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Hydrogen-broadening coefficients in the ν7 band of ethylene at low temperature
Journal of Molecular Spectroscopy 227 (2004) 172–179 www.elsevier.com/locate/jms
Hydrogen-broadening coefficients in the m7 band of ethylene at low temperature Jean-Pierre Bouanich,a,* Ghislain Blanquet,b Jacques Walrand,b and Muriel Lepereb a b
Laboratoire de Photophysique Moleculaire, UPR3361 du CNRS, Universite de Paris-Sud, B^atiment 350, F-91405 Orsay cedex, France Laboratoire de Spectroscopie Moleculaire, Facultes Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium Received 25 November 2003; in revised form 3 June 2004 Available online 15 July 2004
Abstract H2 -broadening coefficients have been measured for 35 lines of C2 H4 at 173.2 K in the P , Q, and R branches of the m7 fundamental band near 10 lm, using a tunable diode-laser spectrometer. These lines were individually fitted with a Voigt and a Rautian profile to determine their collisional widths. The resulting broadening coefficients, as well as those previously measured at room temperature are compared with values calculated on the basis of a semiclassical model of interacting linear molecules, using an atom–atom Lennard-Jones potential in addition to the weak electrostatic contributions. A satisfactory agreement is obtained for the results at room temperature, but the theoretical results at low temperature are generally smaller than the experimental data. Finally, the temperature dependence of the broadening coefficients has been determined both experimentally and theoretically. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Tunable diode-laser; Ethylene; Hydrogen; Broadening coefficients; Semiclassical theory
1. Introduction Ethylene was found as a trace constituent in the atmospheres of Saturn [1], Jupiter [2], and Titan [3]. Therefore, knowledge of accurate spectral parameters, especially the N2 - and H2 -broadening of C2 H4 lines, is useful for modeling planetary atmospheres. We have recently measured these broadenings [4,5] in the m7 band of C2 H4 at room temperature as well as the selfbroadenings [6] at room and low temperatures. To our knowledge, no other N2 - and H2 -broadening coefficients of C2 H4 have been yet reported, except the measurements of Brannon and Varanasi [7] for only one transition in the m7 band at four temperatures ranging from 152 to 295 K. In this work, we measure the H2 -broadening coefficients of 35 lines in the m7 band of C2 H4 at )100 °C, using a tunable diode-laser (TDL) spectrometer and a
*
Corresponding author. Fax: +33-01-69-15-75-30. E-mail address: [email protected] (J.-P. Bouanich). 0022-2852/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2004.06.001
low temperature cell. The collisional widths are obtained by fitting each line to Voigt and Rautian profiles. The experimental and data reduction procedures are similar to those described previously for the study of C2 H4 –H2 broadenings at room temperature [5] and they will be briefly presented in the following sections. The calculation performed previously [5] is based on a semiclassical model [8] using a simple anisotropic dispersion contribution in addition to electrostatic contributions. The results were not satisfactory since the broadening coefficients are significantly underestimated for medium or high J values of the transitions J 0 ; Ka0 J ; Ka . Here, we consider another model, recently applied to CH3 D–H2 [9] as well as PH3 –H2 [10], approximating C2 H4 as a linear molecule for its interaction with H2 and involving the atom–atom Lennard-Jones potential, in addition to electrostatic contributions. It should be noted that this potential describing both long-range and short-range interactions has been successfully used for a number of diatomic and linear molecules perturbed by homopolar molecules such as the N2 O–N2 and N2 O–O2 systems [11]. Finally, although the aim of this work was not the temperature dependence of broadening coefficients, it
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seemed to us interesting to estimate the temperature coefficient n deduced experimentally from measurements at 296.5 and 173.2 K, and theoretically from the calculated results at the same temperatures.
2. Experimental procedure The spectra were recorded using an improved Laser Analytics diode-laser spectrometer described previously [12]. To increase the signal-to noise ratio each record was accumulated over 100 scans with a sweep frequency of 13.5 Hz. The relative wavelength calibration was obtained by introducing in the laser beam a confocal etalon with a free spectral range of 0.007958 cm1 . The ethylene and hydrogen gas samples were supplied by L’ Air Liquide with a stated purity of 99.95 and 99.99%, respectively. The low temperature cell with an optical pathlength of 40.43 cm, similar to that described previously [13], was cooled down at )100 °C and the temperature of the gas was kept constant at 173.2 0.5 K. For each broadened line, we used four different pressures of H2 , ranging from 10 to 42 mbar, the partial pressure of C2 H4 was roughly constant in the mixtures ranging from 0.072 to 1.027 mbar. The pressures were measured at room temperature with two MKS Baratron gauges having a full scale reading of 1.2 and 120 mbar. For each line under study, the following spectra were obtained consecutively: a spectrum of the empty cell which represents the laser emission profile, the four broadened spectra and the etalon fringe pattern with the
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absorption cell evacuated. Using a multipass cell, we also recorded a spectrum of the line at very low pressure (< 0:1 mbar) and small absorption which yields the doppler line at room temperature convoluted with the TDL instrumental function (the ‘‘effective’’ doppler line), as well as the saturated spectrum of this line giving the 0% transmission level. An example of the spectra obtained for the 153;12 154;12 and 71;6 82;6 lines at 923.4693 and 923.5326 cm1 , respectively, is shown in Fig. 1. Due to the non-linear tuning rate of the diodelaser radiation, the wavenumber scale of this figure is approximate. For data reduction, this non-linear tuning rate was corrected from the etalon fringe pattern by means of a cubic spline interpolation giving a constant step of about 1 104 cm1 . The assignments and wavenumbers of the measured lines of C2 H4 are taken from [14] and [15], respectively.
3. Data reduction and experimental results The measured absorbance aðmÞ at wavenumber m of a homogeneous gas sample is defined by the Beer–Lambert law as aðmÞ ¼ ln½I0 ðmÞ=It ðmÞ;
ð1Þ
where I0 ðmÞ and It ðmÞ are transmitted intensities obtained, respectively, with the cell under vacuum and filled with the gas sample. To determine the collisional width, we fitted a Voigt and a Rautian profile to aðmÞ, the position of the baseline I0 ðmÞ was systematically readjusted from a
Fig. 1. Example of the spectra obtained for the 153;12 154;12 and 71;6 82;6 lines in the m7 band of C2 H4 located at 923.4693 and 923.5326 cm1 , respectively. (1–4) Broadened lines at 19.41, 25.84, 31.73, and 37.62 mbar of H2 (T ¼ 173:2 K); (5) spectrum of the pure C2 H4 lines at low pressure (0.023 mbar) representing the effective Doppler lines; (6) diode-laser emission profile recorded with an empty cell; (7) confocal etalon fringes; (8) zero transmission level; and (9) saturated line.
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quadratic polynomial which allows to minimize the discrepancies between calculated and observed lineshapes. In our study, the soft collision profile of Galatry [16] would be preferable to the Rautian profile, since the active mass is greater than the perturber mass, but indeed the two profiles lead to very similar results. Some of the lines were sufficiently isolated to be individually fitted in their unperturbed part, but for four couples of transitions (153;12 154;12 and 71;6 82;6 ; 21;1 32;1 and 50;5 61;5 ; 21;2 32;2 and 91;9 92;7 ; and 182;16 173;14 and 113;9 112;9 ), as well as for the transitions 100;10 101;10 , 80;8 81;8 , 73;5 62;5 , and 191;18 192;18 close to unidentified lines, where the overlapping could not be disregarded, a fit of superposed profiles was performed as in [17] by neglecting line mixing effects. The small instrumental distortions were taken into account through the effective Doppler half-width cDA that was systematically used instead of cD . The typical values of cDA and cD at 173.2 K are respectively, 0.891 and 0.843 103 cm1 . For the Rautian profile (for details see [5]), we have constrained the narrowing parameter to its theoretical value such as bc ¼ b0 P , where P is the perturber pressure and b0 is derived from the diffusion coefficient. A calculation based on the Lennard-Jones potential with the usual mixing rules for the molecular pair parameters, using for C2 H4 [18] and for H2 [19] e ¼ 32 K e ¼ 199:2 K and r ¼ 4:523 A, and r ¼ 2:944 A, leads to b0 ¼ 12:87103 cm1 atm1 for C2 H4 –H2 at 173.2 K. It should be noted that the fitted narrowing parameter of the Rautian profile arising from well isolated lines is generally in reasonable agreement with this theoretical value.
