International Journal of SpectroscopyVolume 2013 (2013), Article ID 492092, 7 pageshttp://dx.doi.org/10.1155/2013/492092

Research Article

Line Intensity Measurements of the Band of Ethylene (¹²C₂H₄)

G. B. Lebron and T. L. Tan

Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore, 637616

Received 22 March 2013; Accepted 23 June 2013

Academic Editor: Hakan Arslan

Copyright © 2013 G. B. Lebron and T. L. Tan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

From the four high-resolution FTIR absorbance spectra recorded at a spectral resolution of 0.0063 cm⁻¹, 123 line intensities belonging to the band of ¹²C₂H₄ were measured and fit. The upper state rovibrational constants up to sextic terms determined using a Watson's -reduced Hamiltonian model in representation were used to calculate the line intensities of the band. Results of the experimental fit of the line intensities agree well with those obtained by calculations.

1. Introduction

Spectroscopists take special interest in ethylene (¹²C₂H₄) for its atmospheric and astrophysical importance. Ethylene is naturally present in the atmosphere and is one of several precursors for the formation of tropospheric ozone, a pollutant that has adverse effects on human health. It also has been detected in the atmospheres of the Jovian planets Jupiter, Saturn, Neptune [1–4] and the satellite Titan [5]. Since accurate rotation-vibration parameters and knowledge of line positions and intensities are needed in the detection and monitoring of ethylene in the atmosphere, there have been a number of ethylene studies on the subject in the literature (e.g., [6–10]). As part of our ongoing FTIR investigation of ethylene and its isotopic variants [11–21], determination of the upper state rovibrational constants and line intensity measurements of the -type band of ¹²C₂H₄ in the 1820–1950 cm⁻¹ region were performed. The present study aims to contribute to the limited but growing body of knowledge on ethylene line positions and intensities.

Previous studies on the band of ¹²C₂H₄ include [22–25] which all considered the Coriolis interactions between the band and the and states. Ben Hassen and coworkers [6] measured the absolute line intensities of ethylene in the 1800–2350 cm⁻¹ region. According to a previous paper [25], 39 of the 264 line intensities they measured belonged to the band.

In the present study, the upper state rovibrational constants up to sextic centrifugal distortion terms were determined first using a standard Watson’s Hamiltonian model. The derived parameters were then used to calculate line intensities and positions of the band of ¹²C₂H₄. From the high-resolution FTIR spectra collected in the laboratory, 123 ethylene line positions and intensities were measured using a peak fitting analysis that implemented the Levenberg-Marquardt algorithm. We found the fit to be satisfactory falling within 6% error when compared to the calculated line intensities.

2. Experimental Details

A Bruker 125HR Fourier transform spectrometer located at the FTIR laboratory of the National Institute of Education, Nanyang Technological University, in Singapore was used to record all high-resolution infrared spectra used for the present study. It was equipped with a Globar mid-infrared source, a high sensitivity liquid nitrogen-cooled Hg-Cd-Te detector, and a KBr beamsplitter. By adjusting for four passes in the multiple absorption gas cell with a 20 cm base length, an absorption length of 80 cm was attained. The background spectra and the infrared spectra of the 99.99% pure ethylene gas samples purchased from Sigma-Aldrich, USA, were recorded at a spectral resolution of 0.0063 cm⁻¹ and at an ambient temperature of 296 K in the atm vapor pressure range. A capacitance pressure gauge was installed on the gas cell.

The sample spectra were coadded, and the resultant average spectrum was ratioed against the background spectrum to generate a transmittance spectrum with a smooth baseline and high signal-to-noise ratio. The gas samples contained water vapor as impurities and the unblended water absorption lines recorded in the  cm⁻¹ region along with the standard water wavenumber values taken from Guelachvili and Rao [26] were used to calibrate the transmittance spectrum. From the least-square fitting of 62 water frequencies, a relative precision of 0.00012 cm⁻¹ for all measured frequencies was achieved. The correction factor applied to the measured spectrum was 1.000000343. The frequencies from the corrected spectrum were used in the determination of the rotation-vibration constants of the band of ¹²C₂H₄.

