# Line Intensity Measurements of theν7+ν8 Band of Ethylene (12C2H4)

Authors: G. B. Lebron; T. L. Tan
Journal: International Journal of Spectroscopy
 (2013)

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## 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 ν7+ν8 band of 12C2H4 were measured and fit. The upper v7+v8=1 state rovibrational constants up to sextic terms determined using a Watson's A-reduced Hamiltonian model in Ir 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.


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## Body

## 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 A-type ν7+ν8 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 theν7+ν8 band of 12C2H4 include [22–25] which all considered the Coriolis interactions between the band and the ν4+ν8 and ν8+ν10 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 ν7+ν8 band.In the present study, the upperv7+v8=1 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 ν7+ν8 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 1.628×10-4–8.954×10-4atm 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 the1607–1831 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 ν7+ν8 band of 12C2H4.Four of the seven sample spectra recorded were also used to measure line intensities of theν7+ν8 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
1.000000339Figure 1
The four high-resolution FTIR spectra showing theν7+ν8 combination band of 12C2H4 in the 1820–1950 cm−1 region collected at different pressures (see Table 1).


## 3. Rovibrational Analysis of theν7+ν8 Band of Ethylene

In Figure2, the 1820–1950 cm−1 region of the transmittance spectrum where the ν7+ν8 combination band of 12C2H4 is located is shown. As evident in Figure 2, the band exhibits the characteristic contour features of an A-type band: moderate P- and R-branches on opposite ends and a strong Q-branch in the middle. A rather straightforward rovibrational analysis of the unperturbed lines of the band was carried out using a standard A-reduced Watson’s Hamiltonian in Ir 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 v7+v8=1 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 upperv7+v8=1 state rovibrational constants (cm−1) for the ν7+ν8 combination band of 12C2H4 (A-reduction and Ir representation).
Ground state [30]
v
7
+
v
8
=
1 state
A
4.8646201954 (464)a
4.870611 (24)a
B
1.0010565039 (119)
0.9895253 (22)
C
0.8280459778 (117)
0.8303283 (11)
Δ
J
×
10
6
1.4702286 (406)
1.3957 (37)
Δ
J
K
×
10
4
0.102319954 (3678)
0.2836 (27)
Δ
K
×
10
4
0.86486844 (1953)
1.17094 (85)
δ
J
×
10
6
0.2816829 (149)
0.2361 (14)
δ
K
×
10
4
0.10161652 (1391)
0.2155 (11)
Φ
J
×
10
9
0.0024347 (503)
[0.0024347]b
Φ
J
K
×
10
9
0.194771 (3364)
0.428 (60)
Φ
K
J
×
10
6
−0.00045941 (1185)
−0.4229 (54)
Φ
K
×
10
9
6.24752 (1300)
[6.24752]b
φ
J
×
10
9
0.00112776 (1669)
[0.00112776]b
φ
J
K
×
10
9
0.110854 (2077)
[0.110854]b
φ
K
×
10
9
3.7555 (1030)
[3.7555]b
ν
0
—
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 theν7+ν8 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 (P=4.569×10-4 atm) with the corresponding residuals in the lower panel (peak nos. 40–43 in Table 3).Beer’s law could be expressed as [31]:
(1)S′=1pl∫lnI0Idυ.
In the above equation, S′ is the experimental line intensity given in cm−1/(cm atm), p is vapor pressure in atm, l is the path length which for this study was 80 cm (see Section 2), and I0 and I are the incident and transmitted intensities of light, respectively, at frequency υ. From the peak fitting analysis that has just been described, lnA=∫ln(I0/I)dυ (in cm−1) was obtained for each peak. To determine the experimental line intensity, lnA=∫ln(I0/I)dυ was plotted against p, 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 P-branch and 1904.99430 cm−1 in the R-branch.Figure 4
Beer’s law plot showing pressure dependence for two lines.The intensitySAB in cm−1/(cm atm) of an individual absorption line with frequency υAB in cm−1 is given by [7]:
(2)SAB=(8π33hc)(Na)(hcυABgAQT)(e-EA/hckT)×[1-e-hcυAB/kT]|〈A|μ|B〉|2.
In (2), h is Planck’s constant in erg · s; c is the speed of light in cm/s; a=0.9773 [32] is the isotopic abundance of 12C2H4; QT is the total partition function; EA is the energy of the lower state in erg; k is Boltzmann constant in erg/K; T is the temperature in K; and |〈A|μ|B〉| is the dipole moment operator. For 12C2H4, the nuclear spin factor gA has a value of 7 if Ka and Kc of the transition are both even and 3 if otherwise. The total population N=T0L0/pT where L0=2.6868×1019 molecules/cm3 at standard temperature and pressure and T0=273.15 K [7]. Using the upper v7+v8=1 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 theν7+ν8 band of 12C2H4.
Peak no.
J
′
K
a
′
K
c
′
J
′
′
K
a
′
′
K
c
′
′
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 theν7+ν8 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 v7+v8=1 rovibrational constants determined for this study.



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*Source: 492092-2013-07-10.xml*