Self-Broadening and Linestrength in the ν2and ν5Bands of CH3F

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO .

180, 100–109 (1996)

0228

Self-Broadening and Linestrength in the n2 and n5 Bands of CH3F Benoit Lance,* Muriel Lepe`re,* Ghislain Blanquet,* Jacques Walrand,* and Jean-Pierre Bouanich† *Laboratoire de Spectroscopie Mole´culaire, Faculte´s Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium; and †Laboratoire de Physique Mole´culaire et Applications,1 CNRS, Universite´ de Paris-Sud, Baˆtiment 350, F-91405 Orsay cedex, France Received March 28, 1996; in revised form June 24, 1996

The self-broadening coefficients and the linestrengths of 30 lines in the n2 and n5 fundamental bands of CH3F have been measured at high resolution in the range 1417–1553 cm01 , using a tunable diode-laser spectrometer. The lineshape parameters were obtained by fitting noncorrelated Galatry and Rautian profiles to the measured shapes of the lines. Both models show good agreement between the self-broadening coefficients derived from the spectra at ‘‘low’’ pressure (0.4 to 3 mbar) and those recorded at ‘‘high’’ pressure (6 to 18 mbar), but feature an overestimation of the dynamical friction parameter. A semiclassical calculation of the self-broadening coefficients, performed by using the main electrostatic interactions only, has provided larger results than the experimental data. q 1996 Academic Press, Inc. INTRODUCTION

These past years, an increased interest arose in the theoretical and experimental study of the lineshapes of infrared absorption by molecular gases. Several authors have underlined the limits of the Voigt model for the description of the shape of reasonably isolated lines. Two principal effects are responsible for this limitation, namely, the speed dependence of the collisional cross section and the presence of velocity changing collisions, also called the Dicke effect. Bouanich et al. (1) have shown evidence of the speed dependence of the collisional cross section by using the General Voigt Profile (GVP). On the other hand, Pine (2–4) has intensively used lineshape models including the averaging effect of the velocity changing collisions. Recently, Saarinen et al. (5) have shown the relative inadequacy of the Voigt model by mean of a fitting technique in the signal domain, and they preferred a stochastic approach. In accordance with the work of Rohart et al. (6), the lines of CH3F seem to be an appropriate candidate for the study of their self-broadenings with the Galatry and Rautian models. We report here the measurements of the intensity and broadening coefficients of 30 lines chosen in the n2 and n5 bands of CH3F. These lines, with J values ranging from 3 to 24 and K from 0 to 6, were recorded in the spectral region near 1500 cm01 using a tunable diode-laser spectrometer. All the records were made at pressures below 18 mbar to minimize interferences with the neighboring lines. EXPERIMENTAL PROCEDURES

The spectra were recorded with an improved Laser Analytics LS3 TDL spectrometer driven by an HP 9000/G30 1

Laboratoire associe´ aux Universite´s Paris-Sud et Pierre et Marie Curie.

computer (7). A home-made signal averager was used for data acquisition. The relative wavenumber calibration was obtained by introducing in the laser beam a confocal e´talon with a free spectral range of 0.0079467 cm01 . Monofluoromethane was supplied by L’Oxydrique with a stated purity of 99%. We have measured the spectra of a total of 30 lines, recorded under the following conditions: 10 lines at 8 to 20 different pressures ranging between 0.4 and 3 mbar (L, ‘‘low’’ pressure), which is a pressure regime ideal for Dicke narrowing evidence; 20 lines at four pressures between 6 and 18 mbar (H, ‘‘high’’ pressure), which is a pressure regime more appropriate for the collisional line-broadening measurements. The following consecutive records were obtained for each line under study: (a) a spectrum of the empty cell, which represents the free running laser emission; (b) the record of the line at very low gas pressure ( £0.2 mbar), which gives the Doppler profile convoluted with the instrumental function (the observed Doppler profile); (c) the spectra of the broadened line at different pressures; (d) the record of the e´talon fringe pattern, with the absorption cell evacuated. We also checked for the laser mode purity with the saturated spectrum of the line and the smoothness of the e´talon fringe pattern. Each record was averaged over 100 scans with a sweep frequency of 13.5 Hz. All the pressures were measured with MKS Baratron gauges with a full scale reading of 1, 10, or 100 mbar. The ambient temperature (between 295 and 297 K) was measured with an Analog Devices AD590 transducer with a precision of {0.1 K. Different

