10.1016/j.jms.2010.03.004

* Corresponding author. Fax: +65 6896 9446.E-mail address: augustine.tan@nie.edu.sg (T.L. Tan

a b s t r a c t

The Fourier transform infrared (FTIR) spectrum of the m12 fundamental band of ethylene-1-13C (or 13C12CH4)was recorded with an unapodized resolution of 0.0063 cm�1 in the wavenumber region of 1360–1520 cm�1.Rovibrational constants for the upper state (m12 = 1) up to five quartic and two sextic centrifugal distortionterms were derived for the first time by assigning and fitting a total of 879 infrared transitions using aWatson’s A-reduced Hamiltonian in the Ir representation. The root-mean-square deviation of the fit was0.00066 cm�1. The ground state rovibrational constants were also determined by a fit of 523 combina-tion-differences from the present infrared measurements, with a rms deviation of 0.00090 cm�1. The A-typem12 band which is centred at 1439.34607 ± 0.00004 cm�1 was found to be relatively free from local fre-quency perturbations. From the m12 = 1 rovibrational constants obtained, the inertial defect D12 was foundto be 0.242826 ± 0.000002 lÅ2.

� 2010 Elsevier Inc. All rights reserved.

1. Introduction

The vibrational structure of ethylene or ethene (C2H4) moleculeand its isotopomers has been studied extensively by low-resolu-tion infrared spectroscopy [1–5] in the past two decades. Further-more, many higher resolution infrared measurements and analyses[6–21] of the fundamental, overtone, and combination bands ofthese molecules were conducted mainly to study their rovibra-tional structures and to determine their rotational and higher orderconstants with high accuracy. Most of the latest high-resolutionFTIR studies are centred on 12C2H4 [7,17], 12C2D4 [8,9,14–16],trans-12C2H2D2 [10,19], cis-12C2H2D2 [11,18], 1,1-ethylene-d2

[20,21], and 13C2H4 [22]. However, infrared spectroscopic studieson 13C12CH4 remain very limited. In 1973, Duncan et al. [1] identi-fied the fundamental vibrational bands of 13C12CH4 and their bandcentres were assigned with an accuracy of 0.05 cm�1. Also, the fun-damental m10, m8, m7, m4, and m6 bands of 13C12CH4 have been studiedat a resolutions of 0.012 cm�1 [23] and 0.0017 cm�1 [24]. So far, thehigh-resolution FTIR spectrum of the m12 band of 13C12CH4 has notbeen measured or analysed.

In 2000, we used high-resolution FTIR spectroscopy to measureand analysed the m12 band of the normal ethylene (12C2H4) and im-proved the upper state (m12 = 1) rovibrational constants up to thesextic terms [17]. Likewise, we had studied the m12 bands of12C2D4 [14], of cis-12C2H2D2 [18], of trans-12C2H2D2 [19], of 13C2H4

[22] and of 12C2H3D [25] at high-resolution to improve on or to de-rive new ground and m12 = 1 rovibrational constants. The present

ll rights reserved.

).

work is aimed at the analysis of the m12 band of 13C12CH4 whichwas measured with a resolution of 0.0063 cm�1. By fitting 879 as-signed transitions for the m12 band, the rovibrational constants ofthe m12 = 1 state were obtained for the first time. Three rotational,five quartic, and two sextic centrifugal distortion constants weresufficient to give an accurate fit of the m12 transitions, with a rmsdeviation of 0.00066 cm�1. The ground state rovibrationalconstants for 13C12CH4 up to two sextic terms were also obtainedby fitting 523 combination-differences derived from the presentinfrared transitions. As the rms deviation of the fit is close to theestimated absolute accuracy (0.0006 cm�1) of the measured transi-tion, the m12 band appears to be relatively free of local frequencyperturbations.