An example of Voigt and Rautian lineshape fits to the measured profile aðmÞ of the 153;12 154;12 and 71;6 82;6 lines broadened by H2 is shown in Fig. 2. The observed minus calculated residuals show a better fit of the Rautian profile yielding slightly narrower and higher lineshapes than the Voigt profile. A typical plot of cc derived from both profiles versus the pressure P of the gas mixture is shown in Fig. 3 for the 71;6 82;6 line. Here, we have systematically considered the small self-broadening contribution (represented by a point close to the origin) derived from the coefficients of
Fig. 3. Pressure dependence of the collisional half-width cc for the 71;6 82;6 line in the m7 band of C2 H4 broadened by H2 at 173.2 K and derived from the fits of Voigt (s) and Rautian profiles (+). The point close to the origin represents the self-broadening contribution. The slopes of the best-fit lines represent the H2 -broadening coefficients for this transition.
Fig. 2. The measured profile for the 153;12 154;12 and 71;6 82;6 lines in the m7 band of C2 H4 diluted by 31.73 mbar of H2 at 173.2 K (—) and fitted superposed theoretical profiles (d). The deviations from the fits (calculated minus observed residuals) are shown at the bottom with an intensity scale expanded by 10: (A) The Voigt profile; (B) the Rautian profile with the narrowing parameter bc fixed to the calculated value (0.403 103 cm1 ) derived from the mass-diffusion coefficient. For clarity, only one calculated value out of five is represented there.
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self-perturbed C2 H4 recently measured at 174 K [6]. The slope of the straight lines obtained from unconstrained linear least-squares procedures gives the H2 -broadening coefficients c0 (cm1 atm1 ). These coefficients are presented in Table 1 for the Voigt and Rautian profiles, along with the experimental errors. The main sources of uncertainties in the c0 values arise from the baseline location, the perturbation due to nearby interfering lines, the non-linear tuning of the laser and the lineshape model used. The absolute errors are estimated to be equal to the statistical error on c0 derived from the linear least-squares fit plus 2–3% of c0 , depending on the extent of overlap from the neighboring lines. As may be seen in Table 1, these errors are notably greater than the differences between the measurements from the Voigt and the Rautian profile (average difference: 0.3%). As a new calculation of broadening coefficients has been performed for C2 H4 –H2 , we also present in Table 2
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these coefficients at room temperature (296.5 K) previously listed in Table 1 of [5]. The J dependence of the broadening coefficients c0 at 296.5 and 173.2 K is shown in Figs. 4 and 5, respectively, for all the studied transitions J 0 ; Ka0 ; Kc0 J ; Ka ; Kc . An overall decrease of c0 with increasing J is observable for both temperatures. Moreover, the broadening coefficients belonging to transitions with same J (Tables 1 and 2) generally increase with increasing Ka values. It would be interesting to determine theoretically these J and Ka behaviors of the broadenings.
4. Theoretical results and comparisons The new calculation of H2 -broadening coefficients of C2 H4 has been carried out on the basis of the model previously developed in [9]. Here, we assume that C2 H4
Table 1 H2 -broadening coefficients c0 measured and calculated in the m7 band of C2 H4 at 173.2 K m0 (cm1 )
919.8311 923.4693 923.5326 926.6493 926.7510 927.0739 927.5198 931.3365 931.5019 931.8042 931.8834 936.1209 939.4905 943.3529 947.0301 947.1985 947.7002 948.2275 951.3717 952.0841 952.3859 952.6277 959.3072 959.4075 963.1025 963.2495 963.4818 966.9867 967.1569 967.2054 970.7542 970.8737 982.7607 1011.8617 1023.1018
J0
9 15 7 7 13 4 12 2 11 2 5 4 13 13 8 19 10 12 6 4 3 2 11 6 16 5 14 3 18 11 8 11 7 20 20
Ka0
1 3 1 0 2 1 2 1 2 1 0 1 3 1 0 1 0 0 1 1 1 1 1 2 2 1 1 2 2 3 1 3 3 3 5
Kc0
8 12 6 7 12 4 11 2 9 1 5 4 10 12 8 18 10 12 6 4 3 2 10 5 14 4 13 2 16 9 7 8 5 18 16
J
10 15 8 8 13 5 12 3 11 3 6 4 14 13 8 19 10 12 6 4 3 2 10 6 15 4 13 2 17 11 7 11 6 19 19
Ka
2 4 2 1 3 2 3 2 3 2 1 2 2 2 1 2 1 1 0 0 0 0 2 1 3 0 2 1 3 2 0 2 2 2 4
Kc
8 12 6 7 10 4 9 2 9 1 5 2 12 12 8 18 10 12 6 4 3 2 8 5 12 4 11 2 14 9 7 10 5 18 16
c0 (103 cm1 atm1 ) Voigt
Rautian
Calc.
174.9 4.3 169.9 5.2 178.8 4.1 180.2 5.6 179.0 8.7 176.1 4.5 177.2 5.4 184.8 7.8 180.9 4.1 195.6 7.2 175.5 5.4 161.1 7.4 178.6 4.7 171.1 4.2 158.7 6.2 162.9 6.1 151.0 5.2 149.2 5.6 165.9 4.3 161.1 7.4 170.3 7.5 170.8 10.8 171.1 6.1 177.5 6.9 177.7 5.6 180.6 6.0 172.9 8.9 182.0 4.9 175.9 6.8 180.1 5.4 180.4 5.0 176.7 5.8 179.8 4.9 162.9 6.1 157.8 8.0
175.1 4.3 170.1 5.3 179.0 4.0 180.5 5.5 180.5 7.8 176.5 4.5 177.6 5.4 185.3 7.8 181.2 4.3 195.9 7.1 175.8 5.2 161.8 7.3 179.2 4.7 171.4 4.2 159.6 6.1 163.6 5.8 151.5 5.0 149.7 5.6 166.1 4.1 161.8 7.3 171.0 7.0 171.1 10.6 171.6 5.8 177.9 6.6 178.2 5.3 180.9 5.9 173.7 7.5 182.4 4.7 176.4 6.6 180.4 5.2 180.8 4.7 177.0 5.5 180.0 4.8 163.6 5.8 159.2 8.4
159.8 158.4 162.2 160.0 158.3 166.3 160.0 186.3 161.7 186.3 161.0 170.0 160.5 155.8 160.4 149.6 158.3 156.0 165.0 169.7 174.2 183.0 159.2 172.3 154.8 166.1 155.1 184.5 152.4 165.6 162.0 165.6 176.7 152.0 157.1
Note. The wavenumbers m0 of the unperturbed C2 H4 lines are taken from [15]. The experimental results are derived from the fits of the Voigt profile and the Rautian profile with a fixed bc parameter. The uncertainty in these results is the standard error derived from the linear least-squares fit plus 2–3% of c0 .
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Table 2 H2 -broadening coefficients c0 measured [5] and calculated in the m7 band of C2 H4 at 296.5 K m0 (cm1 )
919.8311 923.4693 923.5326 926.6493 927.0739 927.5198 931.3365 931.5019 931.8834 936.1209 939.4905 943.3529 947.0301 947.3806 947.7002 948.2275 951.3717 951.7394 959.3072 960.0282 960.0769 962.9599 963.1025 966.9867 967.2054 970.7542 970.8737 982.5852 982.7607 1011.5135 1011.8617 1015.3474 1023.1018 1023.4364
J0
9 15 7 7 4 12 2 11 5 4 13 13 8 9 10 12 6 5 11 22 9 20 16 3 11 8 11 23 7 20 20 20 20 24
Ka0
1 3 1 0 1 2 1 2 0 1 3 1 0 0 0 0 1 1 1 3 4 3 2 2 3 1 3 4 3 1 3 4 5 3
Kc0
8 12 6 7 4 11 2 9 5 4 10 12 8 9 10 12 6 5 10 20 5 17 14 2 9 7 8 19 5 19 18 17 16 22
J
10 15 8 8 5 12 3 11 6 4 14 13 8 9 10 12 6 5 10 21 10 19 15 2 11 7 11 23 6 19 19 19 19 23
Ka
2 4 2 1 2 3 2 3 1 2 2 2 1 1 1 1 0 0 2 4 3 4 3 1 2 0 2 3 2 0 2 3 4 2
Kc
8 12 6 7 4 9 2 9 5 2 12 12 8 9 10 12 6 5 8 18 7 15 12 2 9 7 10 21 5 19 18 17 16 22
c0 (103 cm1 atm1 ) Voigt
Rautian
Calc.
