Diode-laser measurements and calculations of H2-broadening coefficients in the ν3 band of CH3D

Journal of Molecular Spectroscopy 217 (2003) 79–86 www.elsevier.com/locate/jms

Diode-laser measurements and calculations of H2-broadening coefficients in the m3 band of CH3D Christophe Lerot,a Jacques Walrand,a Ghislain Blanquet,a Jean-Pierre Bouanich,b and Muriel Lep
erea,*,1 a

Laboratoire de Spectroscopie Mol eculaire, Facult es Universitaires Notre-Dame de la Paix, 61 rue de Bruxelles, B-5000 Namur, Belgium b Laboratoire de Physique Mol eculaire et Applications, CNRS, Universit e de Paris-Sud, B^ atiment 350, F-91405 Orsay cedex, France Received 13 July 2002; in revised form 23 October 2002

Abstract Using a tunable diode-laser spectrometer, we have measured at room temperature the H2 -broadening coefficients of 12 CH3 D for 36 lines belonging to Q P and Q R branches in the m3 parallel band. The recorded lines with J values ranging from 1 to 15 and K from 0 to 9 (K 6 J ) are located between 1196 and 1412 cm
1 . The H2 -broadening coefficients were determined by fitting each spectral line with Voigt, Rautian, and Galatry profiles. They were also calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the weak electrostatic contributions the atom–atom Lennard-Jones potential. The theoretical results are in reasonable agreement with the experimental data, except for high J transitions where they are overestimated and for K approaching or equal to J with J P 3 where they are underestimated. The latter discrepancy may be caused by the assumption to consider only DK ¼ 0 collision-induced transitions, associated with jDJ j transitions up to 4.
2002 Elsevier Science (USA). All rights reserved. Keywords: Tunable diode-laser; Monodeuterated methane; Broadening coefficients

1. Introduction Monodeuterated methane (CH3 D) is present in the atmosphere of earth, Jupiter, Saturn, Uranus, and Titan, among others. Therefore, determinations of O2 -, N2 -, and H2 -broadening coefficients of CH3 D are very useful in modelling planetary atmospheres [1,2]. We have previously published O2 - and N2 -broadening coefficients [3,4] and we report here measurements of H2 -broadening coefficients. The knowledge of CH3 D parameters allows the determination of its concentration and the estimate of the isotopic ratio ½D=½H  in the planetary atmospheres. This ratio is important because it gives informations about the origin and the evolution of those planetary atmospheres [5]. Several studies have been devoted to monodeuterated methane. In 1974, Tejwani and Fox [6] calculated *

Corresponding author. E-mail address: [email protected] (M. Lep
ere). 1 Postdoctoral Researcher with FNRS, Belgium.

self-, N2 -, O2 -, and H2 -broadening coefficients at room and low temperatures from the Anderson–Tsao–Curnutte theory. In 1987, Tarrago et al. [7] analyzed the intensities and line positions in the triad m3 , m5 , and m6 of 12 CH3 D and in 1997, Nikitin et al. [8] have reexamined the high resolution spectrum of CH3 D in the region of 900–1700 cm
1 . Devi et al. [9,10] measured by diode-laser spectroscopy the absolute intensities as well as self-, N2 -, and air-broadening coefficients of lines belonging to the m3 and m6 bands of CH3 D. Using also a tunable diode-laser spectrometer, Lacome et al. [11] have reported self-, N2 -, and H2 -broadening coefficients of a few lines in the m6 band. Later on, Lance et al. [12] studied self-broadening coefficients in the m3 band of CH3 D. In 1999, Boussin et al. [13] measured with a Fourier transform spectrometer the pressure broadening and shift coefficients for H2 -, He-, and N2 broadening in the 3m2 band of CH3 D. Recently, Devi and her coworkers published several papers [14–19] reporting measurements obtained with a Fourier transform spectrometer on air-, self-, and N2 -broad-

0022-2852/02/$ - see front matter
2002 Elsevier Science (USA). All rights reserved. PII: S 0 0 2 2 - 2 8 5 2 ( 0 2 ) 0 0 0 4 4 - 9

