Journal of Molecular Spectroscopy 303 (2014) 42–45

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Journal of Molecular Spectroscopy

journal homepage: www.elsevier .com/locate / jms

Rovibrational constants of the ground and m12 = 1 states of C2D4

by high-resolution synchrotron FTIR spectroscopy

http://dx.doi.org/10.1016/j.jms.2014.07.0040022-2852/� 2014 Elsevier Inc. All rights reserved.

⇑ Corresponding author. Fax: +65 8969414.E-mail address: augustine.tan@nie.edu.sg (T.L. Tan).

T.L. Tan a,⇑, M.G. Gabona a, Dominique R.T. Appadoo b, Peter D. Godfrey c, Don McNaughton c

a Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singaporeb Australian Synchrotron, 800 Blackburn Rd., Clayton, Victoria 3168, Australiac School of Chemistry, Monash University, Wellington Rd., Clayton, Victoria 3800, Australia

a r t i c l e i n f o

Article history:Received 6 June 2014Available online 24 July 2014

Keywords:Ethylene-d4

C2D4

Deuterated ethyleneHigh-resolution infraredSynchrotron infraredRovibrational constantsFTIR spectroscopy

a b s t r a c t

The Fourier transform infrared (FTIR) absorption spectrum of the m12 fundamental band of ethylene-d4

(C2D4) was recorded in the 1000–1150 cm�1 region with a resolution of 0.00096 cm�1 using the THz/far-infrared beamline of the Australian Synchrotron. Upper state (m12 = 1) rovibrational constants consist-ing of three rotational constants and up to five quartic constants were improved by assigning and fitting3950 rovibrational transitions using Watson’s A-reduced and S-reduced Hamiltonians in the Ir represen-tation. The band centres of the unperturbed A-type m12 band are found to be 1076.984958(14) cm�1 and1076.984813(14) cm�1 for A-reduced and S-reduced Hamiltonians respectively. The present analysis, cov-ering a wider wavenumber range and higher J and Kc values (up to 58) than previous studies, yielded upperstate constants including the band centre which are more accurate than previously reported. The rms devi-ation of the upper state (m12 = 1) fit is 0.00040 cm�1 in the A-reduction and 0.00041 cm�1 in the S-reduction.Improved ground state rovibrational constants were also determined from the fit of 3151 ground statecombination differences (GSCD) from the presently-assigned transitions of the m12 band of C2D4 usingWatson’s A-reduced and S-reduced Hamiltonians in the Ir representation. The rms deviation of the GSCDfit is 0.00036 cm�1 in the A-reduction and 0.00035 cm�1 in the S-reduction. The ground state constants ofC2D4 derived from the experimental GSCD fit are in good agreement with those from theoretical calcula-tions using the B3LYP/cc-pVTZ, MP2/cc-pVTZ, and CSSD/cc-pVTZ levels, up to five quartic constants.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction sured infrared transitions and 1247 ground state combination dif-

Among the earliest studies on the infrared rotation-vibrationalstructures of deuterated ethylene or ethylene-d4 (C2D4) were thoseof Duncan and co-workers [1–5] at a spectral resolution up to0.02 cm�1 which was considered to be high at that time. In partic-ular, in 1981, Harper et al. [2] measured the m12 fundamental bandof C2D4 with a resolution of 0.05 cm�1 and did a rovibrational anal-ysis to obtain up to one quartic centrifugal distortion constant.Later, Mose et al. [6] reported improved rovibrational constantsof the m12 = 1 state of C2D4 and those of the ground state in theirinfrared measurements at a resolution of 0.02 cm�1. Since 2000,Tan and co-workers [7–10] studied the m9, m11, and m12 bands ofC2D4 using FTIR spectra measured at a resolution up to0.004 cm�1. In their latest work, Tan et al. [10] measured the FTIRspectrum of the m12 band of C2D4 in the 1017–1137 cm�1 region ata resolution of 0.0063 cm�1 and derived accurate m12 = 1 andground state constants up to five quartic constants from 2103 mea-

ferences (GSCDs) respectively.As a continuation of our high-resolution infrared investigations

on C2D4, we now report the results of further measurement andanalysis of rovibrational transitions of the m12 band recorded at aresolution of 0.00096 cm�1 at the THz/far-infrared beamline ofthe Australian Synchrotron. This is the highest resolution used sofar to record the m12 band of C2D4. By fitting many more newly-assigned transitions up to high J and Kc quantum numbers, theoverall accuracy of the rovibrational constants of the upper state(m12 = 1) for all three rotational and five quartic constants includingthe band centre of m12 was further improved. Furthermore, groundstate constants were more accurately determined from a GSCD fit.The ground state constants were compared to those derived atthree different levels of theory.