Four of the seven sample spectra recorded were also used to measure line intensities of the band of ¹²C₂H₄. Each of the four sample spectra which are shown in Figure 1 were calibrated using water absorption lines as discussed above. Table 1 presents these spectra and the calibration results for each spectrum. After calibration, each of the spectra was converted to an absorbance spectrum.

Table 1: Infrared spectra collected for this study and wavenumber calibration results.

Spectrum no.
No. of scans
Pressure (×10⁻⁴ atm)
Calibration results

RMS error ×10⁻⁴ (cm⁻¹)
Correction factor

1
200
1.628
1.6
1.000000360

2
200
4.569
1.5
1.000000353

3
150
6.409
1.8
1.000000336

4
60
8.954
1.6
1.000000339

Figure 1: The four high-resolution FTIR spectra showing the combination band of ¹²C₂H₄ in the 1820–1950 cm⁻¹ region collected at different pressures (see Table 1).

3. Rovibrational Analysis of the Band of Ethylene

In Figure 2, the 1820–1950 cm⁻¹ region of the transmittance spectrum where the combination band of ¹²C₂H₄ is located is shown. As evident in Figure 2, the band exhibits the characteristic contour features of an -type band: moderate - and -branches on opposite ends and a strong -branch in the middle. A rather straightforward rovibrational analysis of the unperturbed lines of the band was carried out using a standard -reduced Watson’s Hamiltonian in representation [27]. For this, the nonlinear least-squares fitting program originally written by Maki [28] was used. For the initial assignments and calculations, we used the line list provided by Herman [29] and the ground state constants from [30]. As more lines were assigned and fitted, the upper state rovibrational constants were calculated and improved. A weighting equivalent to the inverse square of the estimated uncertainty (0.0006 cm⁻¹) assigned to each infrared transition was applied to the fitting procedure. The final fit with a root mean square (rms) deviation of 0.000653 cm⁻¹ included a total of 391 infrared transitions. The rovibrational constants determined for the excited state consisted of the three rotational constants, the band center, all five quartic, and two sextic centrifugal distortion parameters. Table 2 presents the results of the rotational analysis.

Table 2: Ground state and upper state rovibrational constants (cm⁻¹) for the combination band of ¹²C₂H₄ (-reduction and representation).

Ground state [30]
state

A
4.8646201954 (464)a
4.870611 (24)a

B
1.0010565039 (119)
0.9895253 (22)

C
0.8280459778 (117)
0.8303283 (11)

1.4702286 (406)
1.3957 (37)

0.102319954 (3678)
0.2836 (27)

0.86486844 (1953)
1.17094 (85)

0.2816829 (149)
0.2361 (14)

0.10161652 (1391)
0.2155 (11)

0.0024347 (503)
[0.0024347]b

0.194771 (3364)
0.428 (60)

−0.00045941 (1185)
−0.4229 (54)

6.24752 (1300)
[6.24752]b

0.00112776 (1669)
[0.00112776]b

0.110854 (2077)
[0.110854]b

3.7555 (1030)
[3.7555]b

—
1888.978834 (92)

no. of IR transitions
—
391

rms deviation (cm⁻¹)
—
0.000653

aThe uncertainty in the last digits (twice the estimated standard error) is given in parentheses.

bFixed to ground state value (see column 2).

Figure 2: An overview of the FTIR absorption spectrum of the combination band of ¹²C₂H₄ in the 1820–1950 cm⁻¹ region collected at a resolution of 0.0063 cm⁻¹.