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Ch. Lerot et al. / Journal of Molecular Spectroscopy 217 (2003) 79–86

ening and pressure shifting in the m3 , m5 , and m6 bands of CH3 D. In this work, we have measured H2 -broadening coefficients in the m3 parallel band of 12 CH3 D at room temperature, using a tunable diode-laser spectrometer. These coefficients are determined for 36 lines in the Q P and Q R branches, with J and K values ranging, respectively, from 1 to 15 and from 0 to 9. For each line, the collisional widths are obtained at four different broadening pressures by fitting Voigt, Rautian, and Galatry lineshapes. The broadening coefficients so determined are finally compared with theoretical calculations performed in the frame of the semiclassical Robert and Bonamy formalism [20] by approximating CH3 D as a linear molecule and considering for the intermolecular potential the atom–atom Lennard-Jones model in addition to electrostatic contributions.

Fig. 1. Example of the spectra recorded for the Q Rð3; 2Þ line at 1336.4094 cm
1 of CH3 D (P ¼ 0:0119 mbar) perturbed by H2 . (1) Diode-laser emission profile recorded without absorption; (2), (3), (4), (5) broadened line by 19.94, 30.03, 40.38, 50.44 mbar of H2 ; (6) lowpressure (0.0012 mbar) line of pure CH3 D; (7) confocal etalon fringes; (8) 0% transmission level.

2. Experimental procedures The experimental setup is presented elsewhere in detail [21]. For our measurements, we used an improved Laser Analytics (LS3 model) tunable diode-laser spectrometer. To increase the signal to noise ratio, each record is the result of an average over 100 scans with a sweep frequency of 13.5 Hz. The relative spectral calibration was obtained by introducing in the laser beam a confocal etalon with a free spectral interval of 0.007958 cm
1 . For each line, the following recording sequence was carried out: • Four spectra with the same pressure of active gas and with different pressures of the perturber. • The saturated line which gives the 0% transmission level. • The line with a very low pressure of active gas and small absorption (apparent Doppler line) which is a convolution of the true Doppler profile with the instrumental distortion function. • A record of the baseline with the empty cell which gives the 100% transmission level. • The record of the etalon fringe pattern with the absorption cell under vacuum. The monodeuterated methane was supplied by Cambridge Isotope Laboratories with a stated purity of 99.0% and the hydrogen was supplied by LÕAir Liquide with a stated purity of 99.99%. The gas mixtures were contained in a multipass White-type cell with an absorption length of 40.17 m. All our measurements were realized at room temperature (296:5  1:5 K). The pressures of CH3 D (ranging from 0.0069 to 0.1534 mbar) and gas mixtures (ranging from 10.22 to 70.43 mbar) were measured with a relative uncertainty of 0.05% by using two MKS Baratron gauges with full scale readings of 1.2 and 120 mbar.

The laser mode purity was checked by the smoothness of the etalon fringe pattern and by the observation of the saturated line. An example of the various recorded spectra for the line Q R(3, 2) is shown in Fig. 1. After being recorded, spectra were linearized to correct the nonlinear tuning of the diode-laser with a constant step of about 10
4 cm
1 by using the etalon fringe pattern.

3. Data reduction and lineshape models The measured absorbance aðmÞ at wavenumber m ðcm
1 Þ of an homogeneous gas sample is given by Beer–LambertÕs law as
 It ðmÞ aðmÞ ¼
ln ; ð1Þ I0 ðmÞ where I0 ðmÞ and It ðmÞ are the transmitted intensities obtained with the cell under vacuum and filled with the gas sample. To measure the collisional half-width at half-maximum (HWHM) cc of an experimental profile, we have fitted a profile to the (apparently) unperturbed part of the observed lineshape. Since the apparent Doppler profile may be well represented by a gaussian function, the instrumental profile is also gaussian. Its half-width cApp is obtained by fitting the observed Doppler line with a convolution product of the true Doppler profile and a gaussian function. The small instrumental distortions were taken into account through the effective Doppler half-width cD that was used instead of the true Doppler half-width cDT [22] such as cD ¼ ðc2DT þ c2App Þ