100 0022-2852/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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CH3F LINESHAPE PARAMETERS

FIG. 1. Example of the spectra obtained for the PQ(11,4) line of CH3F at 1427.6355 cm01 : (1), (2), (3), (4) spectra recorded at different pressures; (5) baseline recorded with the empty cell; (6) confocal e´talon fringe pattern; (7) spectrum of the same line at very low pressure (Doppler regime).

optical path lengths were used depending on the strength of the line under investigation: 4.17 or 20.17 m with a multipass cell and 41.05 cm with a simple cell. When possible, the baseline (0% absorption level) has been corrected, so that we can localize it at {1% or better of the total absorption. All spectra were then linearized with a constant step of 5 1 10 05 cm01 , by mean of cubic splines technique (8). An example of the spectra obtained for the P Q(11,4) line is shown in Fig. 1.

W ( x, y) Å

k( s ) Å ln[I0 ( s )/It ( s )]L,

[1]

where I0 and It are respectively proportional to the incident and transmitted radiation intensities, and L is the optical pathlength. All the measured data for k( s ) were treated by home-made programs, based on an IMSL nonlinear leastsquares fitting routine. We have first used the Voigt profile to fit the shape of the 10 lines recorded between 0.4 and 3 mbar. This profile is defined as k( s 0 s0 ) Å ArRe[W ( x, y)].

[2]

W ( x, y) is the well-known complex error function, that we usually evaluate by the Hui et al. algorithm (9)

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0`

exp( 0t 2 )dt , x 0 t / iy

q

S ln 2 q AÅ , gD p

[3]

q

y Å ln 2

gC , gD

[4]

q

s 0 s0 0 d C . x Å ln 2 gD

S is the line intensity (cm02 ), gC is the collisional halfwidth at half maximum (cm01 ), s0 is the line center wavenumber (cm01 ), dC is the collisional line shift (cm01 ), and gD is the Doppler halfwidth at half maximum (cm01 ) which is related to the molecular weight M (a.m.u.), temperature T (K), and s0 by

r gD Å 3.5812 1 10

07

T s0 . M

[5]

It is worth noting that we have neglected the eventual collisional line shift by setting this to zero. As a matter of fact, strong line shift parameters give rise to small lineshape asymmetries (4). This asymmetry is quite negligible in most gaseous systems for which the collisional line shifts are weak. In order to check for a line-narrowing effect, the Doppler halfwidth parameter was set free in the fitting procedure (10, 11). Actually, in the presence of Dicke narrowing,

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*

/`

where

DATA REDUCTION AND EXPERIMENTAL RESULTS

The absorption coefficient k( s ) at wavenumber s is defined through the Beer-Lambert law

i p

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LANCE ET AL.

the Doppler halfwidth is expected to decrease with increasing pressure. According to Rao and Oka (10), this decrease is, at sufficient pressure, inversely proportional to the pressure. Those fits have shown that the Doppler halfwidth decreases considerably between 0.4 and 2 mbar (a reduction of about 20%) and becomes there of the same order of magnitude as the collisional contribution. Thus a precise study of the self-broadening of CH3F requires one to take into account a narrowing effect of the lines. Rohart et al. (6) have previously studied the rotational relaxation of CH3F with various foreign perturbers and have shown evidence of both speed dependence of the collisional cross section and the presence of velocity changing collisions. In our study, as we measured the spectra at relatively low gas pressure, we expected that the Dicke effect was the principal cause of line narrowing. Therefore we have only considered the Doppler effect, the state perturbing, and the velocity changing collisions through two symmetric lineshape models. We have first chosen the noncorrelated hard collision profile of Rautian and Sobel’man (12), which may be expressed by

k( s 0 s0 ) Å ArRe

F

W ( x, y / z) q 1 0 pzW ( x, y / z)