4. Line Intensity Measurements and Calculations

Extraction of the line positions and intensities in the 1820–1950 cm⁻¹ spectral region of all four high-resolution absorbance spectra of ¹²C₂H₄ (see Table 1) was done using a peak fitting analysis that implemented the Levenberg-Marquardt algorithm. Although the vapor pressure range may be considered to be on the low side, each peak was fitted to a Voigt profile which accounts for the effects of both Doppler and collisional broadening. Figure 3 illustrates the quality of the peak fitting analysis that was performed in Spectrum no. 2 (see Table 1). The blue circles are actual data points extracted from Spectrum no. 2, and the red line traces the Voigt profile fit. The bottom panel of Figure 3 gives the residual plot (observed − calculated).

Figure 3: Part of peak fitting analysis performed in observed Spectrum no. 2 ( atm) with the corresponding residuals in the lower panel (peak nos. 40–43 in Table 3).

Beer’s law could be expressed as [31]: In the above equation, is the experimental line intensity given in cm⁻¹/(cm atm), is vapor pressure in atm, is the path length which for this study was 80 cm (see Section 2), and and are the incident and transmitted intensities of light, respectively, at frequency . From the peak fitting analysis that has just been described, (in cm⁻¹) was obtained for each peak. To determine the experimental line intensity, was plotted against , and the gradient of the best fit line passing through the origin gives the experimental line intensity. An example of this pressure dependence plot is shown in Figure 4 for line positions 1880.27874 cm⁻¹ in the -branch and 1904.99430 cm⁻¹ in the -branch.

Figure 4: Beer’s law plot showing pressure dependence for two lines.

The intensity in cm⁻¹/(cm atm) of an individual absorption line with frequency in cm⁻¹ is given by [7]: In (2), is Planck’s constant in erg · s; is the speed of light in cm/s; [32] is the isotopic abundance of ¹²C₂H₄; is the total partition function; is the energy of the lower state in erg; is Boltzmann constant in erg/K; is the temperature in K; and is the dipole moment operator. For ¹²C₂H₄, the nuclear spin factor has a value of 7 if and of the transition are both even and 3 if otherwise. The total population where molecules/cm³ at standard temperature and pressure and  K [7]. Using the upper rovibrational constants we determined (see Table 2), line positions and assignments were generated which in turn were used in (2) for the line intensity calculations. Calculations were made at the same experimental conditions when the high-resolution FTIR spectra were recorded. The calculated dipole moment was 0.0175 D. Table 3 lists the 123 measured and calculated line intensities along with the observed frequencies and the assignments. The experimental fit was satisfactory with the % error between measured and calculated line intensities within ±6% for all 123 lines. Also, the measured and calculated frequencies agree very closely (see O − C column in Table 3).

Table 3: Line positions, assignments, and intensities of the band of ¹²C₂H₄.

Peak no.

