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.
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.
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).
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.
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).
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.