2. Experimental and theoretical details

The C2D4 gas samples of 98% atomic purity used in theexperiment were purchased from Cambridge Isotope Laboratories

Fig. 1. Experimental high-resolution spectrum of the m12 band of C2D4 at vaporpressures of (a) 15 mTorr, and (b) 5 Torr.

T.L. Tan et al. / Journal of Molecular Spectroscopy 303 (2014) 42–45 43

in Cambridge, MA, USA. The C2D4 spectra were recorded with a res-olution of 0.00096 cm�1 on a Bruker IFS 125HR Michelson Fouriertransform spectrophotometer using the THz/far-infrared beamline(beam current of about 200 mA) at the Australian Synchrotron inthe 600–1350 cm�1 region. All spectra were recorded at the ambi-ent temperature of about 296 K with a liquid nitrogen cooled Hg–Cd–Te detector and KBr beam splitter at two C2D4 vapor pressuresof 15 mTorr and 5 Torr in the cell as measured using a capacitancepressure gauge. The spectra were recorded with a 12.5 mm aper-ture at a scan rate of 80 kHz. A multiple-pass absorption cell witha 55-cm base path length was used and by adjusting for 16 passesin the cell, an optical path length of 8.80 m was achieved. Totalscanning time for the final spectrum was about 9 h to give asignal-to-noise ratio higher than 20. The final interferogram wasFourier transformed using a 4-point apodization function and apost-zero fill factor of 8. The average Doppler full-width at halfmaximum (FWHM) of 20 isolated lines selected from various partsof the spectrum was found to be 0.0026(2) cm�1.

A trace of CO2 which was found as an impurity in the C2D4 gassamples was used for the calibration of absorption lines of the m12

band of C2D4. The CO2 calibration wavenumbers in the620–710 cm�1 region were taken from Guelachvili and Rao [11].By fitting a total of 23 CO2 lines in the calibration of the wavenum-ber scale of the spectrum, a relative precision better than0.0001 cm�1 for all observed transitions was achieved. Allowingfor small systematic errors from wavenumber calibration, theDoppler-limited FWHM value, and the noise level in the spectra,it appears to be reasonable to approximate the absolute accuracyof the measured C2D4 lines to be ±0.00035 cm�1.

Theoretical calculations were performed using GAUSSIAN09[12] at the CSSD/cc-pVTZ, MP2/cc-pVTZ, and B3LYP/cc-pVTZ levelsof theory. Geometry optimizations, followed by vibrational analy-ses were used to predict rotational constants and quartic centrifu-gal distortion constants respectively of the ground state of C2D4.The quantum mechanical calculations of the ground state rovibra-tional constants were then used to compare with the GSCD-fittedvalues. Similar calculations using GAUSSIAN09 were carried outon 1-phosphapropyne [13] and ketenimine [14] by Bane et al.who found that the resultant equilibrium constants matchedexperimental rotational constants to within 0.3–0.6% or betterand quartic centrifugal distortion constants to within 1–2%.

Fig. 2. (a) A detailed section of the Q branch region of the m12 band of C2D4 and (b)its corresponding simulation.

3. Results and discussion

Ethylene-d4 (C2D4) is an asymmetric top planar molecule withasymmetry parameter j of about 0.818 [7–10]. The infrared-activeA-type m12 band is assigned to an in-plane C–H bending with B3u

symmetry [9,10]. The rotational structure of the m12 band has beendescribed and illustrated in details in Tan et al. [10]. Fig. 1(a) showsthe high-resolution spectrum of the whole m12 band in the 1000–1150 cm�1 range, recorded at the C2D4 vapor pressure of 15 mTorr.At this vapor pressure, the transmittance spectrum of the strongestabsorption lines was not saturated. To study absorption lines ofhigh J and Kc values which were weaker and situated further fromthe band centre, another spectrum of higher vapor pressure at5 Torr was recorded, as shown in Fig. 1(b). Fig. 2(a) shows adetailed section of the dense Q-branch region of C2D4 m12 band inthe 1077 to 1080 cm�1 region. The simulated spectrum in thisregion is shown in Fig. 2(b). The absorption lines were simulatedby convolving with a Gaussian line shape with appropriate fullwidth at half maximum (FWHM) of 0.0026 cm�1.