2. Experimental details

The spectrum of the m12 band of 13C12CH4 was recorded using aBruker IFS 125 HR Michelson Fourier transform spectrophotometerwhich was set up in the Spectroscopy Laboratory of the NationalInstitute of Education, Singapore. An unapodized resolution of0.0063 cm�1 was used. A globar infrared source, and a high-sensi-tivity liquid nitrogen cooled Hg–Cd–Te detector, and KBr beamsplitter were used. The final spectrum was produced by coaddingthree runs of 200 scans each with the total scanning time of about10 h, to achieve a signal-to-noise ratio of about 30. The linewidth(FWHM) in the spectrum was observed to be about 0.0065 cm�1.

The ethylene-1-13C (or 13C12CH4) gas samples used in thesemeasurements were supplied by Aldrich Chemical Company,USA. The sample of 13C12CH4 has a chemical purity better than99 atom % in 13C. For the spectral measurements at the ambient

64 T.L. Tan, G.B. Lebron / Journal of Molecular Spectroscopy 261 (2010) 63–67

temperature of about 296 K, we used a multiple-pass absorptioncell of base path 20 cm, and by adjusting for 40 passes in the cell,an absorption path length of 8.0 m was achieved. The vapour pres-sure of about 5 torr in the cell was measured using a capacitancepressure gauge. A spectrum of the evacuated cell was recordedusing 200 scans at a resolution 0.1 cm�1. It was then transformedat 0.0063 cm�1 with zero-filling in order to obtain a backgroundspectrum. The ratio of the sample spectrum of 13C12CH4 to thatof the background gave a transmittance spectrum. Small oscilla-tions of period of about 1 cm�1 were observed in the baseline ofthe transmittance spectrum. However, a careful consistency checkon this channel spectrum showed that the absorption line posi-tions were not critically affected by the oscillations.

The spectrum was found with some strong absorption lines dueto H2O trace impurity in the gas cell. However, interference fromH2O lines was minor since the line positions of H2O are knownaccurately [26] and the lines are widely spaced. Calibration ofthe absorption lines of m12 of 13C12CH4 was done using some ofthese unblended and unsaturated H2O lines in the range of

Fig. 1. Low-resolution (0.5 cm�1) plot of the spectrum of m12 band of 13C12CH4.

Fig. 2. High-resolution (0.0063 cm�1) plot of the spectrum of m

1337–1487 cm�1. The selected H2O calibration frequencies weretaken from Guelachvili and Rao [26]. A correction factor of1.000000938 was required to bring the observed wavenumbersinto agreement with the calibrated frequencies. Fitting the posi-tions of 33 water vapour transitions for calibrating the wavenum-ber scale of the spectrum, it was possible to achieve a relativeprecision of 0.00037 cm�1 for all the measured transitions. There-fore, it is reasonable to estimate the absolute accuracy of the mea-sured 13C12CH4 lines to be approximately ±0.00060 cm�1 afterconsidering small systematic errors in the experiments. The sys-tematic errors could be caused by the channelling and noise levelin the spectrum, and by the wavenumber calibration.

3. Assignments and frequency analysis

The ethylene-1-13C (H213C12CH2) molecule is a simple asym-

metric top planar molecule of C2v symmetry with asymmetryparameter j of about �0.92. The m12 band is infrared active withA1 symmetry using the numbering of normal modes according toHerzberg [2], and is one of the 12 fundamental modes of vibrations[1,5]. The m12 vibration mode is ascribed to the in-plane C–H bend-ing. The low-resolution (0.5 cm�1) and high-resolution (0.0063cm�1) plots of the m12 spectrum in the 1390–1490 cm�1 region,showing the P, Q and R branches and its band centre, are illustratedin Figs. 1 and 2, respectively. It shows the presence of a prominentstrong central Q branch at about 1439.35 cm�1, which is typical ofan A-type band. In the rotational analysis, the band has been con-firmed to be A-type. Some strong absorption lines due to H2Oimpurity are also shown in Fig. 2.