118.7 2.3 116.7 4.3 117.8 3.1 117.7 3.7 119.7 4.8 118.7 2.9 121.5 4.4 119.9 3.1 119.9 2.8 121.6 2.7 120.4 3.0 115.2 3.2 107.2 3.2 107.0 2.8 105.1 3.3 99.9 3.3 111.4 2.7 108.7 5.6 120.2 2.7 112.9 3.7 121.2 4.1 118.3 3.5 118.1 3.3 124.0 3.5 121.6 4.0 119.2 2.8 120.5 3.2 115.7 4.9 121.9 2.8 105.4 4.0 113.6 3.5 112.4 4.5 116.8 2.7 109.7 3.5
119.8 2.8 118.2 3.9 119.8 3.4 119.7 4.2 121.7 4.0 120.4 3.5 123.2 4.0 121.4 3.0 121.6 2.5 123.0 2.7 121.4 3.2 116.5 3.0 108.4 3.3 108.1 2.8 106.2 3.6 101.7 3.1 112.8 2.4 111.3 5.3 120.7 3.0 114.8 4.1 122.4 4.3 119.5 3.4 119.3 2.9 124.8 3.7 122.7 3.8 120.1 3.0 121.1 3.5 117.2 4.6 122.6 3.1 107.1 3.6 115.0 3.5 113.7 3.7 118.1 2.6 110.4 3.6
113.6 114.1 114.2 113.1 115.8 114.4 126.3 115.0 113.2 117.8 115.1 112.6 113.4 113.2 113.0 112.4 115.4 116.2 113.6 110.2 121.1 111.3 112.4 125.3 117.0 114.2 117.0 110.2 121.5 109.5 111.0 112.2 113.6 108.9
Note. The experimental results are derived from the fits of the Voigt profile and the Rautian profile with a fixed bc parameter. The uncertainty in these results is the standard error derived from the linear least-squares fit plus 2–3% of c0 .
behaves like the linear molecule C2 H2 for its interaction with H2 , i.e., the two H atoms of each extremity of the molecule are considered as a single atom (noted 2 H) situated on the principal symmetry axis of C2 H4 . Then, we used the semiclassical formalism of Robert and Bonamy [20] for the interaction of linear molecules. Within this framework, the collisional half-width of an isolated pressure broadened rotational or rovibrational line f i may be expressed as Z 1 n2 v X cfi ¼ qJ2 Sfi ðb; J2 Þ 2pb db; ð2Þ 2pc j2 0
where S2;i2 , S2;f 2 , and S2;f 2i2 are the second-order terms of the perturbation of Sfi derived from the anisotropic part of the potential [21]. The total intermolecular potential VT involves the atom–atom Lennard-Jones (LJ) interactions Vaa in addition to the electrostatic interactions Ve , such that VT ¼ Ve þ Vaa
where n2 is the number density of the perturbing molecules, v is the mean relative velocity, qj2 is the relative population for the j J2 , v2 ¼ 0i state of the perturber including the nuclear spin factor f ðJ2 Þ ¼ ð1ÞJ2 þ1 þ 2, and Sfi is the real part of the differential cross-section given by
where the index 1 refers to the absorber (C2 H4 ) and 2 to the perturber (H2 ); Q, and / are the quadrupole and hexadecapole moments of the molecules; eij and rij are the LJ parameters for the interaction of the i th atom considered for C2 H4 (2 H, C, C, and 2 H) and the jth atom of H2 and rij is the distance between these atoms. By expanding rij in power series of the intermolecular distance r, Vaa can be expressed in terms of the intra-
Sfi ðb; J2 Þ ¼ 1 exp½ðS2;i2 þ S2;f 2 þ S2;f 2i2 Þ;
ð3Þ
¼ VQ1 Q2 þ VQ1 /2 þ V/1 Q2 þ V/1 /2 " 6 # 12 X rij rij þ 4eij ; rij rij i;j
ð4Þ
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Fig. 4. J dependence of H2 -broadening coefficients for J 0 ; Ka0 ; Kc0 J ; Ka ; Kc transitions in the m7 band of C2 H4 at 296.5 K. Experimental results derived from the fits of Voigt (s) and Rautian () profiles with their error bars. Theoretical results (d) calculated for all transitions J 0 ; Ka0 J ; Ka studied experimentally at room and low temperatures (the quantum numbers Kc0 and Kc are not considered in our calculations).
Fig. 5. J dependence of H2 -broadening coefficients for J 0 ; Ka0 ; Kc0 J ; Ka ; Kc transitions in the m7 band of C2 H4 at 173.2 K. Experimental results derived from the fits of Voigt (s) and Rautian () profiles with their error bars. Theoretical results (d) calculated for all transitions J 0 ; Ka0 J ; Ka studied experimentally at room and low temperatures (the quantum numbers Kc0 and Kc are not considered in our calculations).
177
molecular distances r1i , r2j (distance of each atom i or j to the mass center of 2 H–C@C–2 H or H2 ) and the spherical harmonics considered for each molecule. The trajectory model [22] includes the influence of the isotropic potential in energy conservation and in the equation of motion around the distance of closest approaches rc . The actual trajectory is replaced by an equivalent straight-line trajectory described at the relative velocity v0c . The isotropic potential considered here is a LJ m–n potential fitting the spherical average of the atom–atom model u000 ðrÞ [23]. In Table 3, we present the rotational constants for the ground state of H2 , the effective rotational constants B* for the ground and m7 states of C2 H4 obtained from B ¼ ðB þ CÞ=2, where B and C are taken from [14], as well as the values used for the electric multipole moments of these molecules. The atom–atom LJ parameters considered for H–H interactions are those calculated by Wang [27] from second virial coefficients of H2 with introduction of quantum effects; the 2 H–2 H parameters are derived from these values by considering the intramolecular distances of C2 H4 . The C–C LJ parameters are calculated by fitting as in [28] nine experimental values of second virial coefficients of C2 H4 [29] similarly considered as linear. The LJ parameters of 2 H–H and C–H for 2 HCC2 H–H2 interactions are obtained from the usual mixing rules eij ¼ ðeii ejj Þ1=2 and rij ¼ ðrii þ rjj Þ=2. The atom–atom LJ parameters eii , rii , ejj , and rjj , the intramolecular distances used for 2 H– C@C–2 H and H2 , and the LJ m–n parameters fitting u000 ðrÞ are listed in Table 4. The contributions to the differential cross-section [8] include in the Clebsch-Gordan coefficients the quantum numbers Ka and Ka0 with Ka0 ¼ Ka 1 (the quantum numbers Kc and Kc0 are quite disregarded here). We have only considered the transitions induced by collisions with DKa ¼ 0 for the absorbing molecule associated with the usual selection rules (DJ ¼ 0, 1, 2 for a quadrupolar transition, and DJ ¼ 0, 1, 2, 3, 4 for an hexadecapolar transition). The H2 -broadening coefficients at 296.5 and 173.2 K were computed by including the contributions of H2 in the fundamental state with J2 values up to 7 or 5, respectively. The single electrostatic contributions yield almost negligible broadening coefficients at room and
Table 3 Molecular parameters used for C2 H4 and H2 in the calculations of broadening coefficients D0 (cm1 )
Q (D A)
3 ) U (D A
—
—
59.33451b
0.045651b
3.30c 0.6522d
7.85e 0.1264d
Molecule
B (cm1 )
B0 (cm1 )
B0 (cm1 )
C2 H4 H2
0.914551a
0.915386a
—
—
a
Calculated from the parameters B and C given in [14] for the ground and m7 states of C2 H4 . Ref. [24]. c Ref. [6]. d Ref. [25]. e Ref. [26]. b
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Table 4 Atom–atom LJ parameters, intramolecular distances r1i and r2j , and LJ m–n parameters fitting the isotropic radial function u000 ðrÞ for 2 HCC2 H–H2 interactions eii , ejj (K)
rii , rjj (A)
r1i , r2j (A)
m
n
e (K)
r (A)
e2 H–2 H ¼ 14:498 eC–C ¼ 67:064 eH–H ¼ 14:498
r2 H–2 H ¼ 3:619 rC–C ¼ 3:1506 rH–H ¼ 2:68224
jr12 H j ¼ 1:226 jr1C j ¼ 0:669 jr2H j ¼ 0:3754
6.2
15.1
68.2576
3.6822
low temperatures. The total potential VT defined by Eq. (4) leads to a very good agreement at room temperature with the experimental data (Table 2, Fig. 4) with an average difference of only 2.3%, smaller than the average estimated uncertainty (3.2%) in these data. The theoretical results are in much better agreement than the previous results [5] which decrease with increasing J values, significantly more than the measurements. This discrepancy was due to the insufficient potential used represented by only one simple expression for the nonelectrostatic contributions which are predominant for C2 H4 –H2 . Here the potential parameters have all been taken in the literature or calculated from second virial coefficients. At low temperature, however, the theoretical broadening coefficients (Table 1, Fig. 5) are generally smaller than the measurements (average difference 6.2% vs 3.4% for the average uncertainty). To determine the theoretical Ka dependence of the broadening coefficients at room and low temperatures, we have considered the lines belonging to a given DJ branch and DKa subbranch. As may be seen in Fig. 6 for the P QðJ ; Ka Þ (or J , Ka 1 J , Ka ) transitions with J ¼ 3, 6, 12, and 20, c0 increases with Ka to a maximum value then (for J P 5) c0 decreases to rather low values for Ka approaching or equal to J . Similar Ka variations of the broadening coefficients are obtained for other DJ branches and/or DKa subbranches of C2 H4 . If the theoretical increase of c0 with Ka is generally in agreement with the observed Ka behavior of broadening coefficients
Fig. 6. Theoretical Ka dependencies of the H2 -broadening coefficients c0 ðJ ; Ka Þ at 173.2 and 296.5 K for P QðJ ; Ka Þ or (J ; Ka 1 J ; Ka ) transitions in the m7 band of C2 H4 with J ¼ 3, 6, 12, and 20.