Measured wavenumber (cm⁻¹)
O − C (cm⁻¹)
Line intensities [cm⁻¹/(cm atm)]
% Error

Expt’l
Calc’d

1
19
3
16
20
3
17
1848.10619
0.00069
0.01606
0.01560
−2.971

2
21
1
20
22
1
21
1848.64789
−0.00055
0.01446
0.01426
−1.444

3
16
2
14
17
2
15
1854.62328
−0.00084
0.02340
0.02448
4.416

4
19
0
19
20
0
20
1855.23843
−0.00074
0.05011
0.05116
2.047

5
19
1
19
20
1
20
1855.28243
−0.00065
0.02256
0.02266
0.440

6
16
4
13
17
4
14
1856.28998
−0.00058
0.04276
0.04532
5.650

7
15
2
13
16
2
14
1856.70408
−0.00090
0.06124
0.06292
2.675

8
16
1
15
17
1
16
1856.76313
−0.00044
0.02648
0.02639
−0.325

9
18
0
18
19
0
19
1856.82825
−0.00067
0.02456
0.02458
0.076

10
15
3
12
16
3
13
1857.35152
−0.00017
0.02509
0.02532
0.902

11
15
4
12
16
4
13
1858.33672
−0.00039
0.02055
0.02115
2.876

12
14
2
12
15
2
13
1858.81149
−0.00096
0.02864
0.02930
2.245

13
16
0
16
17
0
17
1860.01569
−0.00065
0.03085
0.02989
−3.240

14
16
1
16
17
1
17
1860.11702
−0.00073
0.02960
0.02988
0.934

15
14
1
13
15
1
14
1860.18831
−0.00043
0.03299
0.03133
−5.310

16
14
4
11
15
4
12
1860.37046
−0.00024
0.05120
0.05299
3.380

17
13
2
11
14
2
12
1860.93859
−0.00086
0.06963
0.07323
4.921

18
15
1
15
16
1
16
1861.74391
−0.00072
0.03209
0.03239
0.927

19
13
6
7
14
6
8
1862.56749
0.00067
0.04786
0.04859
1.513

20
12
2
10
13
2
11
1863.07805
−0.00085
0.03328
0.03311
−0.510

21
13
2
12
14
2
13
1863.15373
−0.00080
0.03355
0.03254
−3.104

22
14
0
14
15
0
15
1863.21161
−0.00058
0.03543
0.03471
−2.079

23
14
1
14
15
1
15
1863.37938
−0.00069
0.03465
0.03469
0.123

24
12
1
11
13
1
12
1863.78464
−0.00054
0.03439
0.03536
2.747

25
12
3
9
13
3
10
1863.94266
−0.00074
0.02858
0.02960
3.440

26
11
3
8
12
3
9
1866.04610
−0.00088
0.03105
0.03049
−1.836

27
12
1
12
13
1
13
1866.67826
−0.00071
0.03791
0.03828
0.963

28
11
2
10
12
2
11
1866.80502
−0.00078
0.03435
0.03516
2.313

29
10
2
8
11
2
9
1867.36336
−0.00095
0.03383
0.03504
3.444

30
10
1
9
11
1
10
1867.54113
−0.00063
0.03787
0.03765
−0.588

31
10
3
7
11
3
8
1868.10596
−0.00077
0.03138
0.03081
−1.853

32
10
3
8
11
3
9
1868.28975
−0.00089
0.03255
0.03089
−5.360

33
9
1
8
10
1
9
1869.46527
−0.00067
0.03780
0.03786
0.176

34
9
2
7
10
2
8
1869.49207
−0.00081
0.07921
0.08174
3.103

35
10
1
10
11
1
11
1870.01782
−0.00067
0.03948
0.03990
1.037

36
9
3
6
10
3
7
1870.12636
−0.00092
0.03106
0.03045
−2.017

37
9
3
7
10
3
8
1870.23830
−0.00100
0.03038
0.03050
0.379

38
9
4
6
10
4
7
1870.31021
−0.00038
0.08089
0.08210
1.470

39
9
5
5
10
5
6
1870.40586
0.00016
0.03628
0.03704
2.035

40
9
0
9
10
0
10
1871.28500
−0.00062
0.08776
0.09346
6.102

41
8
1
7
9
1
8
1871.41065
−0.00066
0.03654
0.03734
2.132

42
8
2
6
9
2