In the high-resolution plot, strong absorption lines were easilyobserved with a regular spacing of about 1.8 cm�1 which is aboutB + C. During the initial assignment of the P and R branches ofthe band, the strongest of these lines was assigned as J = Kc andKa = 0 or 1 which were resolved with decreasing magnitude, upto J0 = 32 and 31 in the P and R branches, respectively. Fig. 3 showsthe asymmetry splitting for J0 = Kc

0 = 3, Ka = 0 and 1 transitions inthe J0 = 3 cluster in the P branch. Asymmetry splitting was also ob-served for Ka = 2 in the J0 = 3 cluster, while the transitions of Ka = 3

12 band of 13C12CH4 (H2O lines are indicated with an ‘‘�”).

Fig. 3. A detailed high-resolution (0.0063 cm�1) section of the P branch of m12 bandof 13C12CH4.

T.L. Tan, G.B. Lebron / Journal of Molecular Spectroscopy 261 (2010) 63–67 65

were not split and were unresolved doublets, as shown in Fig. 3.Intensity of the transitions decreases in the same J0 cluster as Ka in-creases. As J0 value increases, the asymmetry splitting occurs foreven higher Ka values for both P and R branches. Fig. 4 shows thespectrum of the transitions in the J0 = 6 cluster, and part of theJ0 = 7 cluster in the R branch region. For the J0 = 6 cluster, asymme-try splitting occurs for Ka = 0, 1, and 2, while the transition of Ka = 3shows early sign of splitting.

Since the rovibrational constants for m12 = 1 state of 13C12CH4

were not available, initial assignment of the transitions could bemade with the knowledge of the rovibrational constants of m12

bands of 12C2H4 [17] and of 13C2H4 [22]. These assignments wereinitially made for the transitions with low J values. Those low Jtransitions were fit to get preliminary constants that were usedto predict the higher J transitions. These transitions were then as-signed and the process repeated to extend the assignments to evenhigher quantum numbers. This bootstrap procedure allowed us toassign all the transitions with confidence and to remove any wrong

Fig. 4. A detailed high-resolution (0.0063 cm�1) section of the R branch of m12 bandof 13C12CH4.

assignments in the process. Accurate band constants up to two sex-tic terms obtained from the fitting of the P and R branch transitionswere used to calculate the Q branch transitions with high preci-sion. A total of 186 well-resolved Q branch transitions were confi-dently assigned and used in the final fit. The strongest lines wereall doublets with two possible values of Kc. There were enoughfairly unblended lines in the strong Q branch to ensure theaccuracy of the present assignments. Fig. 5 shows the 1440–1444 cm�1 region of m12 Q branch with Ka

0 = 4–8 well-defined clus-ters. For each Ka

0 cluster, the line intensity is maximum for J0 = Ka0,

and Kc0 = 0 or 1, and the intensity decreases as J0 increases.

4. Results and discussion

The nonlinear least-squares program which was previouslyused for the m12 bands of 12C2H4 [17] and of 13C2H4 [22] was alsoemployed to fit the assigned transitions of m12 of 13C12CH4. Thatprogram for fitting asymmetric rotor spectra uses a Watson Ham-iltonian [27] with an Ir representation in an A-reduction.

In the fitting process, the initial values used for the ground stateand upper state (m12 = 1) constants of 13C12CH4 were average valuescalculated from the respective constants of the m12 bands of 12C2H4