1=2

:

ð2Þ

Ch. Lerot et al. / Journal of Molecular Spectroscopy 217 (2003) 79–86

81

The typical values of cD and cDT are, respectively, 2.15 and 2:00 10
3 cm
1 . In this study, we have considered the usual Voigt profile as well as the Rautian and Galatry profiles which incorporate the Dicke narrowing. This effect consists in a reduction of Doppler broadening due to a confinement of molecules when the perturber pressure increases. The Voigt profile is defined by [23,24] Z y þ1 expð
t2 Þ aV ðx; yÞ ¼ A dt p
1 y 2 þ ðx
tÞ2 ¼ ARe½W ðx; yÞ;

ð3Þ

with W ðx; yÞ ¼

i p

Z

þ1
1

expð
t2 Þ dt; x þ iy
t

where pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi m
m0 pffiffiffiffiffiffiffiffi c S ln 2 pffiffiffi ; y ¼ ln 2 c ; x ¼ ln 2 A¼ : cD cD cD p

ð4Þ

ð5Þ

Here S is the line intensity ðcm
2 Þ at the experimental pathlength and pressure of the absorber, cc ðcm
1 Þ is the collisional half-width, and m0 ðcm
1 Þ is the line center wavenumber. The uncorrelated hard collision lineshape model developed by Rautian and SobelÕman [25] is best suited when the perturber mass is more important than the radiator one. This profile may be described as   W ðx; y þ zÞ p ffiffiffi aR ðx; y; zÞ ¼ ARe ; ð6Þ 1
pzW ðx; y þ zÞ where the pffiffiffiffiffiffiffi ffi parameters are the same as above and z ¼ ln 2bc =cD with bc (cm
1 ) representing the average effect of collisions on Doppler broadening. The uncorrelated soft collision profile model proposed by Galatry [26] is best suited when the active molecule mass is much greater than the perturber one. It can be defined by

Fig. 2. The measured profile for the Q Rð3; 2Þ line in the m3 band of 12 CH3 D perturbed by 19.94 mbar of H2 (—) and fitted by Voigt, Rautian, and Galatry profiles ðdÞ. The observed–calculated residuals are shown at the bottom of the profiles with an intensity scale multiplied by 10. For clarity one calculated value out of five is represented here.

aG ðx; y; zÞ

 Z þ1
  A zt
1 þ e
zt p ffiffiffi Re ¼ exp
ixt
yt
dt 2z2 p
1 ð7Þ

with the same definition of the parameters. To obtain the line-broadening parameters we have first fitted the Voigt profile to the measured absorbance aðmÞ. In the fitting procedure, fixed values are used for the Doppler width taken as the effective Doppler width and three parameters are calculated through a nonlinear least-squares subroutine: an intensity factor, the line center position and cc . Next we have fitted the Rautian and Galatry lineshapes to aðmÞ where an additional parameter is adjusted, the narrowing parameter bc . Fig. 2 presents an example of experimental data fitted by Voigt, Rautian, and Galatry profiles for the Q R(3, 2) line

Fig. 3. Typical plot of the collisional half-widths cc derived from the Voigt ðdÞ and the Rautian ð Þ profiles versus the total broadening pressure for the Q Rð3; 2Þ line in the m3 band of 12 CH3 D. The slopes of the best-fit lines represent the H2 -broadening coefficients.

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Ch. Lerot et al. / Journal of Molecular Spectroscopy 217 (2003) 79–86

at 1336.4094 cm
1 , with CH3 D (P ¼ 0:0119 mbar) diluted by 19.94 mbar of H2 . The residuals (Observed
Calculated multiplied by 10) show a better adequation of the Galatry and Rautian profiles than the usual Voigt profile, due to the fact that these two models account for the Dicke narrowing. In our study, the active molecule mass is greater than the perturber mass. So, the Galatry profile is preferable to the Rautian profile but indeed the two profiles lead to very similar results. From our measurements we deduced, for each line under study, the collisional half-widths cc for four different pressures of the perturber. Fig. 3 shows a typical plot of the collisional half-widths cc derived from the Voigt and the Rautian profiles versus the mixing pressure for the Q R(3, 2) line. We have systematically taken