7
1871.59872
−0.00082
0.03386
0.03427
1.192

43
9
1
9
10
1
10
1871.70380
−0.00041
0.04055
0.03974
−2.031

44
8
0
8
9
0
9
1872.94192
−0.00074
0.03965
0.03931
−0.865

45
8
1
8
9
1
9
1873.39988
−0.00066
0.03836
0.03885
1.264

46
7
2
5
8
2
6
1873.67558
0.00003
0.07336
0.07621
3.739

47
7
3
4
8
3
5
1874.07039
−0.00074
0.02819
0.02735
−3.083

48
7
4
4
8
4
5
1874.18383
−0.00073
0.06605
0.06964
5.155

49
7
2
6
8
2
7
1874.2107
−0.00061
0.03404
0.03289
−3.484

50
7
5
3
8
5
4
1874.27146
−0.00066
0.02911
0.02857
−1.869

51
7
0
7
8
0
8
1874.62617
−0.00062
0.08373
0.08825
5.122

52
6
5
2
7
5
3
1876.18440
−0.00072
0.02076
0.02160
3.899

53
6
0
6
7
0
7
1876.34147
−0.00057
0.03586
0.03554
−0.909

54
6
1
6
7
1
7
1876.82250
−0.00061
0.03563
0.03465
−2.824

55
5
1
4
6
1
5
1877.30902
−0.00069
0.03059
0.03073
0.458

56
5
2
3
6
2
4
1877.71216
−0.00056
0.06023
0.06230
3.326

57
5
1
5
6
1
6
1878.54707
−0.00056
0.03122
0.03130
0.256

58
4
2
2
5
2
3
1879.67047
−0.00048
0.02164
0.02223
2.661

59
4
1
4
5
1
5
1880.27874
−0.00061
0.02718
0.02713
−0.200

60
3
1
2
4
1
3
1881.2420
−0.00060
0.02281
0.02194
−3.970

61
3
2
1
4
2
2
1881.59210
−0.00029
0.03805
0.03881
1.951

62
3
1
3
4
1
4
1882.01624
−0.00051
0.02253
0.02213
−1.780

63
2
1
2
3
1
3
1883.75761
−0.00057
0.01734
0.01630
−6.386

64
4
1
4
3
1
3
1895.92667
−0.00056
0.02389
0.02306
−3.592

65
4
0
4
3
0
3
1896.15857
−0.00065
0.02545
0.02499
−1.835

66
4
2
3
3
2
2
1896.23848
−0.00044
0.04011
0.04055
1.083

67
4
2
2
3
2
1
1896.28176
−0.00034
0.01777
0.01738
−2.226

68
4
1
3
3
1
2
1896.47926
−0.00063
0.02295
0.02295
0.008

69
5
1
5
4
1
4
1897.64824
−0.00057
0.02920
0.02856
−2.219

70
5
0
5
4
0
4
1897.90300
−0.00069
0.06879
0.07038
2.260

71
6
1
6
5
1
5
1899.36413
−0.00061
0.03363
0.03330
−0.981

72
6
0
6
5
0
5
1899.62494
−0.00064
0.03432
0.03465
0.955

73
6
2
5
5
2
4
1899.77723
−0.00054
0.06549
0.06667
1.769

74
6
1
5
5
1
4
1900.10630
−0.00061
0.03410
0.03289
−3.656

75
7
1
7
6
1
6
1901.07464
−0.00064
0.03734
0.03724
−0.261

76
7
0
7
6
0
6
1901.32589
−0.00069
0.08671
0.08953
3.142

77
7
4
3
6
4
2
1901.67885
−0.00084
0.06004
0.06347
5.407

78
7
2
5
6
2
4
1901.72320
−0.00076
0.07384
0.07622
3.127

79
7
5
2
6
5
1
1901.74327
−0.00048
0.02443
0.02331
−4.805

80
8
1
8
7
1
7
1902.78030
−0.00068
0.04118
0.04035
−2.046

81
8
0
8
7
0
7
1903.00952
−0.00067
0.04122
0.04128
0.131

82
8
2
7
7
2
6
1903.26718
−0.00069
0.07925
0.08368
5.293

83
8
3
6
7
3
5
1903.38554
−0.00083
0.03151
0.02986
−5.501

84
8
3
5
7
3
4
1903.40236
−0.00088
0.02999
0.02986
−0.408

85
8
5
4
7
5
3
1903.48914
−0.00039
0.02967
0.03117
4.811

86
8
2
6
7
2
5
1903.53266
−0.00072
0.03610
0.03582
−0.796