(Tables 1 and 2), the decrease of c0 cannot be checked experimentally since we have only studied transitions with Ka 6 4, then not any Ka values close to J for J > 4. It should be noted that this decrease of c0 is much less important than predicted by the previous calculation [5]. The dependence of the broadening coefficients upon temperature is usually well represented by the simple power law n T0 c0 ðT Þ ¼ c0 ðT0 Þ ; ð5Þ T where T0 ¼ 296:5 K is our reference temperature. By comparing the experimental results at 296.5 and 173.2 K derived from the fits of Voigt and Rautian profiles, we have determined the experimental n exponent as a function of J (Fig. 7). Assuming quite independent errors in the broadening measurements, the uncertainty in the values of n is very large, about 0.11. As shown in Fig. 7, the theoretical values of n deduced from the calculated broadening coefficients at 296.5 and 173.2 K for the studied transitions are lying generally at the lower limit of the estimated error bars. They are almost Ka independent and decrease regularly from 0.72 to 0.58 as J increases, whereas the experimental n values are more or less constant (average value: 0.73 for the Voigt profile and 0.71 for the Rautian profile).
Fig. 7. Variation of the temperature coefficient n with J for the H2 J ; Ka ; Kc broadening coefficients of the studied transitions J 0 ; Ka0 ; Kc0 in the m7 band of C2 H4 . Experimental results derived from the fits of Voigt (s) and Rautian profiles () with their error bars. Theoretical results (d) calculated for all transitions J 0 ; Ka0 J ; Ka studied experimentally at room and low temperatures.
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5. Conclusion The H2 -broadening coefficients in the m7 band of C2 H4 derived from the fits of Voigt and Rautian profiles are nearly the same and do not strongly depend on the transition studied since they vary in the range 0.105– 0.125 cm1 atm1 at room temperature and 0.150– 0.190 cm1 atm1 at )100 °C. The theoretical results are very satisfactory by considering the different approximations used in our calculations: the C2 H4 molecule is treated as a linear molecule, the semiclassical model is not appropriate to the light H2 perturber and the predominant atom–atom potential, where the pairwise additivity is assumed without any adjustable parameters, cannot be very precise. Moreover, to our knowledge, this is at this time, the only method to perform accurately these calculations. Since ethylene is an important constituent of the atmosphere of Jupiter and Saturn, our results may be useful for modeling the atmosphere of these planets.
Acknowledgments Support by the ‘‘Programme de Cooperation Scientifique entre le CNRS (France) et le CGRI de la Communaute Francßaise de Belgique’’ is gratefully acknowledged. This work is accomplished in the framework of the European associated Laboratory HiRes.
References [1] T. Encrenaz, M. Combes, Y. Zeau, L. Vapillon, J. Berezne, Astron. Astrophys. 42 (1975) 355–356. [2] T. Kostiuk, P. Romani, F. Espenak, T.A. Livengood, J.J. Goldstein, JGR-Planets 98 (1993) 18823–18830. [3] V. Kunde, A.C. Aiken, R. Hanel, D.E. Jennings, V.G. Kunde, R.C. Samuelson, Nature 292 (1981) 686–688. [4] G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 201 (2000) 56–61.
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[5] J.P. Bouanich, G. Blanquet, J. Walrand, M. Lepere, J. Mol. Spectrosc. 218 (2003) 22–27. [6] G. Blanquet, J.P. Bouanich, J. Walrand, M. Lepere, J. Mol. Spectrosc. 222 (2003) 284–290. [7] J.F. Brannon Jr., P. Varanasi, J. Quant. Spectrosc. Radiat. Transfer 47 (1992) 237–242; J. Quant. Spectrosc. Radiat. Transfer 49 (1993) 695–696. [8] J.P. Bouanich, G. Blanquet, J. Walrand, J. Mol. Spectrosc. 161 (1993) 416–426. [9] C. Lerot, J. Walrand, G. Blanquet, J.P. Bouanich, M. Lepere, J. Mol. Spectrosc. 217 (2003) 79–86. [10] J.P. Bouanich, J. Salem, H. Aroui, J. Walrand, G. Blanquet, J. Quant. Spectrosc. Radiat. Transfer 84 (2004) 195–205. [11] F. Rohart, J.M. Colmont, G. Wlodarczak, J.P. Bouanich, J. Mol. Spectrosc. 222 (2003) 159–171. [12] M. Lepere, G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 180 (1996) 218–226. [13] C. Schmidt, J.C. Populaire, J. Walrand, G. Blanquet, J.P. Bouanich, J. Mol. Spectrosc. 158 (1993) 423–432. [14] E. Rusinek, H. Fichoux, M. Khelkhal, F. Herlemont, J. Legrand, A. Fayt, J. Mol. Spectrosc. 189 (1998) 64–73. [15] A. Fayt, private communication, 1998. [16] L. Galatry, Phys. Rev. 122 (1960) 1218–1224. [17] G. Blanquet, C. Coupe, J. Walrand, J.P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 51 (1994) 671–678. [18] J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1967. [19] J.P. Bouanich, C. Brodbeck, J. Quant. Spectrosc. Radiat. Transfer 17 (1977) 777–782. [20] D. Robert, J. Bonamy, J. Phys. (Paris) 40 (1979) 923–943. [21] C.J. Tsao, B.J. Curnutte, J. Quant. Spectrosc. Radiat. Transfer 2 (1962) 41–91. [22] J. Bonamy, L. Bonamy, D. Robert, J. Chem. Phys. 67 (1977) 4441–4453. [23] J.P. Bouanich, D. Lambot, G. Blanquet, J. Walrand, J. Mol. Spectrosc. 140 (1990) 195–213. [24] S.L. Bragg, J.W. Brault, W.H. Smith, Astrophys. J. 263 (1984) 999–1004. [25] J. Komasa, A.J. Thakkar, Mol. Phys. 78 (1993) 1039–1046. [26] F. Mulder, M. van Hemert, P.E.S. Wormer, A. van der Avoird, Theor. Chim. Acta (Berl) 46 (1977) 39–62. [27] W.F. Wang, J. Quant. Spectrosc. Radiat. Transfer 76 (2003) 23– 30. [28] J.P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 47 (1992) 243–250. [29] J.H. Dymond, E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Oxford University Press (Clarendon), London, 1980.