into account the small self-broadening contribution which is represented by the point very close to the origin. That contribution has been calculated using the selfbroadening coefficients of CH3 D measured in [12,17]. The Rautian profile as well as the Galatry model lead to larger collisional widths than the Voigt profile. The straight lines obtained from a linear regression using a least-squares procedure are a verification of the linearity of cc with pressure. The H2 -broadening coefficients c0 that are given by the slope of these straight lines, are presented in Table 1 for the three profiles, along with the experimental errors. The main sources of uncertainty arise from the baseline location, the small perturbations due to interfering lines (the lines of the light CH3 D molecule are generally well isolated), the lineshape

Table 1 H2 -broadening coefficients c0 in the m3 band of CH3 D Line

m0 ðcm
1 Þa

c0 ð10
3 cm
1 atm
1 ) Experimental

Q

P (13,6,A) P (13,9,A) Q P (9,1,E) Q P (9,2,E) Q P (9,5,E) Q P (8,3,A) Q P (8,5,E) Q P (7,2,E) Q P (7,4,E) Q R(1,0,A+) Q R(1,1,E) Q R(3,0,A+) Q R(3,1,E) Q R(3,2,E) Q R(3,3,A) Q R(4,3,A) Q R(4,4,E) Q R(5,3,A) Q R(6,3,A) Q R(6,4,E) Q R(7,5,E) Q R(7,6,A) Q R(8,0,A+) Q R(8,1,E) Q R(8,2,E) Q R(9,5,E) Q R(10,2,E) Q R(9,8,E) Q R(10,5,E) Q R(10,7,E) Q R(11,0,A+) Q R(12,4,E) Q R(13,5,E) Q R(13,7,E) Q R(14,6,A) Q R(15,6,A) Q

a

1196.8660 1201.7502 1230.6472 1230.9806 1233.3388 1240.6671 1242.5026 1249.0880 1250.4772 1321.7803 1321.8989 1335.9471 1336.0624 1336.4094 1336.9916 1343.7832 1344.5909 1350.4024 1356.8597 1357.6320 1364.8990 1366.1084 1368.3892 1368.4939 1368.8083 1377.0310 1380.7900 1381.1458 1382.9258 1385.3898 1386.2152 1393.5361 1400.0723 1402.4981 1406.7615 1412.3004

Voigt

Rautian

Galatry

52.6  1.8 57.4  2.0 66.6  3.9 62.4  1.9 61.1  2.6 59.4  2.2 62.9  2.8 64.1  2.7 63.3  2.1 68.9  1.9 68.3  3.0 67.4  2.5 64.8  3.1 64.0  2.0 69.1  4.0 64.7  1.7 69.7  2.4 60.9  1.8 59.6  2.1 59.6  2.8 64.1  3.7 65.0  1.7 66.2  3.3 64.1  1.9 61.2  3.5 55.7  2.9 61.8  1.9 61.2  4.1 57.3  3.9 59.3  2.6 65.8  1.8 56.2  1.3 53.1  1.9 51.1  2.0 50.2  2.0 49.1  2.3

53.7  3.2 58.6  3.4 68.1  5.2 63.6  3.6 62.0  5.0 60.1  2.4 64.2  4.6 66.0  5.2 65.0  2.7 70.1  1.6 70.0  2.6 69.2  2.7 65.9  2.7 64.6  1.7 70.3  4.8 65.4  2.2 71.3  2.2 62.0  2.4 60.7  1.5 60.7  3.7 65.4  2.9 65.8  3.3 68.3  3.6 65.7  1.8 62.5  3.0 57.5  2.5 62.5  2.8 63.2  2.3 61.0  3.4 61.1  2.3 68.7  2.3 57.3  1.7 54.3  2.3 51.9  2.5 51.1  2.0 51.0  2.3