87
8
1
7
7
1
6
1903.64766
−0.00060
0.03873
0.03942
1.754

88
9
1
9
8
1
8
1904.48187
−0.00069
0.04269
0.04261
−0.181

89
9
0
9
8
0
8
1904.68064
−0.00068
0.09736
0.10117
3.759

90
9
2
8
8
2
7
1904.99430
−0.00073
0.03804
0.03814
0.258

91
9
3
7
8
3
6
1905.13308
−0.00097
0.03196
0.03239
1.312

92
9
5
5
8
5
4
1905.22533
0.00033
0.03566
0.03708
3.823

93
9
2
7
8
2
6
1905.33298
−0.00080
0.08518
0.08876
4.041

94
9
1
8
8
1
7
1905.38538
−0.00066
0.04257
0.04135
−2.948

95
10
1
10
9
1
9
1906.18023
−0.00068
0.04431
0.04404
−0.606

96
10
0
10
9
0
9
1906.34476
−0.00062
0.04372
0.04462
2.022

97
10
2
9
9
2
8
1906.71002
−0.00079
0.08937
0.09230
3.178

98
10
1
9
9
1
8
1907.10144
−0.00056
0.04345
0.04241
−2.436

99
10
2
8
9
2
7
1907.11905
−0.00094
0.03971
0.03936
−0.868

100
12
1
12
11
1
11
1909.57111
−0.00073
0.04447
0.04453
0.149

101
12
0
12
11
0
11
1909.67100
−0.00035
0.04414
0.04486
1.608

102
12
3
9
11
3
8
1910.40373
−0.00068
0.03404
0.03492
2.519

103
12
1
11
11
1
10
1910.47072
−0.00054
0.04105
0.04215
2.613

104
13
1
13
12
1
12
1911.26574
−0.00064
0.04612
0.04373
−5.480

105
13
2
12
12
2
11
1911.79607
−0.00068
0.03899
0.03920
0.539

106
14
0
14
13
0
13
1913.01332
−0.00060
0.04431
0.04249
−4.279

107
14
2
13
13
2
12
1913.47402
−0.00060
0.08445
0.08824
4.298

108
14
3
11
13
3
10
1913.85956
−0.00042
0.03315
0.03317
0.039

109
14
2
12
13
2
11
1914.04936
−0.00093
0.03640
0.03694
1.465

110
15
2
14
14
2
13
1915.14502
−0.00055
0.03635
0.03597
−1.073

111
15
3
12
14
3
11
1915.57036
0.00013
0.03122
0.03153
0.977

112
15
2
13
14
2
12
1915.72204
−0.00072
0.07749
0.08138
4.779

113
16
2
15
15
2
14
1916.81050
−0.00032
0.07632
0.07876
3.102

114
16
3
13
15
3
12
1917.26494
0.00018
0.02985
0.02953
−1.094

115
16
2
14
15
2
13
1917.37156
−0.00090
0.03252
0.03247
−0.157

116
17
1
16
16
1
15
1918.63389
−0.00040
0.03193
0.03197
0.117

117
17
3
14
16
3
13
1918.94100
0.00062
0.02739
0.02725
−0.515

118
18
1
18
17
1
17
1919.76121
−0.00056
0.03258
0.03271
0.389

119
18
0
18
17
0
17
1919.77121
−0.00077
0.03172
0.03274
3.106

120
18
1
17
17
1
16
1920.25070
−0.00056
0.03080
0.02914
−5.706

121
20
3
17
19
3
16
1923.83142
0.00046
0.02002
0.01974
−1.386

122
21
3
18
20
3
17
1925.41296
−0.00049
0.01821
0.01728
−5.359

123
22
1
21
21
1
20
1926.76828
−0.00060
0.01859
0.01809
−2.752

5. Conclusion

In the present study, 123 line intensities of the band of ¹²C₂H₄ were measured by carrying out a peak fitting analysis based on Levenberg-Marquardt algorithm. Results of the experimental fit agree well when compared with the line intensities calculated using the upper rovibrational constants determined for this study.