G

.

q

z . gD

[7]

The other model considered was the noncorrelated soft collision profile of Galatry (13) in its standardized form, i.e.,

k( s 0 s0 ) Å

F S

A 1 rRe (1/2z) / y 0 ix p

q

1M

1 y 0 ix 1 1; 1 / 2 / ; 2 2z z 2z

DG

[8] ,

where M(rrr; rrr; rrr) is a hypergeometric function. The parameter z is related, through the Brownian motion model, to the dynamical friction parameter b by

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We have used the routine proposed by Varghese and Hanson (14) to compute the standardized Galatry function, with the slight difference that we have preferred the Hui et al. algorithm instead of the one of Humlicek (15) for the calculations in region I of the (Y, Z ) plan. We have explicitly considered the instrumental function fA ( s 0 si ) as a normalized Gaussian profile (16)

r f A ( s 0 si ) Å

F S

ln 2 1 s 0 si r rexp 0ln 2 p gA gA

DG 2

,

[10]

where gA is the apparatus halfwidth. The effect of the instrumental distortions can be well represented by kobs ( si ) Å 0ln

F*

G

fA ( s 0 si )exp[ 0k( s )r L]ds r L

[11] 01

such that the observed transmission at the wavenumber si is derived from a convolution between the transmission and the apparatus function. The convolution is performed for each line by an IMSL routine using limits of integration taken as si { 20gD (i.e., Çsi { 0.032 cm01 ). An example of the Rautian and Galatry lineshape fits to the observed kobs ( s ) of the PQ(11,4) line at 9.79 mbar is shown in Fig. 2. It appears that the two models give equally satisfactory fits. A typical plot of the collisional halfwidth gC and of the line intensity S, derived from the Rautian and the Galatry profiles, versus pressure, is shown for the same line in Fig. 3. The slope of the straight lines constrained to pass through the origin, obtained from a linear least-squares procedure, gives the self-broadening coefficient g 0 and the linestrength S0 . It should be noted that the quality of the fit and the linear behavior of the collisional halfwidth versus pressure are generally slightly better for the Galatry model. At ‘‘low’’ pressure, between 0.4 and 3 mbar, the collisional halfwidth has only the same order of magnitude as the apparatus function (0.55 to 1.2 1 10 03 cm01 ). To reduce the error due to this lack of collisional contribution, it has been necessary to record the spectra with a minimum of eight pressures. We show in Fig. 4 the self-broadening coefficients vs ÉmÉ (m Å 0 J in the P branch, m Å J in the Q branch, and m Å J / 1 in the R branch) obtained from the Galatry model, for any K values considered. Within the experimental errors, no systematic difference between the broadening coefficients derived from the spectra recorded at ‘‘low’’ and ‘‘high’’ pressures are observable. The experi-

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b . gD

[6]

In this model, the collision creates either a dephasing of the absorbed radiation or a velocity change of the active molecule, but never the two effects simultaneously. The averaging effect of the velocity changing collisions is expressed through the z parameter, with z being the effective frequency of the velocity changing collisions:

z Å ln 2

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z Å ln 2

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CH3F LINESHAPE PARAMETERS

103

mental values plotted in Fig. 4 with the theoretical results (see next section) are given in Table 1, along with the experimental errors estimated to be twice the standard deviation derived from the linear least squares procedure plus 2 to 4% of g 0 , depending on the extent of overlap from the neighboring lines. The Galatry and the Rautian profiles are in close agreement, but the first one gives larger collisional contribution for pressures below 6 mbar. Indeed, the Dicke narrowing parameter is more important in the noncorrelated Galatry model, leading to a larger collisional broadening. The self-broadening coefficients vs ÉmÉ, obtained from the Galatry model for any K values considered, are also compared in Fig. 5. with the previous results of Guerin et al. (17). Their results seem to be consistent with our experimental data, although we cannot compare the broadening coefficients for ÉmÉ õ 4. Within the experimental errors, the agreement between the two kinds of values in the n2 and n5 bands is satisfactory, which implies that the vibrational dependence of the broadening coefficients should be small.

FIG. 3. Pressure dependence of the lineshape parameters for the Q(11,4) line of CH3F: (a) collisional halfwidth gc versus pressure, where the slope of the best-fit line (in the sense of the linear least squares) is the self-broadening coefficient g 0 ; (b) line intensity S versus pressure, where the slope of the best-fit line is the linestrength S0 . P

FIG. 2. Measured profile kobs ( s ) of the PQ(11,4) line of CH3F at 9.79 mbar ( —) and fitted theorical profiles ( / ): (a) the Galatry profile; (b) the Rautian profile. The deviations from the fits (calculated minus observed residuals) are shown at the bottom with an intensity scale expanded by 10.

The values of the linestrengths obtained in the same fitting procedure are listed in Table 2. We have already shown the consistency of the results obtained from this method with those derived from the equivalent width method (18). The estimated errors are equal to twice the standard deviation derived from the linear least-squares procedure plus 1 to 2% of S0 , depending on the extent of overlap with the neighboring lines. Note that these absolute intensities, derived in the Galatry model, have been corrected for the purity percentage and normalized at 296 K using Eq. (A.10) of Ref. (19). Our values greatly diverge from the results of Dunjko et al. (20), for the same eight lines under study. It should be noted that the Rautian and the Galatry profiles provide nearly the same line intensities and may be used indistinctly to determine them. The number of recorded lines is not enough to provide a sufficiently accurate value of the band strength, all the more because of the interaction be-

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FIG. 4. Experimental and theoretical self-broadening coefficients g 0 vs ÉmÉ in the n2 and n5 bands of CH3F: ( l ) ‘‘high’’ pressure measurements; ( s ) ‘‘low’’ pressure measurements; ( ∗ ) theoretical calculations.

tween the two bands n2 and n5 ; thus, a forthcoming paper may be devoted to such research. We have tried to get a significant information about the narrowing parameter z, which is known to be very sensitive to baseline uncertainties. This is not a simple task. At ‘‘high’’ pressure, when the extent of the neighboring lines is important, it is often impossible to correct the baseline location and the overlapping wings due to the other lines may have the same influence as an incorrect baseline. At ‘‘low’’ pressure, the collisional contribution is so small that we cannot afford some imprecisions in the apparatus function. Despite these limits, it was possible to see identical features for the Galatry and the Rautian models. Both lineshapes have reasonable values of z at ‘‘low’’ pressure. Once the pressure goes over 6 mbar, the parameter z generally expands too much (by an order of 100 or even 1000 in magnitude) to have a physical meaning. So we can only report here the values between which the dynamical friction coefficients b 0 and z 0 vary: 0.30 to 290 and 0.27 to 220 cm01 /atm, respectively, for the soft and the hard collision models. As is well known (4), the larger Dicke narrowing parameter of the noncorrelated Galatry model implies that more weak velocity changing collisions lead to the same Doppler narrowing as the Rautian model. A theoretical calculation (21), based on a Lennard–Jones potential modelization, provides a CH3F self-diffusion coefficient of 0.1637 cm2 /sec, leading to b 0 Å 0.0233 cm01 /atm.