53.7  3.5 58.7  3.8 68.1  5.6 63.7  3.9 62.0  5.3 60.2  2.6 64.3  5.1 66.1  5.6 65.2  2.9 70.2  1.8 70.1  3.0 69.4  3.1 66.0  2.9 64.6  1.8 70.5  5.7 65.4  2.3 71.5  2.6 62.1  2.6 60.8  1.5 60.7  4.0 65.5  2.8 65.9  3.7 68.5  3.7 65.9  2.2 62.7  2.9 57.7  2.3 62.7  2.9 63.6  3.6 61.2  3.5 61.3  2.2 68.9  2.1 57.4  1.9 54.3  2.7 51.9  2.8 51.2  2.3 51.3  2.8

Calculatedb

ðO
CÞ C

64.4 57.5 67.5 67.6 64.5 68.9 62.9 68.5 65.0 70.9 68.8 69.8 69.8 67.7 59.4 64.8 52.2 67.2 68.4 65.0 62.9 58.5 67.5 67.5 67.6 65.2 66.3 50.9 65.2 61.0 65.4 64.7 63.8 62.6 64.0 63.5

)15.8 1.9 0.9 )5.9 )3.9 )12.8 2.1 )3.7 0.0 )1.1 1.7 )0.9 )5.6 )4.6 18.4 0.9 36.6 )7.7 )11.3 )6.6 4.0 17.5 1.2 )2.7 )7.5 )11.8 )5.7 24.2 )6.4 0.2 5.1 )11.4 )14.9 )17.1 )20.2 )19.7

(63.8)

(67.6)

(57.1) (64.8) (67.0) (67.6)

(56.0)

(62.8) (62.1)

Ref. [8]. The calculated results in parentheses have been obtained by neglecting the split transitions in the lines with K ¼ 3 or 6. c Relative differences (in %) between the observed (O) values derived from the Rautian profile and the calculated (C) ones. b

(%)c

Ch. Lerot et al. / Journal of Molecular Spectroscopy 217 (2003) 79–86

model used, and the corrections due to the slightly nonlinear tuning of the diode. The experimental errors which do not account for the uncertainties due to the lineshape model are estimated to be twice the standard deviation derived from the linear least-squares procedure plus 2–3% of c0 depending on the spectral line studied. Within these errors, the broadening coefficients are only K and m dependent with m ¼ J in the P branch and m ¼ J þ 1 in the R branch. As may be seen in Fig. 4, the global trend of c0 ðJ ; KÞ is to decrease as J increases. The agreement between our measurements and those of Boussin et al. [13] in the 3m2 band of CH3 D is excellent (Table 2), which implies that the vibrational dependence of the H2 -broadening coefficients is negligible. The Dicke narrowing parameter (b0 ¼ bc =P ) derived from the soft and hard models is very sensitive to small baseline uncertainties and cannot be accurately determined. Within the experimental errors, b0 is, as expected, independent of the rotational state. We found from the Rautian profile b0 -values in the range 5–27 10
3 cm
1 atm
1 with an average value of

83

Fig. 4. H2 -Broadening coefficients c0 in the m3 band of 12 CH3 D versus m ðm ¼ J in the Q P branch and J þ 1 in the Q R branch). Experimental results derived from the fits of the Rautian profile: ðÞ in the Q P branch and ðsÞ in the Q R branch. Calculated results from the atom– atom contributions in addition to the electrostatic contributions ð Þ. They are displayed for all J and K values for which experimental data were obtained.