In the previous work of Tan et al. [10], a total of 2103 assignedtransitions were measured and fitted to derive accuraterovibrational constants for the upper state (m12 = 1) of C2D4 up tofive quartic terms. Also, ground state constants of C2D4 were

improved by a combination-difference fit of 1247 transitions fromthese infrared measurements. In comparison, the present analysisconsisted of a total of 3950 infrared transitions within the widerrange of 1015–1140 cm�1, resulting in the most accurate rovibra-tional constants of the m12 = 1 state reported for C2D4 so far. More-over, the assigned transitions from the present work span quantumnumbers J0 = 0 through 58, Ka

0 = 0 through 21, and Kc0 = 0 through

57 compared to the previous work’s quantum number ranges ofJ0 = 0 through 46, Ka

0 = 0 through 17, and Kc0 = 0 through 45. The

present work also gives the most accurate rovibrational groundstate constants for C2D4 to date, as a result of fitting 3151 groundstate combination differences (GSCD’s) from the present m12 transi-tions, compared to the previous work [10] where 1247 GSCD’swere used. For the fitting of the IR transitions of the m12 = 1 stateand of the GSCD’s, both Watson’s A-reduced and S-reduced Hamil-tonians in the Ir representation [15] were used.

GSCD’s from the present infrared measurements of m12 wereused to derive and improve the ground state constants of C2D4.Upper state (m12 = 1) constants were fitted with the improvedground state constants fixed in the fitting program. The ground

44 T.L. Tan et al. / Journal of Molecular Spectroscopy 303 (2014) 42–45

state constants were further refined as more assigned transitionswere gradually included in the fitting procedure to expand theset of data. In Table 1, the ground state constants consisting ofrotational constants, and all five quartic centrifugal distortionconstants (A-reduced in the Ir representation) accurately derivedfrom this work are presented. The rms deviation of the combina-tion differences fit is 0.00036 cm�1. Previously-derived groundstate constants [10] are included in Table 1 for comparison. Alsogiven in Table 1 are the equilibrium constants which were pre-dicted using theoretical calculations at three different levels:CSSD/cc-pVTZ, MP2/cc-pVTZ, and B3LYP/cc-pVTZ levels using Wat-son’s A-reduced Hamiltonian in the Ir representation. Relativelygood agreement of less than 0.6% for the ground state constantsand a few % for the five quartic terms is observed, as given inTable 1. All three equilibrium rotational constants derived fromcalculations at the three levels were found to be slightly higherthan experimentally determined ground state values, as expected.

Table 1Ground state rovibrational constants (cm�1) of C2D4 (A-reduction of the Ir representation)

CSSD/cc-pVTZ MP2/cc-pVTZ

A 2.45859787 2.45875778B 0.73848562 0.73925980C 0.56790483 0.56837110DJ � 106 0.77599 0.78334DJK � 105 0.27016 0.27997DK � 104 0.19694 0.19576dJ � 106 0.20656 0.20837dK � 105 0.37203 0.37795No. of IR transitionsrms deviation (cm�1)D12 (u Å2)

a The uncertainty in the last digits (twice the estimated standard error) is given in pab For the ground state the number of infrared transitions is actually the number of co

Table 2Ground state rovibrational constants (cm�1) of C2D4 (S-reduction of the Ir representation)

CSSD/cc-pVTZ MP2/cc-p

A 2.45859787 2.45875B 0.73848562 0.73925C 0.56790483 0.56837DJ � 106 0.68811 0.69388DJK � 105 0.32289 0.33365DK � 104 0.19254 0.19128d1 � 106 �0.20656 �0.20837d2 � 107 �0.43938 �0.44729No. of IR transitionsrms deviation (cm�1)D12 (u Å2)

a The uncertainty in the last digits (twice the estimated standard error) is given in pab For the ground state the number of infrared transitions is actually the number of co

Table 3Rovibrational constants (cm�1) for the m12 = 1 state of C2D4 (Ir representation).