Acknowledgments

The authors thank Dr. Arthur G. Maki for the set of FORTRAN codes they used for their rovibrational analyses. We are also indebted to the National Institute of Education, Nanyang Technological University, Singapore, for the support through research Grants RS 3/08 TTL and RI 9/09 TTL. Ms. G. B. Lebron thanks Nanyang Technological University for her Ph.D. research scholarship. She also acknowledges the support of the NIE Advancement Fund. Partial results of the research were presented in the 13th Symposium on Molecular Spectroscopy, Okayama, Japan.

References

B. Bezard, J. L. Moses, J. Lacy, T. Greathouse, M. Richter, and C. Griffith, “Detection of ethylene (C₂H₄) on jupiter and saturn in non-auroral regions,” Bulletin of the American Astronomical Society, vol. 33, p. 1079, 2001.

H. Feuchtgruber, E. Lellouch, B. Bézard, T. Encrenaz, T. de Graauw, and G. R. Davis, “Detection of HD in the atmospheres of Uranus and Neptune: a new determination of the D/H ratio,” Astronomy and Astrophysics, vol. 341, no. 1, pp. L17–L21, 1999.

L. N. Fletcher, P. Drossart, M. Burgdorf, G. S. Orton, and T. Encrenaz, “Neptune's atmospheric composition from AKARI infrared spectroscopy,” Astronomy and Astrophysics, vol. 514, no. 1, article A17, 2010.

R. Hanel, B. Conrath, F. M. Flasar et al., “Infrared observations of the Saturnian system from voyager 1,” Science, vol. 212, no. 4491, pp. 192–200, 1981.

A. Bar-nun and M. Podolak, “The photochemistry of hydrocarbons in Titan's atmosphere,” Icarus, vol. 38, no. 1, pp. 115–122, 1979.

A. Ben Hassen, F. Kwabia Tchana, J. M. Flaud, W. J. Lafferty, X. Landsheere, and H. Aroui, “Absolute line intensities for ethylene from 1800 to 2350 cm⁻¹,” Journal of Molecular Spectroscopy, vol. 282, pp. 30–33, 2012.

W. E. Blass, J. J. Hillman, A. Fayt et al., “10 μm ethylene: spectroscopy, intensities and a planetary modeler's atlas,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 71, no. 1, pp. 47–60, 2001.

D. C. Reuter and J. M. Sirota, “Absolute intensities and foreign gas broadening coefficients of the 111,10←112,10 and 180,18←181,18 lines in the ν ₇ band of C₂H₂,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 50, no. 5, pp. 477–482, 1993.

M. Rotger, V. Boudon, and J. Vander Auwera, “Line positions and intensities in the ν ₁₂ band of ethylene near 1450 cm⁻¹: an experimental and theoretical study,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 109, no. 6, pp. 952–962, 2008.

J. Walrand, M. Lengelé, G. Blanquet, and M. Lepère, “Absolute line intensities determination in the ν ₇ band of C₂H₄,” Spectrochimica Acta A, vol. 59, pp. 421–426, 2003.

G. B. Lebron and T. L. Tan, “High-resolution FTIR measurement and analysis of the ν ₃ band of C₂H₂D,” Journal of Molecular Spectroscopy, vol. 261, no. 2, pp. 119–123, 2010.

G. B. Lebron and T. L. Tan, “Improved rovibrational constants for the ν ₁₂ band of C₂H₃D,” Journal of Molecular Spectroscopy, vol. 265, no. 1, pp. 55–57, 2011.

G. B. Lebron and T. L. Tan, “Integrated Band Intensities of Ethylene (¹²C₂H₂) by Fourier Transform Infrared Spectroscopy,” International Journal of Spectroscopy, vol. 2012, Article ID 474639, 5 pages, 2012.

G. B. Lebron and T. L. Tan, “The high-resolution FTIR spectrum of the ν ₄ + ν ₄ band of trans-d ₂-ethylene (trans-C₂H₂D₂),” Journal of Molecular Spectroscopy, vol. 271, no. 1, pp. 44–49, 2012.