[17] and of 13C2H4 [22]. This is acceptable because the rovibrationalstructure of all three molecules is expected to be very similar andfree from local frequency perturbations [17,22]. In the presentanalysis to obtain the ground state constants, we added combina-tion-differences from the infrared measurements as they were as-signed. The improved ground state constants were then fixed in thefitting program to fit the upper state (m12 = 1) constants. As morenewly assigned infrared transitions were gradually included inthe fitting procedure to expand the set of data, the ground stateconstants were systematically refined and expanded to higher or-ders. Accurate ground state constants were needed because theywould be used as fixed values for the analyses of the m12 bandand other fundamental bands of 13C12CH4. A total of 523 groundstate combination-differences (GSCD) from the present infraredtransitions of the m12 band of 13C12CH4 were eventually used inthe final refinement to obtain the ground state constants. Becauseof the symmetry of 13C12CH4, there are no available microwavedata for a rotational analysis. By using combination-differencesto fit the ground state constants separately from the upper stateconstants, any perturbations (known or unknown) of the upperstates will not affect the ground state constants. The rovibrationalground state constants consisting of three rotational, five quarticconstants and two sextic terms were accurately derived from this

Fig. 5. A detailed high-resolution (0.0063 cm�1) section of the Q branch of m12 bandof 13C12CH4.

Table 1Ground state and upper state (m12 = 1) constants (cm�1) for 13C12CH4 (A-reduction, Ir representation).

12C2H413C12CH4 (this work) 13C2H4 (Ref. [22])

Ground state (Ref. [6]) m12 = 1 (Ref. [17]) Ground state m12 = 1 Ground state m12 = 1

A 4.864620(4) 4.9248646(18) 4.8653(8)a 4.925321(6)a 4.86501(35) 4.9250441(29)B 1.00105650(1) 1.00755112(35) 0.97609(1) 0.9822421(9) 0.9506876(35) 0.95651326(52)C 0.82804599(1) 0.82650582(20) 0.810884(9) 0.8093785(5) 0.7932777(33) 0.79181432(32)DJ � 105 0.1470224(41) 0.153993(22) 0.13926(68) 0.14575(8) 0.132945(191) 0.138857(34)DJK � 105 1.023214(36) 0.87317(62) 0.9976(68) 0.8595(15) 0.98023(155) 0.84491(103)DK � 103 0.0864798(16) 0.112414(21) 0.197(103) 0.22333(13) 0.0967(184) 0.122952(38)dJ � 106 0.281684(15) 0.31873(13) 0.25733(418) 0.29147(49) 0.24166(97) 0.27296(21)dK � 104 0.101590(14) 0.132392(83) 0.1118(150) 0.14135(33) 0.0928(24) 0.121506(154)HK � 106 0.006196(13) 0.014000(67) 6.64(4.48) 6.6536(7) 0 0.7827(135)hK � 106 0.00346(12) 0.00565(17) 0.108(67) 0.1112(12) 0 0.00180(29)m0 – 1442.442990(31) – 1439.34607(4) – 1436.654113(46)Number of infrared transitions 1387 523b 879 738b 1177Rms deviation (cm�1) 0.000334 0.0009 0.00066 0.0006 0.00045D12 (lÅ2) 0.053133(3) 0.242010(2) 0.05376(4) 0.242826(2) 0.05349(4) 0.242997(2)

a The uncertainty in the last digits (twice the estimated standard error) is given in parentheses.b For the ground state the number of infrared transitions is actually the number of combination-differences used in the fit.

66 T.L. Tan, G.B. Lebron / Journal of Molecular Spectroscopy 261 (2010) 63–67

work, as presented in Table 1. Inclusion of more sextic constantsdid not improve the accuracy of the ground state fit and are thusfixed at zero. The rms deviation of the combination-difference fitto obtain the final set of ground state constants is 0.00099 cm�1.All three rotational constants of the ground state from this fit agreewell to those given in Flaud et al. [24].