Hydrogen-broadening coefficients in the m7 band of ethylene at low temperature Jean-Pierre Bouanich,a,* Ghislain Blanquet,b Jacques Walrand,b and Muriel Lepereb a b
Laboratoire de Photophysique Moleculaire, UPR3361 du CNRS, Universite de Paris-Sud, B^atiment 350, F-91405 Orsay cedex, France Laboratoire de Spectroscopie Moleculaire, Facultes Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium Received 25 November 2003; in revised form 3 June 2004 Available online 15 July 2004
Abstract H2 -broadening coefficients have been measured for 35 lines of C2 H4 at 173.2 K in the P , Q, and R branches of the m7 fundamental band near 10 lm, using a tunable diode-laser spectrometer. These lines were individually fitted with a Voigt and a Rautian profile to determine their collisional widths. The resulting broadening coefficients, as well as those previously measured at room temperature are compared with values calculated on the basis of a semiclassical model of interacting linear molecules, using an atom–atom Lennard-Jones potential in addition to the weak electrostatic contributions. A satisfactory agreement is obtained for the results at room temperature, but the theoretical results at low temperature are generally smaller than the experimental data. Finally, the temperature dependence of the broadening coefficients has been determined both experimentally and theoretically. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Tunable diode-laser; Ethylene; Hydrogen; Broadening coefficients; Semiclassical theory
1. Introduction Ethylene was found as a trace constituent in the atmospheres of Saturn [1], Jupiter [2], and Titan [3]. Therefore, knowledge of accurate spectral parameters, especially the N2 - and H2 -broadening of C2 H4 lines, is useful for modeling planetary atmospheres. We have recently measured these broadenings [4,5] in the m7 band of C2 H4 at room temperature as well as the selfbroadenings [6] at room and low temperatures. To our knowledge, no other N2 - and H2 -broadening coefficients of C2 H4 have been yet reported, except the measurements of Brannon and Varanasi [7] for only one transition in the m7 band at four temperatures ranging from 152 to 295 K. In this work, we measure the H2 -broadening coefficients of 35 lines in the m7 band of C2 H4 at )100 °C, using a tunable diode-laser (TDL) spectrometer and a
*
Corresponding author. Fax: +33-01-69-15-75-30. E-mail address: [email protected] (J.-P. Bouanich). 0022-2852/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2004.06.001
low temperature cell. The collisional widths are obtained by fitting each line to Voigt and Rautian profiles. The experimental and data reduction procedures are similar to those described previously for the study of C2 H4 –H2 broadenings at room temperature [5] and they will be briefly presented in the following sections. The calculation performed previously [5] is based on a semiclassical model [8] using a simple anisotropic dispersion contribution in addition to electrostatic contributions. The results were not satisfactory since the broadening coefficients are significantly underestimated for medium or high J values of the transitions J 0 ; Ka0 J ; Ka . Here, we consider another model, recently applied to CH3 D–H2 [9] as well as PH3 –H2 [10], approximating C2 H4 as a linear molecule for its interaction with H2 and involving the atom–atom Lennard-Jones potential, in addition to electrostatic contributions. It should be noted that this potential describing both long-range and short-range interactions has been successfully used for a number of diatomic and linear molecules perturbed by homopolar molecules such as the N2 O–N2 and N2 O–O2 systems [11]. Finally, although the aim of this work was not the temperature dependence of broadening coefficients, it
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seemed to us interesting to estimate the temperature coefficient n deduced experimentally from measurements at 296.5 and 173.2 K, and theoretically from the calculated results at the same temperatures.
2. Experimental procedure The spectra were recorded using an improved Laser Analytics diode-laser spectrometer described previously [12]. To increase the signal-to noise ratio each record was accumulated over 100 scans with a sweep frequency of 13.5 Hz. The relative wavelength calibration was obtained by introducing in the laser beam a confocal etalon with a free spectral range of 0.007958 cm1 . The ethylene and hydrogen gas samples were supplied by L’ Air Liquide with a stated purity of 99.95 and 99.99%, respectively. The low temperature cell with an optical pathlength of 40.43 cm, similar to that described previously [13], was cooled down at )100 °C and the temperature of the gas was kept constant at 173.2 0.5 K. For each broadened line, we used four different pressures of H2 , ranging from 10 to 42 mbar, the partial pressure of C2 H4 was roughly constant in the mixtures ranging from 0.072 to 1.027 mbar. The pressures were measured at room temperature with two MKS Baratron gauges having a full scale reading of 1.2 and 120 mbar. For each line under study, the following spectra were obtained consecutively: a spectrum of the empty cell which represents the laser emission profile, the four broadened spectra and the etalon fringe pattern with the
173
absorption cell evacuated. Using a multipass cell, we also recorded a spectrum of the line at very low pressure (< 0:1 mbar) and small absorption which yields the doppler line at room temperature convoluted with the TDL instrumental function (the ‘‘effective’’ doppler line), as well as the saturated spectrum of this line giving the 0% transmission level. An example of the spectra obtained for the 153;12 154;12 and 71;6 82;6 lines at 923.4693 and 923.5326 cm1 , respectively, is shown in Fig. 1. Due to the non-linear tuning rate of the diodelaser radiation, the wavenumber scale of this figure is approximate. For data reduction, this non-linear tuning rate was corrected from the etalon fringe pattern by means of a cubic spline interpolation giving a constant step of about 1 104 cm1 . The assignments and wavenumbers of the measured lines of C2 H4 are taken from [14] and [15], respectively.
3. Data reduction and experimental results The measured absorbance aðmÞ at wavenumber m of a homogeneous gas sample is defined by the Beer–Lambert law as aðmÞ ¼ ln½I0 ðmÞ=It ðmÞ;
ð1Þ
where I0 ðmÞ and It ðmÞ are transmitted intensities obtained, respectively, with the cell under vacuum and filled with the gas sample. To determine the collisional width, we fitted a Voigt and a Rautian profile to aðmÞ, the position of the baseline I0 ðmÞ was systematically readjusted from a
Fig. 1. Example of the spectra obtained for the 153;12 154;12 and 71;6 82;6 lines in the m7 band of C2 H4 located at 923.4693 and 923.5326 cm1 , respectively. (1–4) Broadened lines at 19.41, 25.84, 31.73, and 37.62 mbar of H2 (T ¼ 173:2 K); (5) spectrum of the pure C2 H4 lines at low pressure (0.023 mbar) representing the effective Doppler lines; (6) diode-laser emission profile recorded with an empty cell; (7) confocal etalon fringes; (8) zero transmission level; and (9) saturated line.
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quadratic polynomial which allows to minimize the discrepancies between calculated and observed lineshapes. In our study, the soft collision profile of Galatry [16] would be preferable to the Rautian profile, since the active mass is greater than the perturber mass, but indeed the two profiles lead to very similar results. Some of the lines were sufficiently isolated to be individually fitted in their unperturbed part, but for four couples of transitions (153;12 154;12 and 71;6 82;6 ; 21;1 32;1 and 50;5 61;5 ; 21;2 32;2 and 91;9 92;7 ; and 182;16 173;14 and 113;9 112;9 ), as well as for the transitions 100;10 101;10 , 80;8 81;8 , 73;5 62;5 , and 191;18 192;18 close to unidentified lines, where the overlapping could not be disregarded, a fit of superposed profiles was performed as in [17] by neglecting line mixing effects. The small instrumental distortions were taken into account through the effective Doppler half-width cDA that was systematically used instead of cD . The typical values of cDA and cD at 173.2 K are respectively, 0.891 and 0.843 103 cm1 . For the Rautian profile (for details see [5]), we have constrained the narrowing parameter to its theoretical value such as bc ¼ b0 P , where P is the perturber pressure and b0 is derived from the diffusion coefficient. A calculation based on the Lennard-Jones potential with the usual mixing rules for the molecular pair parameters, using for C2 H4 [18] and for H2 [19] e ¼ 32 K e ¼ 199:2 K and r ¼ 4:523 A, and r ¼ 2:944 A, leads to b0 ¼ 12:87103 cm1 atm1 for C2 H4 –H2 at 173.2 K. It should be noted that the fitted narrowing parameter of the Rautian profile arising from well isolated lines is generally in reasonable agreement with this theoretical value.