G. B. Lebron and T. L. Tan, “Improved rovibrational constants for the ν ₆ + ν ₁₀ band of ethylene (¹²C₂H₄) by high-resolution Fourier transform infrared spectroscopy,” Journal of Molecular Spectroscopy, vol. 283, pp. 29–31, 2013.

T. L. Tan, M. G. Gabona, and G. B. Lebron, “The ν ₁₂ band of C₂D₄,” Journal of Molecular Spectroscopy, vol. 266, no. 2, pp. 113–115, 2011.

T. L. Tan and G. B. Lebron, “The high-resolution FTIR spectrum of the ν ₆ band of C₂H₃D,” Journal of Molecular Spectroscopy, vol. 263, no. 2, pp. 160–165, 2010.

T. L. Tan and G. B. Lebron, “The ν ₁₂ band of ethylene-1-¹³C (¹³C¹²CH₄) by high-resolution FTIR spectroscopy,” Journal of Molecular Spectroscopy, vol. 261, no. 1, pp. 63–67, 2010.

T. L. Tan and G. B. Lebron, “High-resolution infrared analysis of the ν ₇ band of cis-ethylene-d₂ (cis-C₇H₇D₇),” Journal of Molecular Spectroscopy, vol. 261, no. 2, pp. 87–90, 2010.

T. L. Tan and G. B. Lebron, “Rovibrational constants for the ground state and ν ₈ = 1 state of ethylene-d₃ (C₂HD₃) by high-resolution FTIR spectroscopy,” Journal of Molecular Spectroscopy, vol. 269, no. 1, pp. 109–112, 2011.

G. B. Lebron and T. L. Tan, “High-resolution Fourier transform infrared spectrum of the ν ₁₁ band of ethylene (¹²C₂H₄),” Journal of Molecular Spectroscopy, vol. 288, pp. 11–13, 2013.

D. Hurtmans, A. Rizopoulos, M. Herman, L. M. S. Hassan, and A. Perrin, “Vibration-rotation analysis of the jet-cooled ν ₁₂, ν ₇ + ν ₈ and vν ₆ + ν ₁₀ absorption bands of ¹²C₂H₄,” Molecular Physics, vol. 99, no. 5, pp. 455–461, 2001.

C. Lambeau, M. de Vleeschouwer, D. van Lerberghe et al., “Spin-flip laser spectra of ethylene in the 2000 cm⁻¹ region,” Molecular Physics, vol. 46, no. 5, pp. 981–990, 1982.

D. van Lerberghe and A. Fayt, “High resolution study of the ν ₇ + ν ₈ band of ethylene (C₂H₄) at 1889 cm⁻¹,” Molecular Physics, vol. 31, pp. 1875–1886, 1976.

W. J. Lafferty, J.-M. Flaud, and F. K. Tchana, “The high-resolution infrared spectrum of ethylene in the 1800–2350 cm⁻¹ spectral region,” Molecular Physics, vol. 109, no. 21, pp. 2501–2510, 2011.

G. Guelachvili and K. N. Rao, Handbook of Infrared Standards, Academic Press, Orlando, Fla, USA, 1986.

J. K. G. Watson, “Aspects of quartic and sextic centrifugal effects of rotational energy levels,” in Vibrational Spectra and Structure: A Series of Advances, J. R. Durig, Ed., Elsevier, New York, NY, USA, 1977.

A. G. Maki, ASYM91

M. Herman, Private communication

F. Willaert, J. Demaison, L. Margules et al., “The spectrum of ethylene from microwave to submillimetre-wave,” Molecular Physics, vol. 104, no. 2, pp. 273–292, 2006.

P. F. Bernath, Spectra of Atoms and Molecules, Oxford University Press, New York, NY, USA, 2005.

P. de Bievre, M. Gallet, N. E. Holden, and I. L. Barnes, “Isotopic abundances and atomic weights of the elements,” Journal of Physical and Chemical Reference Data, vol. 13, pp. 809–891, 1984.