In our rotational analysis, the ground state constants were fixedto determine the upper state (m12 = 1) constants of 13C12CH4 up totwo sextic terms (HK and hK). Inclusion of more sextic constantsdid not improve the accuracy of the fit. A total of 879 infrared tran-sitions was finally assigned and fitted in the determination of them12 = 1 rovibrational constants as given in Table 1. The m12 bandcentre is found to be 1439.34607 ± 0.00004 cm�1. This value issmaller than that of 1440.5 cm�1 given by Duncan et al. [1], in1973, in their study of 13C frequency shifts in ethylene. The m12

band centre of 13C12CH4 is close to the average value of1439.54855 cm�1 calculated from the m12 band centres of 12C2H4

[17] and 13C2H4 [22], as given in Table 1. The fitting program,though written in terms of prolate matrix elements, presented nodifficulty in rapidly converging to the correct solution after severaliterations. In the least-square analysis, the infrared measurementswere weighted by the inverse square of the estimated uncertainty.The infrared transitions were given an uncertainty of 0.0006 cm�1

which is the absolute accuracy of the measured line. The rms devi-ation of the fit with all weighted lines was 0.00066 cm�1, which isclose to the absolute accuracy (0.0006 cm�1) of the measurements.The transitions included values of Ka ranging from 0 to 12. For the Pbranch, we had J0 and Kc

0 ranging from 0 to 34. For the R branch, J0

and Kc0 valued range from 1 to 34. The values of J and Kc ranged

from 2 to 19 and 0 to 12, respectively for the Q branch. The wideranging values of J0, Ka

0 and Kc0 used in the analysis effectively cover

the whole frequency range of 1360–1520 cm�1 for the m12 band of13C12CH4. A total of 366 transitions for the P branch, 186 for the Qbranch, and 327 for the R branch were finally assigned and in-cluded in the final fit.

The inertial defect D12 of 0.242826(2) lÅ2 of 12C13CH4 derivedfrom the present analysis, as given in Table 1, is between the valuesof D12 = 0.242010(2) lÅ2 of 12C2H4 [17] and of D12 = 0.242997(2)lÅ2 of 13C2H4 [22], as expected. The upper state rotational constantA = 4.925321(6) cm�1 of m12 of 13C12CH4 is close to those of 12C2H4

[17] and 13C2H4 [22], as given in Table 1, because the constant Acorresponds to the molecular axis which lies on the C@C bond. Sim-ilarly, the ground state constant A = 4.8653(8) cm�1 of 13C12CH4 is ingood agreement with those of 12C2H4 and of 13C2H4 as given in Table1. A simple calculation shows that the upper state (m12 = 1) and

ground state rotational constants B and C (as given in Table 1) of12C13CH4 are very close to the average values of those of 12C2H4

[6,17] and of 13C2H4 [22]. All five quartic ground state and upper stateconstants of m12 of 12C13CH4 (provided in Table 1) were found to berelatively close to those of 12C2H4 and 13C2H4. However, the two sex-tic (HK and hK) ground state and upper state constants of m12 of13C12CH4 are found to be larger than those of 12C2H4 and 13C2H4.The sign of all rovibrational constants of the three molecules ispositive.

It can be observed from Table 1 that the ground state constantsA and particularly DK of 13C12CH4 are less well determined as com-pared to the other ground state parameters. The reason is that onlya-type transitions are available from the m12 band in the presentGSCD analysis. Further studies with the addition of GSCD’s fromb- or c-type transitions would considerably improve the precisionof A and DK.

In this study, numerous infrared transitions of the m12 band of13C12CH4 were measured, assigned and fitted in its entirety to giveaccurate upper state (m12 = 1) constants up to two sextic terms forthe first time. In addition, the accurate ground state constants of13C12CH4 were also derived from a fit of combination-differencesfrom the present infrared measurements. These infrared spectraldata would be useful for a greater understanding of the molecularstructure of ethylene.

Acknowledgments

The authors are indebted to the financial support of this projectby the National Institute of Education, Singapore through researchGrant Nos. RS 3/08 TTL and RI 9/09 TTL.

Appendix A. Supplementary data

Supplementary data for this article are available on ScienceDi-rect (www.sciencedirect.com) and as part of the Ohio State Univer-sity Molecular Spectroscopy Archives (http://library.osu.edu/sites/msa/jmsa_hp.htm). Supplementary data associated with this arti-cle can be found, in the online version, at doi:10.1016/j.jms.2010.03.004.