This inconsistency could be explained by a speed dependence of the collisional cross section which is also responsible of some narrowing of the lines ( 22). Indeed, the large values obtained for the narrowing parameter z, which have no physical meaning, may imply that the speed dependence of the dephasing contribution ( gC and dC ) must be taken into account, especially for the measurements at ‘‘high’’ pressure ( ú6 mbar). In any case it would be interesting to test other models on the same spectra; for example, a speed-dependent model or the correlated Rautian and Galatry profiles. The best model would incorporate all the principal effects, i.e., the Doppler effect, the velocity changing and dephasing collisions, and the speed dependence of the collisional cross section. THEORETICAL RESULTS

The calculations of self-broadening coefficients that we have considered for symmetric-top molecules were first applied to the n3 band of CH3Cl (24). These calculations are based on the Anderson–Tsao–Curnutte theory ( 25) and include some of the improvements proposed by Robert and Bonamy (26). The broadening coefficient g 0 for a £i Ji Ki r £f Jf K f transition may be expressed as J

g0 Å

2 n£V ∑ ∑ f ( K2 ) rJ2K2 s Jif2K2 , 2pc J2 K2Å0

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[12]

CH3F LINESHAPE PARAMETERS

TABLE 1 Self-Broadening Coefficients g 0 in the n2 and n5 Bands of CH3F Derived from the Noncorrelated Galatry and Rautian Lineshapes

Note. The line wavenumbers have been measured by Papousek et al. (23). The letter L refers to the ‘‘low’’ pressure regime (0.4 to 3 mbar) and H to the ‘‘high’’ pressure regime (6 to 18 mbar). Copyright q 1996 by Academic Press, Inc.

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FIG. 5. Experimental self-broadening coefficients g 0 vs ÉmÉ in the n2 and n5 bands of CH3F. Our results and those of Guerin et al. (17) are displayed for all K values for which data were obtained. This work: ( l ) n5 band; ( s ) n2 band. Guerin et al.: ( / ) n5 band; ( 1 ) n2 band.

where n is the number density of perturbing molecules, £V is the mean relative velocity, rJ2K2 is the Boltzmann factor for the J2K2 state of the perturbing molecules assumed to be in the ground vibrational state, f ( K2 ) is a nuclear spin factor (1 for K2 Å 0, 1, 2, 4, rrr and 2 for K2 Å 3, 6, 9, rrr), and s Jif2K2 is the optical cross section. For rigid symmetrictop molecules, rJ2K2 is given by rJ2K2 Å

2J2 / 1 Qr

H

hc 1 exp 0 [B0 J2 (J2 / 1) / (A0 0 B0 )K 22 ] kBT

J

[13] ,

Vaniso Å Vm1m2 / Vm1Q2 / VQ1m2 / VQ1Q2 ,

where kB is the Boltzmann constant, A0 and B0 are spectral constants for £i Å 0, and Qr the rotational partition function is evaluated from J2max K2max

∑ ∑ f ( K2 ) rJ2K2 Å 1.

Lennard–Jones (LJ) potential, in energy conservation and in the equation of motion have been considered. The parameters of the LJ potential have been calculated, as in Ref. ( 28), by fitting eight recommended values of the second virial coefficients B(T ) of CH3F in the temperature range 280– 420 K (29). The resulting parameters are 1 /k Å 195.9 K ˚. and s Å 3.427 A Since electrostatic contributions dominate the collisional line broadening on account of the large dipole moment of CH3F ( m Å 1.8585 D in the ground vibrational state), we have only considered the electrostatic interactions such that

[14]