Tan et al. [10] (A-reduction) Pre

A 2.4640741(6)a

B 0.7398056(1)C 0.5627944(1)DJ � 106 0.84985(6)DJK � 105 0.21414(6)DK � 104 0.24823(2)dJ � 106 0.23813(4)dK � 105 0.4714(1)m0 1076.98480(2) 10No. of infrared transitions 2103 39rms deviation (cm�1) 0.00045D12 (u Å2) 0.32551(1)

a The uncertainty in the last digits (twice the estimated standard error) is given in pa

Similar trends in direction and % deviation were observed in therotational constants from B3LYP/cc-pVTZ calculations comparedwith those derived from IR bands in the study of ketenimine usingsynchrotron infrared spectroscopy [14]. Furthermore, relativelygood agreement was observed between the ground state constantsfrom the present GSCD’s fit and those from theoretical calculationsusing the Watson’s S-reduced Hamiltonian in the Ir representation,as provided in Table 2.

In the upper state analysis, a total of 3950 assigned a-type tran-sitions were fitted in the determination of the upper state (m12 = 1)rovibrational constants up to five quartic terms, as provided inTable 3, using both Watson’s A-reduced and S-reduced Hamiltoni-ans [15] in the Ir representation. A fitting program developed byMaki [16,17] was used for this analysis. In the least square analysis,the infrared measurements were weighted by the inverse square ofthe estimated uncertainty. The rms deviation of 0.00040 cm�1

(A-reduced in the Ir representation) and 0.00041 cm�1 (S-reduced

.

B3LYP/cc-pVTZ Tan et al. [10] Present work

2.46899775 2.44156(25)a 2.4415848(14)a

0.74133143 0.7349294(9) 0.7349280(2)0.57014266 0.5635226(7) 0.5635218(2)0.78506 0.8040(4) 0.80280(8)0.27060 0.2671(3) 0.26662(12)0.20644 0.209(5) 0.2089(2)0.20991 0.2147(2) 0.21417(4)0.37869 0.387(2) 0.38750(17)

1247b 3151b

0.00049 0.000360.0725(2) 0.07260(2)

rentheses.mbination differences used in the fit.

.

VTZ B3LYP/cc-pVTZ Present work

778 2.46899775 2.4415888(14)a

980 0.74133143 0.7349216(2)110 0.57014266 0.5635309(2)

0.69568 0.71171(7)0.32423 0.32251(13)0.20197 0.2044(2)�0.20991 �0.21423(4)�0.44690 �0.4603(2)

3151b

0.000350.07193(2)

rentheses.mbination differences used in the fit.

sent work (A-reduction) Present work (S-reduction)

2.4640957(3)a A 2.4641007(3)a

0.73980301(6) B 0.73979574(6)0.56279354(6) C 0.56280504(6)0.84772(2) DJ � 106 0.735127(14)0.21436(2) DJK � 105 0.28377(2)0.247944(8) DK � 104 0.242382(8)0.237318(13) d1 � 106 �0.237439(14)0.47058(5) d2 � 107 �0.56963(6)

76.984958(14) 1076.984813(14)50 3950

0.00040 0.000410.325537(7) 0.324715(6)

rentheses.

T.L. Tan et al. / Journal of Molecular Spectroscopy 303 (2014) 42–45 45

in the Ir representation) are not far from the absolute accuracy of0.00035 cm�1 for the measured lines. The wide ranging values ofJ0, Ka

0 and Kc0 used in the analysis effectively cover the whole

frequency range of 1015–1140 cm�1 for the m12 band of C2D4.

4. Conclusion

The present investigation reports many new measurements ofinfrared transitions of the m12 band of C2D4 using a higher resolu-tion of 0.00096 cm�1 and covering a wider wavenumber region.By assigning and fitting 3950 rovibrational transitions of the m12

band of C2D4, improved ground state and upper state (m12 = 1) con-stants up to all quartic terms were derived. Ground state constantswere calculated at three different levels, and compared favourablywith those derived from this work. This additional spectral data onC2D4 together with data on other isotopologues will be useful indetermining an accurate experimental molecular structure ofethylene.

Acknowledgments

The authors are grateful to the Australian Synchrotron, Victoria,Australia for the recording of the C2D4 spectra using the high-resolution THz/far-infrared beamline. Financial support by theNational Institute of Education, Singapore through research grantnumbers RS 7/11 TTL and RI 9/09 TTL is acknowledged.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jms.2014.07.004.

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