Table 2 Comparison of the H2 -broadening coefficients from this work in the m3 band using the Voigt and Rautian profiles with results of Boussin [13] in the 3m2 band derived from a Voigt profile Line

m0 (cm
1 )a

ðR
BÞ B

c0 (10
3 cm
1 atm
1 ) This work

Q

P (13,6,A) P (9,1,E) Q P (9,2,E) Q P (9,5,E) Q P (8,3,A) Q P (8,5,E) Q P (7,2,E) Q P (7,4,E) Q R(1,0,A+) Q R(1,1,E) Q R(3,0,A+) Q R(3,1,E) Q R(3,2,E) Q R(3,3,A) Q R(4,3,A) Q R(4,4,E) Q R(5,3,A) Q R(6,3,A) Q R(6,4,E) Q R(7,5,E) Q R(7,6,A) Q R(8,0,A+) Q R(8,1,E) Q R(8,2,E) Q R(9,5,E) Q R(10,2,E) Q R(10,5,E) Q R(11,0,A+) Q R(12,4,E) Q

a b

1196.8660 1230.6472 1230.9806 1233.3388 1240.6671 1242.5026 1249.0880 1250.4772 1321.7803 1321.8989 1335.9471 1336.0624 1336.4094 1336.9916 1343.7832 1344.5909 1350.4024 1356.8597 1357.6320 1364.8990 1366.1084 1368.3892 1368.4939 1368.8083 1377.0310 1380.7900 1382.9258 1386.2152 1393.5361

Ref. [13]

Voigt

Rautian

Voigt

52.6 66.6 62.4 61.1 59.4 62.9 64.1 63.3 68.9 68.3 67.4 64.8 64.0 69.1 64.7 69.7 60.9 59.6 59.6 64.1 65.0 66.2 64.1 61.2 55.7 61.8 57.3 65.8 56.2

53.7 68.1 63.6 62.0 60.1 64.2 66.0 65.0 70.1 70.0 69.2 65.9 64.6 70.3 65.4 71.3 62.0 60.7 60.7 65.4 65.8 68.3 65.7 62.5 57.5 62.5 61.0 68.7 57.3

52.6 64.8 63.2 59.9 60.8 63.1 61.8 62.6 69.8 69.1 68.1 65.6 64.4 70.3 66.6 70.9 62.5 63.8 64.4 63.6 66.5 65.8 65.1 65.4 58.7 59.8 58.7 64.9 58.7

Ref. [8]. Relative differences (in %) between our measurements (R) derived from the Rautian profile and those (B) of Boussin.

2.1 5.1 0.6 3.5 )1.2 1.7 6.8 3.8 0.4 1.3 1.6 0.5 0.3 0 )1.8 0.6 )0.8 )4.9 )5.8 2.8 )1.1 3.8 0.9 )4.4 )2.0 4.5 3.9 5.9 )2.4

(%)b

84

Ch. Lerot et al. / Journal of Molecular Spectroscopy 217 (2003) 79–86

11:8 10
3 cm
1 atm
1 . From the Galatry profile, the b0 -values are obtained in the range 6–37 10
3 cm
1 atm
1 with an average value of 16:1 10
3 cm
1 atm
1 . Those results can be compared to a theoretical value bdiff deduced from [27] 0 bdiff ¼ 0

kB T ; 2pcm1 D12

ð8Þ

where kB is the Boltzmann constant, T ¼ 297 K; c is the light velocity, m1 is the molecular weight of the active molecule, and D12 is the mass-diffusion coefficient for the pair CH3 D–H2 . This coefficient as estimated from a Lennard-Jones potential leads to the theoretical value bdiff ¼ 11:1 10
3 cm
1 atm
1 , in reasonable agreement 0 with the narrowing parameters derived from the lineshape fits.

4. Theoretical results In this study we have assumed that CH3 D behaves like a linear molecule for its interaction with H2 . Then the H2 -broadening coefficients are calculated on the basis of the semiclassical model of Robert and Bonamy [20]. The collisional half-width of an isolated pressure broadened rotational or rovibrational line i ! f line may be expressed as Z 1 n2 v X cif ¼ qJ2 2pbSif ðb; J2 Þ db; ð9Þ 2pc J2 0 where n2 is the number density of the perturbing molecules, v is the mean relative velocity, qJ2 is the relative population for the jJ2 ; v2 ¼ 0i state of the perturber including the nuclear spin factor f ðJ2 Þ ¼ ð
1ÞJ2 þ1 þ 2 and Sif is the real part of the differential cross-section given with a good approximation by Leavitt and Korff [28] outer outer
l1 l2 S2;f
l1 l2 S2middle Þ; Sif ðb; J2 Þ ¼ 1
expð
l1 l2 S2;i

ð10Þ outer outer where S2;i , S2;f , and S2middle are the second-order terms of the perturbation development of Sif ðb; J2 Þ derived from the anisotropic part of the interaction potential [29] and l1 , l2 represent the orders of the spherical harmonics considered for the absorber and the perturber.