J2Å0 K2Å0

In our calculations, we have considered J2max Å 60 and K2max Å J2 (if J2 £ 18) or K2max Å 18 (if J2 ú 18). For the trajectory model, a straight-line trajectory tangential to the real trajectory near the distance of closest approach rc and described at the relative velocity £*c has been assumed (27). The influences of the isotropic potential, taken as a

where the subscripts 1 and 2 refer to the absorbing and perturbing molecules, and m and Q are the dipole and quadrupole moments of CH3F. We have considered the following selection rules for the rotational transitions induced by collisions: D J Å 0, {1 and DK Å 0 (dipolar transition); D J Å 0, {1, {2 and DK Å 0 (quadrupolar transition). These rules have been applied to the initial ( £i Å 0, Ji , Ki ) and final ( £ f , J f , K f ) levels of the radiating molecule, as well as the levels ( £2 Å 0, J2 , K2 ) of the perturbing molecule. Self-broadening coefficients g 0 at 296 K were computed for the transitions experimentally studied in the n2 parallel-type band for which Kf Å Ki and in the n5 perpendicular-type band for which Kf Å Ki { 1. The molecular parameters used in the computations are given in Table

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CH3F LINESHAPE PARAMETERS

TABLE 2 Linestrengths S0 in the n2 and n5 Bands of CH3F Derived from the Galatry Lineshape

Note. These linestrengths are all normalized at 296 K. The letter L refers to the ‘‘low’’ pressure regime (0.4 to 3 mbar) and H to the ‘‘high’’ pressure regime (6 to 18 mbar).

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TABLE 3 Spectroscopic and Molecular Parameters Used in the Calculations of Self-Broadening Coefficients of CH3F

Note. The spectroscopic parameters used are those given in Table I (column III) of Ref. ( 30). a Ref. (31). b Ref. (32). c This work.

3. These computations have provided broadening coefficients ( Table 1 and Fig. 4 ) that are significantly larger 0 0 than our experimental data. The mean ratio g calc / g obs is 1.09 for the lines with Ji õ 10 and 1.17 for the lines with Ji § 10. The overestimation of the self-broadening coefficients is not surprising, since it is generally observed for strongly polar and / or quadrupolar molecules such as OCS ( 33 ) or CH3Cl ( 24 ) . However, as may be seen in Fig. 4, the calculated and experimental results of g 0 ( J , K ) have the same J or ÉmÉ dependence. As ÉmÉ increases from 4, g 0 increases to a maximum value for ÉmÉ Å 14 0 0 ( g obs Å 0.600 cm01 / atm; g calc Å 0.647 cm01 / atm) , and decreases at higher ÉmÉ. Moreover, our calculations show that, at a given J , g 0 ( J , K ) decreases with increasing K more significantly at low J than at high J for which g 0 is nearly constant. Although we have not measured broadenings for lines belonging to a given branch and subbranch with same J and different K values, this result is in agreement with the g 0 values obtained for the line couples R R ( 19,3 ) and P R ( 19,6 ) , PP ( 14,2 ) and R R ( 14,3 ) , P Q ( 18,2 ) and RQ ( 18,5 ) if we consider that the broadening of the lines with DK Å {1 and / or D J Å {1 is nearly the same. ACKNOWLEDGMENTS One of the authors (B. Lance) gratefully acknowledges the ‘‘Fonds pour la formation a` la Recherche dans l’Industrie et l’Agriculture’’ for its support. Support by the ‘‘Accords Culturels entre le CNRS (France) et la Communaute´ Franc¸aise de Belgique’’ is also gratefully acknowledged.

REFERENCES 1. J.-P. Bouanich, C. Boulet, Gh. Blanquet, J. Walrand and D. Lambot, J. Quant. Spectrosc. Radiat. Transfer 46, 317–324 (1991). 2. A. S. Pine, J. Mol. Spectrosc. 122, 41–55 (1987).