An example of Voigt and Rautian lineshape fits to the measured profile aðmÞ of the 153;12 154;12 and 71;6 82;6 lines broadened by H2 is shown in Fig. 2. The observed minus calculated residuals show a better fit of the Rautian profile yielding slightly narrower and higher lineshapes than the Voigt profile. A typical plot of cc derived from both profiles versus the pressure P of the gas mixture is shown in Fig. 3 for the 71;6 82;6 line. Here, we have systematically considered the small self-broadening contribution (represented by a point close to the origin) derived from the coefficients of
Fig. 3. Pressure dependence of the collisional half-width cc for the 71;6 82;6 line in the m7 band of C2 H4 broadened by H2 at 173.2 K and derived from the fits of Voigt (s) and Rautian profiles (+). The point close to the origin represents the self-broadening contribution. The slopes of the best-fit lines represent the H2 -broadening coefficients for this transition.
Fig. 2. The measured profile for the 153;12 154;12 and 71;6 82;6 lines in the m7 band of C2 H4 diluted by 31.73 mbar of H2 at 173.2 K (—) and fitted superposed theoretical profiles (d). The deviations from the fits (calculated minus observed residuals) are shown at the bottom with an intensity scale expanded by 10: (A) The Voigt profile; (B) the Rautian profile with the narrowing parameter bc fixed to the calculated value (0.403 103 cm1 ) derived from the mass-diffusion coefficient. For clarity, only one calculated value out of five is represented there.
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self-perturbed C2 H4 recently measured at 174 K [6]. The slope of the straight lines obtained from unconstrained linear least-squares procedures gives the H2 -broadening coefficients c0 (cm1 atm1 ). These coefficients are presented in Table 1 for the Voigt and Rautian profiles, along with the experimental errors. The main sources of uncertainties in the c0 values arise from the baseline location, the perturbation due to nearby interfering lines, the non-linear tuning of the laser and the lineshape model used. The absolute errors are estimated to be equal to the statistical error on c0 derived from the linear least-squares fit plus 2–3% of c0 , depending on the extent of overlap from the neighboring lines. As may be seen in Table 1, these errors are notably greater than the differences between the measurements from the Voigt and the Rautian profile (average difference: 0.3%). As a new calculation of broadening coefficients has been performed for C2 H4 –H2 , we also present in Table 2
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these coefficients at room temperature (296.5 K) previously listed in Table 1 of [5]. The J dependence of the broadening coefficients c0 at 296.5 and 173.2 K is shown in Figs. 4 and 5, respectively, for all the studied transitions J 0 ; Ka0 ; Kc0 J ; Ka ; Kc . An overall decrease of c0 with increasing J is observable for both temperatures. Moreover, the broadening coefficients belonging to transitions with same J (Tables 1 and 2) generally increase with increasing Ka values. It would be interesting to determine theoretically these J and Ka behaviors of the broadenings.
4. Theoretical results and comparisons The new calculation of H2 -broadening coefficients of C2 H4 has been carried out on the basis of the model previously developed in [9]. Here, we assume that C2 H4
Table 1 H2 -broadening coefficients c0 measured and calculated in the m7 band of C2 H4 at 173.2 K m0 (cm1 )
919.8311 923.4693 923.5326 926.6493 926.7510 927.0739 927.5198 931.3365 931.5019 931.8042 931.8834 936.1209 939.4905 943.3529 947.0301 947.1985 947.7002 948.2275 951.3717 952.0841 952.3859 952.6277 959.3072 959.4075 963.1025 963.2495 963.4818 966.9867 967.1569 967.2054 970.7542 970.8737 982.7607 1011.8617 1023.1018
J0
9 15 7 7 13 4 12 2 11 2 5 4 13 13 8 19 10 12 6 4 3 2 11 6 16 5 14 3 18 11 8 11 7 20 20
Ka0
1 3 1 0 2 1 2 1 2 1 0 1 3 1 0 1 0 0 1 1 1 1 1 2 2 1 1 2 2 3 1 3 3 3 5
Kc0
8 12 6 7 12 4 11 2 9 1 5 4 10 12 8 18 10 12 6 4 3 2 10 5 14 4 13 2 16 9 7 8 5 18 16
J
10 15 8 8 13 5 12 3 11 3 6 4 14 13 8 19 10 12 6 4 3 2 10 6 15 4 13 2 17 11 7 11 6 19 19
Ka
2 4 2 1 3 2 3 2 3 2 1 2 2 2 1 2 1 1 0 0 0 0 2 1 3 0 2 1 3 2 0 2 2 2 4
Kc
8 12 6 7 10 4 9 2 9 1 5 2 12 12 8 18 10 12 6 4 3 2 8 5 12 4 11 2 14 9 7 10 5 18 16
c0 (103 cm1 atm1 ) Voigt
Rautian
Calc.
174.9 4.3 169.9 5.2 178.8 4.1 180.2 5.6 179.0 8.7 176.1 4.5 177.2 5.4 184.8 7.8 180.9 4.1 195.6 7.2 175.5 5.4 161.1 7.4 178.6 4.7 171.1 4.2 158.7 6.2 162.9 6.1 151.0 5.2 149.2 5.6 165.9 4.3 161.1 7.4 170.3 7.5 170.8 10.8 171.1 6.1 177.5 6.9 177.7 5.6 180.6 6.0 172.9 8.9 182.0 4.9 175.9 6.8 180.1 5.4 180.4 5.0 176.7 5.8 179.8 4.9 162.9 6.1 157.8 8.0
175.1 4.3 170.1 5.3 179.0 4.0 180.5 5.5 180.5 7.8 176.5 4.5 177.6 5.4 185.3 7.8 181.2 4.3 195.9 7.1 175.8 5.2 161.8 7.3 179.2 4.7 171.4 4.2 159.6 6.1 163.6 5.8 151.5 5.0 149.7 5.6 166.1 4.1 161.8 7.3 171.0 7.0 171.1 10.6 171.6 5.8 177.9 6.6 178.2 5.3 180.9 5.9 173.7 7.5 182.4 4.7 176.4 6.6 180.4 5.2 180.8 4.7 177.0 5.5 180.0 4.8 163.6 5.8 159.2 8.4
159.8 158.4 162.2 160.0 158.3 166.3 160.0 186.3 161.7 186.3 161.0 170.0 160.5 155.8 160.4 149.6 158.3 156.0 165.0 169.7 174.2 183.0 159.2 172.3 154.8 166.1 155.1 184.5 152.4 165.6 162.0 165.6 176.7 152.0 157.1
Note. The wavenumbers m0 of the unperturbed C2 H4 lines are taken from [15]. The experimental results are derived from the fits of the Voigt profile and the Rautian profile with a fixed bc parameter. The uncertainty in these results is the standard error derived from the linear least-squares fit plus 2–3% of c0 .
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Table 2 H2 -broadening coefficients c0 measured [5] and calculated in the m7 band of C2 H4 at 296.5 K m0 (cm1 )
919.8311 923.4693 923.5326 926.6493 927.0739 927.5198 931.3365 931.5019 931.8834 936.1209 939.4905 943.3529 947.0301 947.3806 947.7002 948.2275 951.3717 951.7394 959.3072 960.0282 960.0769 962.9599 963.1025 966.9867 967.2054 970.7542 970.8737 982.5852 982.7607 1011.5135 1011.8617 1015.3474 1023.1018 1023.4364
J0
9 15 7 7 4 12 2 11 5 4 13 13 8 9 10 12 6 5 11 22 9 20 16 3 11 8 11 23 7 20 20 20 20 24
Ka0
1 3 1 0 1 2 1 2 0 1 3 1 0 0 0 0 1 1 1 3 4 3 2 2 3 1 3 4 3 1 3 4 5 3
Kc0
8 12 6 7 4 11 2 9 5 4 10 12 8 9 10 12 6 5 10 20 5 17 14 2 9 7 8 19 5 19 18 17 16 22
J
10 15 8 8 5 12 3 11 6 4 14 13 8 9 10 12 6 5 10 21 10 19 15 2 11 7 11 23 6 19 19 19 19 23
Ka
2 4 2 1 2 3 2 3 1 2 2 2 1 1 1 1 0 0 2 4 3 4 3 1 2 0 2 3 2 0 2 3 4 2
Kc
8 12 6 7 4 9 2 9 5 2 12 12 8 9 10 12 6 5 8 18 7 15 12 2 9 7 10 21 5 19 18 17 16 22
c0 (103 cm1 atm1 ) Voigt
Rautian
Calc.