Assuming that the three H atoms (noted as 3 H) of CH3 D are situated at the position of their projection in the C–D axis, the intermolecular potential VT used involves in addition to the electrostatic interactions the usual atom–atom Lennard-Jones (LJ) model such that VT ¼ Vl1 Q2 þ Vl1 U2 þ VX1 Q2 þ VX1 U2 þ VU1 Q2 þ VU1 U2 "

6 # 12 X rij rij þ 4eij
; r rij ij i;j

ð11Þ

where the index 1 refers to the absorber ðCH3 DÞ and 2 to the perturber ðH2 Þ; l, Q, X, and U are the dipole, quadrupole, octopole, and hexadecapole moments of molecules; eij and rij are the LJ parameters for the interaction of the ith atom for molecule 1 and jth atom of molecule 2 and rij is the distance between these atoms. The trajectory model used [30] includes the influence of an isotropic LJ potential in the equation of motion around the distance of closest approach rc . The atom– atom parameters considered for C–C interactions are those obtained for C2 H2 [31]; the D–D and H–H parameters were calculated by Wang [32] with introduction of quantum effects, from second virial coefficients of D2 and H2 ; the 3 H–3 H parameters were determined by fitting as in [33] seven experimental values of the second virial coefficients of CH3 D which is similarly considered as linear ð3 HCDÞ. The LJ parameters 3 H–H, C–H, and D–H for 3 HCD–H2 interactions, were obtained from the 1=2 usual mixing rules eij ¼ ðeii ejj Þ and rij ¼ ðrii þ rjj Þ=2. The spherical average of the atom–atom model U000 ðrÞ [34] used in the trajectory model may be well fitted by a classical LJ m–n potential. The rotational constants and electric multipole moments of CH3 D and H2 , as well as the atom–atom potential parameters used in the calculations are given in Tables 3 and 4, respectively. The contributions to S2 include in the Clebsch–Gordan coefficients the quantum numbers Ki and Kf with Kf ¼ Ki for the parallel m3 band of CH3 D. We have only considered the transitions induced by collisions with DK ¼ 0 for the absorber associated with the usual selection rules DJ ¼ 0; 1 for a dipolar transition ðl1 ¼ 1Þ, up to DJ ¼ 0; 1; 2; 3; 4 for an hexadecapolar transition ðl1 ¼ 4Þ. The coefficients c0 were computed for T ¼ 297 K by including the contributions of H2 molecules with J2

Table 3 Molecular parameters used in the calculations Molecule

Bi (cm
1 )

Bf (cm
1 )

Di (cm
1 )

l (D)

) Q (D A

2 ) X (D A

3 ) U (D A

CH3 D H2

3.880195a 59.3341d

3.8584a

5.2614 10
5a 0.045651d

0.0057b 0

0 0.6522e

3.10c 0

6.55 c 0.1264e

a

Ref. [7]. Ref. [37]. c Ref. [4]. d Ref. [38]. e Ref. [39]. b

—

Ch. Lerot et al. / Journal of Molecular Spectroscopy 217 (2003) 79–86

85

Table 4 Atom–atom LJ parameters, intramolecular distances r1i and r2j , and LJ ðm
nÞ parameters e; r fitting U000 ðrÞ for 3 HCD–H2 interactions eij (K)