References

[1] J.L. Duncan, D.C. McKean, P.D. Mallinson, J. Mol. Spectrosc. 45 (1973) 221–246.[2] G. Herzberg, Molecular Spectra and Molecular Structure, vol. 2, D. Van

Nostrand, New York, USA, 1945.

T.L. Tan, G.B. Lebron / Journal of Molecular Spectroscopy 261 (2010) 63–67 67

[3] J.L. Duncan, A.M. Ferguson, J. Chem. Phys. 89 (1988) 4216–4226.[4] J.L. Duncan, A.M. Ferguson, S.T. Goodlad, Spectrochim. Acta 49A (1993) 149–

160.[5] R. Georges, M. Bach, M. Herman, Mol. Phys. 97 (1999) 279–292.[6] E. Rusinek, H. Fichoux, M. Khelkhal, F. Herlemont, J. Legrand, A. Fayt, J. Mol.

Spectrosc. 189 (1998) 64–73.[7] R. Georges, M. Bach, M. Herman, Mol. Phys. 90 (1997) 381–387.[8] J.L. Duncan, Mol. Phys. 83 (1994) 159–169.[9] A.K. Mose, F. Hegelund, F.M. Nicolaisen, J. Mol. Spectrosc. 137 (1989) 286–295.

[10] F. Hegelund, J. Mol. Spectrosc. 135 (1989) 45–58.[11] F. Hegelund, F.M. Nicolaisen, J. Mol. Spectrosc. 128 (1988) 321–333.[12] B.G. Sartakov, J. Oomens, J. Reuss, A. Fayt, J. Mol. Spectrosc. 185 (1997) 31–47.[13] T. Platz, W. Demtroder, Chem. Phys. Lett. 294 (1998) 397–405.[14] T.L. Tan, K.L. Goh, P.P. Ong, H.H. Teo, Chem. Phys. Lett. 315 (1999) 82–86.[15] K.L. Goh, T.L. Tan, P.P. Ong, H.H. Teo, Mol. Phys. 98 (2000) 583–587.[16] T.L. Tan, K.L. Goh, P.P. Ong, H.H. Teo, J. Mol. Spectrosc. 202 (2000) 249–252.

[17] T.L. Tan, S.Y. Lau, P.P. Ong, K.L. Goh, H.H. Teo, J. Mol. Spectrosc. 203 (2000) 310–313.

[18] K.L. Goh, T.L. Tan, P.P. Ong, H.H. Teo, Chem. Phys. Lett. 325 (2000) 584–588.[19] H.H. Teo, P.P. Ong, T.L. Tan, K.L. Goh, J. Mol. Spectrosc. 204 (2000) 145–147.[20] F. Hegelund, J. Mol. Spectrosc. 139 (1990) 286–298.[21] F. Hegelund, J. Mol. Spectrosc. 148 (1991) 415–426.[22] T.L. Tan, K.L. Goh, P.P. Ong, H.H. Teo, J. Mol. Spectrosc. 207 (2001) 189–192.[23] M. De Vlesschouwer, Ch. Lambeau, A. Fayt, J. Mol. Spectrosc. 93 (1982) 405–

415.[24] J.M. Flaud, W.J. Lafferty, R. Sams, V. Malathy Devi, J. Mol. Spectrosc. 259 (2010)

39–45.[25] T.L. Tan, K.L. Goh, H.H. Teo, J. Mol. Spectrosc. 228 (2004) 105–109.[26] G. Guelachvili, K. Narahari Rao, Handbook of Infrared Standards, Academic

Press, Orlando, Florida, USA, 1986.[27] J.K.G. Watson, in: J.R. Durig (Ed.), Vibrational Spectra and Structure, A Series of

Advances, vol. 6, Elsevier, New York, USA, 1977 (Chapter 1).