118.7 2.3 116.7 4.3 117.8 3.1 117.7 3.7 119.7 4.8 118.7 2.9 121.5 4.4 119.9 3.1 119.9 2.8 121.6 2.7 120.4 3.0 115.2 3.2 107.2 3.2 107.0 2.8 105.1 3.3 99.9 3.3 111.4 2.7 108.7 5.6 120.2 2.7 112.9 3.7 121.2 4.1 118.3 3.5 118.1 3.3 124.0 3.5 121.6 4.0 119.2 2.8 120.5 3.2 115.7 4.9 121.9 2.8 105.4 4.0 113.6 3.5 112.4 4.5 116.8 2.7 109.7 3.5
119.8 2.8 118.2 3.9 119.8 3.4 119.7 4.2 121.7 4.0 120.4 3.5 123.2 4.0 121.4 3.0 121.6 2.5 123.0 2.7 121.4 3.2 116.5 3.0 108.4 3.3 108.1 2.8 106.2 3.6 101.7 3.1 112.8 2.4 111.3 5.3 120.7 3.0 114.8 4.1 122.4 4.3 119.5 3.4 119.3 2.9 124.8 3.7 122.7 3.8 120.1 3.0 121.1 3.5 117.2 4.6 122.6 3.1 107.1 3.6 115.0 3.5 113.7 3.7 118.1 2.6 110.4 3.6
113.6 114.1 114.2 113.1 115.8 114.4 126.3 115.0 113.2 117.8 115.1 112.6 113.4 113.2 113.0 112.4 115.4 116.2 113.6 110.2 121.1 111.3 112.4 125.3 117.0 114.2 117.0 110.2 121.5 109.5 111.0 112.2 113.6 108.9
Note. The experimental results are derived from the fits of the Voigt profile and the Rautian profile with a fixed bc parameter. The uncertainty in these results is the standard error derived from the linear least-squares fit plus 2–3% of c0 .
behaves like the linear molecule C2 H2 for its interaction with H2 , i.e., the two H atoms of each extremity of the molecule are considered as a single atom (noted 2 H) situated on the principal symmetry axis of C2 H4 . Then, we used the semiclassical formalism of Robert and Bonamy [20] for the interaction of linear molecules. Within this framework, the collisional half-width of an isolated pressure broadened rotational or rovibrational line f i may be expressed as Z 1 n2 v X cfi ¼ qJ2 Sfi ðb; J2 Þ 2pb db; ð2Þ 2pc j2 0
where S2;i2 , S2;f 2 , and S2;f 2i2 are the second-order terms of the perturbation of Sfi derived from the anisotropic part of the potential [21]. The total intermolecular potential VT involves the atom–atom Lennard-Jones (LJ) interactions Vaa in addition to the electrostatic interactions Ve , such that VT ¼ Ve þ Vaa
where n2 is the number density of the perturbing molecules, v is the mean relative velocity, qj2 is the relative population for the j J2 , v2 ¼ 0i state of the perturber including the nuclear spin factor f ðJ2 Þ ¼ ð1ÞJ2 þ1 þ 2, and Sfi is the real part of the differential cross-section given by
where the index 1 refers to the absorber (C2 H4 ) and 2 to the perturber (H2 ); Q, and / are the quadrupole and hexadecapole moments of the molecules; eij and rij are the LJ parameters for the interaction of the i th atom considered for C2 H4 (2 H, C, C, and 2 H) and the jth atom of H2 and rij is the distance between these atoms. By expanding rij in power series of the intermolecular distance r, Vaa can be expressed in terms of the intra-
Sfi ðb; J2 Þ ¼ 1 exp½ðS2;i2 þ S2;f 2 þ S2;f 2i2 Þ;
ð3Þ
¼ VQ1 Q2 þ VQ1 /2 þ V/1 Q2 þ V/1 /2 " 6 # 12 X rij rij þ 4eij ; rij rij i;j
ð4Þ
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Fig. 4. J dependence of H2 -broadening coefficients for J 0 ; Ka0 ; Kc0 J ; Ka ; Kc transitions in the m7 band of C2 H4 at 296.5 K. Experimental results derived from the fits of Voigt (s) and Rautian () profiles with their error bars. Theoretical results (d) calculated for all transitions J 0 ; Ka0 J ; Ka studied experimentally at room and low temperatures (the quantum numbers Kc0 and Kc are not considered in our calculations).
Fig. 5. J dependence of H2 -broadening coefficients for J 0 ; Ka0 ; Kc0 J ; Ka ; Kc transitions in the m7 band of C2 H4 at 173.2 K. Experimental results derived from the fits of Voigt (s) and Rautian () profiles with their error bars. Theoretical results (d) calculated for all transitions J 0 ; Ka0 J ; Ka studied experimentally at room and low temperatures (the quantum numbers Kc0 and Kc are not considered in our calculations).
177
molecular distances r1i , r2j (distance of each atom i or j to the mass center of 2 H–C@C–2 H or H2 ) and the spherical harmonics considered for each molecule. The trajectory model [22] includes the influence of the isotropic potential in energy conservation and in the equation of motion around the distance of closest approaches rc . The actual trajectory is replaced by an equivalent straight-line trajectory described at the relative velocity v0c . The isotropic potential considered here is a LJ m–n potential fitting the spherical average of the atom–atom model u000 ðrÞ [23]. In Table 3, we present the rotational constants for the ground state of H2 , the effective rotational constants B* for the ground and m7 states of C2 H4 obtained from B ¼ ðB þ CÞ=2, where B and C are taken from [14], as well as the values used for the electric multipole moments of these molecules. The atom–atom LJ parameters considered for H–H interactions are those calculated by Wang [27] from second virial coefficients of H2 with introduction of quantum effects; the 2 H–2 H parameters are derived from these values by considering the intramolecular distances of C2 H4 . The C–C LJ parameters are calculated by fitting as in [28] nine experimental values of second virial coefficients of C2 H4 [29] similarly considered as linear. The LJ parameters of 2 H–H and C–H for 2 HCC2 H–H2 interactions are obtained from the usual mixing rules eij ¼ ðeii ejj Þ1=2 and rij ¼ ðrii þ rjj Þ=2. The atom–atom LJ parameters eii , rii , ejj , and rjj , the intramolecular distances used for 2 H– C@C–2 H and H2 , and the LJ m–n parameters fitting u000 ðrÞ are listed in Table 4. The contributions to the differential cross-section [8] include in the Clebsch-Gordan coefficients the quantum numbers Ka and Ka0 with Ka0 ¼ Ka 1 (the quantum numbers Kc and Kc0 are quite disregarded here). We have only considered the transitions induced by collisions with DKa ¼ 0 for the absorbing molecule associated with the usual selection rules (DJ ¼ 0, 1, 2 for a quadrupolar transition, and DJ ¼ 0, 1, 2, 3, 4 for an hexadecapolar transition). The H2 -broadening coefficients at 296.5 and 173.2 K were computed by including the contributions of H2 in the fundamental state with J2 values up to 7 or 5, respectively. The single electrostatic contributions yield almost negligible broadening coefficients at room and
Table 3 Molecular parameters used for C2 H4 and H2 in the calculations of broadening coefficients D0 (cm1 )
Q (D A)
3 ) U (D A
—
—
59.33451b
0.045651b
3.30c 0.6522d
7.85e 0.1264d
Molecule
B (cm1 )
B0 (cm1 )
B0 (cm1 )
C2 H4 H2
0.914551a
0.915386a
—
—
a
Calculated from the parameters B and C given in [14] for the ground and m7 states of C2 H4 . Ref. [24]. c Ref. [6]. d Ref. [25]. e Ref. [26]. b
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Table 4 Atom–atom LJ parameters, intramolecular distances r1i and r2j , and LJ m–n parameters fitting the isotropic radial function u000 ðrÞ for 2 HCC2 H–H2 interactions eii , ejj (K)
rii , rjj (A)
r1i , r2j (A)
m
n
e (K)
r (A)
e2 H–2 H ¼ 14:498 eC–C ¼ 67:064 eH–H ¼ 14:498
r2 H–2 H ¼ 3:619 rC–C ¼ 3:1506 rH–H ¼ 2:68224
jr12 H j ¼ 1:226 jr1C j ¼ 0:669 jr2H j ¼ 0:3754
6.2
15.1
68.2576
3.6822
low temperatures. The total potential VT defined by Eq. (4) leads to a very good agreement at room temperature with the experimental data (Table 2, Fig. 4) with an average difference of only 2.3%, smaller than the average estimated uncertainty (3.2%) in these data. The theoretical results are in much better agreement than the previous results [5] which decrease with increasing J values, significantly more than the measurements. This discrepancy was due to the insufficient potential used represented by only one simple expression for the nonelectrostatic contributions which are predominant for C2 H4 –H2 . Here the potential parameters have all been taken in the literature or calculated from second virial coefficients. At low temperature, however, the theoretical broadening coefficients (Table 1, Fig. 5) are generally smaller than the measurements (average difference 6.2% vs 3.4% for the average uncertainty). To determine the theoretical Ka dependence of the broadening coefficients at room and low temperatures, we have considered the lines belonging to a given DJ branch and DKa subbranch. As may be seen in Fig. 6 for the P QðJ ; Ka Þ (or J , Ka 1 J , Ka ) transitions with J ¼ 3, 6, 12, and 20, c0 increases with Ka to a maximum value then (for J P 5) c0 decreases to rather low values for Ka approaching or equal to J . Similar Ka variations of the broadening coefficients are obtained for other DJ branches and/or DKa subbranches of C2 H4 . If the theoretical increase of c0 with Ka is generally in agreement with the observed Ka behavior of broadening coefficients
Fig. 6. Theoretical Ka dependencies of the H2 -broadening coefficients c0 ðJ ; Ka Þ at 173.2 and 296.5 K for P QðJ ; Ka Þ or (J ; Ka 1 J ; Ka ) transitions in the m7 band of C2 H4 with J ¼ 3, 6, 12, and 20.