) rij (A

) r1;i , r2;j (A

eC–C ¼ 61.365 eD–D ¼ 13.232 e3 H–3 H ¼ 14.7057 eH–H ¼ 14.498

rC–C ¼ 3.141 rC–C ¼ 2.66179 r3 H–3 H ¼ 3.8454 rH–H ¼ 2.68224

jr1C j ¼ 0:06384 jr1D j ¼ 1:02788 jr13 H j ¼ 0:43131 jr2H j ¼ 0:3754

values in the fundamental state up to 7 that are weighted by the Boltzmann and nuclear spin factors. It should be noted that the lines of the m3 band with K ¼ 3 are indeed composed of doublets (not observed) of A1 ðwþ Þ and A2 ðw
Þ symmetry (selection rule A1 $ A2 ) with a very small separation ([8]). Some of them have been analyzed by Devi et al. [18]. This leads to S2middle ¼ 0 (instead of being negative) for l1 ¼ 2 or 4 which increases slightly their theoretical values (Table 1). We have also considered a splitting in K ¼ 6 transitions, although this splitting has not been directly or indirectly observed. The calculated results in the P - and R-branches are identical for the same m and K values so that all the results may be given as c0 ðm; KÞ. Owing to the weak or null multipole moments of CH3 D and H2 and the very large rotational B value of H2 leading to nearly zero resonance functions fn (k) [20], it is not surprising that the single electrostatic contributions yield almost negligible broadening coefficients ðc0 6 4 10
3 cm
1 atm
1 Þ. The atom–atom contributions in addition to the electrostatic contributions lead to a satisfactory agreement with the experimental data (Fig. 4), except for the high J transitions and the lines with K approaching or equal to J ðJ P 3Þ. For J > 11, the calculated broadening coefficients are larger than the experimental results and for K  J they are significantly smaller. The latter discrepancy may be partly due to the consideration of only collision-induced transitions with DK ¼ 0. Let us consider for example a RðJ ; KÞ line with K ¼ J ðJ P 3Þ. The transitions J ! J
1;
2;
3 are

Fig. 5. Theoretical K dependence of H2 -broadening coefficients c0 for Q P ðJ ; KÞ and Q RðJ ; KÞ transitions in the m3 band of 12 CH3 D with m ¼ 4 (+), m ¼ 9 ð Þ, and m ¼ 11 ðsÞ.

e (K)

) r (A

m

n

63.512

3.3264

6.0

13.8

forbidden with DK ¼ 0, but they become allowed for DK ¼ 3. Transitions such as j DK j ¼ 3n (n ¼ 1; 2; . . .) have been indeed observed with positive or negative values of K by Oka [35] in the case of NH3 –rare gas collisions. Nevertheless if we admit that the interactions of the potential giving rise to DK ¼ 0 and DK ¼ 3 transitions are not the same, equivalent contributions to the broadening can be derived from the selection rule DK ¼ 3, whatever the K component of a given J transition [36]. In order to obtain a significant contribution (missing in our calculation) only for the lines with K approaching m ðm > 3Þ it would be necessary that a same interaction could induce DK ¼ 0 as well as DK ¼ 3 (or more generally j DK j ¼ 3n) transitions. The theoretical broadening coefficients are found to decrease on the whole more slightly as J increases than our experimental results. Concerning their K-dependence, our calculation predicts that for a given m value (m P 3), c0 ðm; KÞ increases slightly with increasing K (up to K ¼ 1 for m 6 4; K ¼ 2 for m ¼ 5; 6 and K ¼ 3 for m P 7), then decreases more significantly for K values approaching m (Fig. 5). From our measurements however, we cannot derive, within the experimental errors, a general trend for the K behavior of these broadenings.

5. Conclusion The H2 -broadening coefficients of CH3 D derived from the Rautian and Galatry profiles are nearly the same and significantly larger than those derived from the Voigt profile. Their global trend is to decrease as J increases. The theoretical results are very satisfactory by considering the different approximations used in the calculations: the CH3 D molecule is treated as a linear molecule, the semiclassical model (where the translational and rotational motions are assumed independent) is not appropriate to the light H2 perturber and there are probably deficiencies in the predominant atom–atom potential related to the assumed pairwise additivity [40]. The agreement with the experimental data is quite good except for the high J transitions and the lines with K approaching or equal to J . As CH3 D and H2 are important constituents of the atmospheres of the outer planets, our results may be useful for modelling the atmospheres of these planets.

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