3. A. S. Pine, J. Chem. Phys. 97(2), 773–785 ( 1992). 4. A. S. Pine, J. Chem. Phys. 101(5), 3444–3452 (1994). 5. P. E. Saarinen, J. K. Kauppinen, and J. O. Partanen, Appl. Spectrosc. 49(10), 1438–1453 (1995). 6. F. Rohart, H. Ma¨der, and H. W. Nicolaisen, J. Chem. Phys. 101(8), 6475–6486 (1994). 7. Gh. Blanquet and J. Walrand, Comput. Enhanced Spectrosc. 2, 135– 140 (1984). 8. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, ‘‘Numerical Recipes—The Art of Scientific Computing (FORTRAN Version).’’ Cambridge Univ. Press, Cambridge, 1992. 9. A. K. Hui, B. H. Armstrong, and A. A. Wray, J. Quant. Spectrosc. Radiat. Transfer 19, 509–516 (1978). 10. D. R. Rao and T. Oka, J. Molec. Spectrosc. 122, 16–27 (1987). 11. T. Giesen, R. Schieder, G. Winnewisser, and K. M. T. Yamada, J. Mol. Spectrosc. 153, 406–418 (1992). 12. S. G. Rautian and I. I. Sobel’man, Sov. Phys. Usp. Engl. Transl. 9, 701–716 (1967). 13. L. Galatry, Phys. Rev. 122(4), 1218–1223 (1961). 14. J. Humlicek, J. Quant. Spectrosc. Radiat. Transfer 21, 309–313 (1979). 15. Ph. L. Varghese and R. K. Hanson, Appl. Opt. 23(14), 2376–2385 (1984). 16. Gh. Blanquet, J. Walrand, and J.-P. Bouanich, J. Mol. Spectrosc. 159, 137–143 (1993). 17. D. Guerin, M. Nischan, D. Clark, V. Dunjko, and A. W. Mantz, J. Mol. Spectrosc. 166, 130–136 (1994). 18. Gh. Blanquet, B. Lance, J. Walrand, and J.-P. Bouanich, J. Mol. Spectrosc. 170, 466–477 (1995). 19. A. Goldman, M. Dang-Nhu, and J.-P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 41(1), 17–21 ( 1989). 20. V. Dunjko, M. Nischan, D. Clark, and A. W. Mantz, J. Mol. Spectrosc. 159, 24–32 (1993). 21. J. O. Hirschfelder, Ch. F. Curtiss, and R. B. Bird, ‘‘Molecular Theory of Gases and Liquids.’’ Wiley, New York, 1954. 22. H. M. Pickett, J. Chem. Phys. 73(12), 6090–6094 (1980). 23. D. Papousek, J. Demaison, G. Wlodarczak, P. Pracna, S. Klee, and M. Winnewisser, J. Mol. Spectrosc. 164, 351–367 (1994). 24. Gh. Blanquet, J. Walrand, J. C. Populaire, and J. P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 53, 211–219 (1995).

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CH3F LINESHAPE PARAMETERS 25. C. J. Tsao and B. Curnutte, J. Quant. Spectrosc. Radiat. Transfer 2, 41–91 (1962). 26. D. Robert and J. Bonamy, J. Phys. 40, 923–943 (1979). 27. J. Bonamy, L. Bonamy, and D. Robert, J. Chem. Phys. 67, 4441–4453 (1977). 28. J. P. Bouanich, J. Quant. Spectrosc. Radiat. Transfer 47, 243–250 (1992). 29. J. H. Dymond and E. B. Smith, ‘‘The Virial Coefficients of Pure Gases and Mixtures.’’ Oxford Univ. Press, Oxford, 1980.

30. D. Papousek, Z. Papouskova, J. F. Ogilvie, P. Pracna, S. Civis, and M. Winnewisser, J. Mol. Spectrosc. 153, 145–166 (1992). 31. S. C. Wofsy, J. S. Muenter, and W. Klemperer, J. Chem. Phys. 55, 2014–2019 (1971). 32. C. G. Gray and K. E. Gubbins, ‘‘Theory of Molecular Fluids.’’ Oxford Univ. Press, New York, 1984. 33. J. P. Bouanich, Gh. Blanquet, J. Walrand, and C. P. Courtoy, J. Quant. Spectrosc. Radiat. Transfer 36, 295–306 (1986).

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