(Tables 1 and 2), the decrease of c0 cannot be checked experimentally since we have only studied transitions with Ka 6 4, then not any Ka values close to J for J > 4. It should be noted that this decrease of c0 is much less important than predicted by the previous calculation [5]. The dependence of the broadening coefficients upon temperature is usually well represented by the simple power law n T0 c0 ðT Þ ¼ c0 ðT0 Þ ; ð5Þ T where T0 ¼ 296:5 K is our reference temperature. By comparing the experimental results at 296.5 and 173.2 K derived from the fits of Voigt and Rautian profiles, we have determined the experimental n exponent as a function of J (Fig. 7). Assuming quite independent errors in the broadening measurements, the uncertainty in the values of n is very large, about 0.11. As shown in Fig. 7, the theoretical values of n deduced from the calculated broadening coefficients at 296.5 and 173.2 K for the studied transitions are lying generally at the lower limit of the estimated error bars. They are almost Ka independent and decrease regularly from 0.72 to 0.58 as J increases, whereas the experimental n values are more or less constant (average value: 0.73 for the Voigt profile and 0.71 for the Rautian profile).
Fig. 7. Variation of the temperature coefficient n with J for the H2 J ; Ka ; Kc broadening coefficients of the studied transitions J 0 ; Ka0 ; Kc0 in the m7 band of C2 H4 . Experimental results derived from the fits of Voigt (s) and Rautian profiles () with their error bars. Theoretical results (d) calculated for all transitions J 0 ; Ka0 J ; Ka studied experimentally at room and low temperatures.
J.-P. Bouanich et al. / Journal of Molecular Spectroscopy 227 (2004) 172–179
5. Conclusion The H2 -broadening coefficients in the m7 band of C2 H4 derived from the fits of Voigt and Rautian profiles are nearly the same and do not strongly depend on the transition studied since they vary in the range 0.105– 0.125 cm1 atm1 at room temperature and 0.150– 0.190 cm1 atm1 at )100 °C. The theoretical results are very satisfactory by considering the different approximations used in our calculations: the C2 H4 molecule is treated as a linear molecule, the semiclassical model is not appropriate to the light H2 perturber and the predominant atom–atom potential, where the pairwise additivity is assumed without any adjustable parameters, cannot be very precise. Moreover, to our knowledge, this is at this time, the only method to perform accurately these calculations. Since ethylene is an important constituent of the atmosphere of Jupiter and Saturn, our results may be useful for modeling the atmosphere of these planets.
Acknowledgments Support by the ‘‘Programme de Cooperation Scientifique entre le CNRS (France) et le CGRI de la Communaute Francßaise de Belgique’’ is gratefully acknowledged. This work is accomplished in the framework of the European associated Laboratory HiRes.
References [1] T. Encrenaz, M. Combes, Y. Zeau, L. Vapillon, J. Berezne, Astron. Astrophys. 42 (1975) 355–356. [2] T. Kostiuk, P. Romani, F. Espenak, T.A. Livengood, J.J. Goldstein, JGR-Planets 98 (1993) 18823–18830. [3] V. Kunde, A.C. Aiken, R. Hanel, D.E. Jennings, V.G. Kunde, R.C. Samuelson, Nature 292 (1981) 686–688. [4] G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 201 (2000) 56–61.
179
[5] J.P. Bouanich, G. Blanquet, J. Walrand, M. Lepere, J. Mol. Spectrosc. 218 (2003) 22–27. [6] G. Blanquet, J.P. Bouanich, J. Walrand, M. Lepere, J. Mol. Spectrosc. 222 (2003) 284–290. [7] J.F. Brannon Jr., P. Varanasi, J. Quant. Spectrosc. Radiat. Transfer 47 (1992) 237–242; J. Quant. Spectrosc. Radiat. Transfer 49 (1993) 695–696. [8] J.P. Bouanich, G. Blanquet, J. Walrand, J. Mol. Spectrosc. 161 (1993) 416–426. [9] C. Lerot, J. Walrand, G. Blanquet, J.P. Bouanich, M. Lepere, J. Mol. Spectrosc. 217 (2003) 79–86. [10] J.P. Bouanich, J. Salem, H. Aroui, J. Walrand, G. Blanquet, J. Quant. Spectrosc. Radiat. Transfer 84 (2004) 195–205. [11] F. Rohart, J.M. Colmont, G. Wlodarczak, J.P. Bouanich, J. Mol. Spectrosc. 222 (2003) 159–171. [12] M. Lepere, G. Blanquet, J. Walrand, J.P. Bouanich, J. Mol. Spectrosc. 180 (1996) 218–226. [13] C. Schmidt, J.C. Populaire, J. Walrand, G. Blanquet, J.P. Bouanich, J. Mol. Spectrosc. 158 (1993) 423–432. [14] E. Rusinek, H. Fichoux, M. Khelkhal, F. Herlemont, J. Legrand, A. Fayt, J. Mol. Spectrosc. 189 (1998) 64–73. [15] A. Fayt, private communication, 1998. [16] L. Galatry, Phys. Rev. 122 (1960) 1218–1224. [17] G. Blanquet, C. Coupe, J. Walrand, J.P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 51 (1994) 671–678. [18] J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1967. [19] J.P. Bouanich, C. Brodbeck, J. Quant. Spectrosc. Radiat. Transfer 17 (1977) 777–782. [20] D. Robert, J. Bonamy, J. Phys. (Paris) 40 (1979) 923–943. [21] C.J. Tsao, B.J. Curnutte, J. Quant. Spectrosc. Radiat. Transfer 2 (1962) 41–91. [22] J. Bonamy, L. Bonamy, D. Robert, J. Chem. Phys. 67 (1977) 4441–4453. [23] J.P. Bouanich, D. Lambot, G. Blanquet, J. Walrand, J. Mol. Spectrosc. 140 (1990) 195–213. [24] S.L. Bragg, J.W. Brault, W.H. Smith, Astrophys. J. 263 (1984) 999–1004. [25] J. Komasa, A.J. Thakkar, Mol. Phys. 78 (1993) 1039–1046. [26] F. Mulder, M. van Hemert, P.E.S. Wormer, A. van der Avoird, Theor. Chim. Acta (Berl) 46 (1977) 39–62. [27] W.F. Wang, J. Quant. Spectrosc. Radiat. Transfer 76 (2003) 23– 30. [28] J.P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 47 (1992) 243–250. [29] J.H. Dymond, E.B. Smith, The Virial Coefficients of Pure Gases and Mixtures, Oxford University Press (Clarendon), London, 1980.