CH3CN self-broadening coefficients and their temperature dependences for the Earth and Titan atmospheres

Icarus 250 (2015) 76–82

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CH3CN self-broadening coefficients and their temperature dependences for the Earth and Titan atmospheres A.S. Dudaryonok a,b,c,⇑, N.N. Lavrentieva b,c, J.V. Buldyreva a a

Institute UTINAM, UMR CNRS 6213, University of Franche-Comte, 16 Gray Road, 25030 Besancon cedex, France V.E. Zuev Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences, 1 Akademishian Zuev Square, 634021 Tomsk, Russia c National Research Tomsk State University, 36 Lenina Avenue, 634050 Tomsk, Russia b

a r t i c l e

i n f o

Article history: Received 29 September 2014 Revised 7 November 2014 Accepted 16 November 2014 Available online 27 November 2014 Keywords: Earth Titan, atmosphere

a b s t r a c t Theoretical self-broadening coefficients and associated temperature dependences for methyl cyanide lines in parallel (DK = 0) bands are reported for large ranges of rotational quantum numbers (0 6 J 6 70, K 6 20) requested by spectroscopic databases. The calculations are performed by a semi-empirical method, particularly suitable for active molecules with large dipole moments, which needs only a few experimental data for model parameters fitting. Since the common power law for the temperature-dependence exponents is invalid for wide temperature ranges, two separate sets of temperature exponents are provided for Earth and Titan atmospheres applications. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Acetonitrile (methyl cyanide) CH3CN is the simplest organic nitrile and one of long-living pollutants in the terrestrial atmosphere produced by industrial processes (Singh et al., 2003; Li et al., 2003). It is also a molecule of astrophysical interest detected, for example, in the upper stratosphere of Titan (Lara et al., 1996; Coustenis et al., 2007), in comets (Remijan et al., 2006) and in interstellar medium as well (Remijan et al., 2005). Because of the important role played by this gas in planetary atmospheres and increasing request of high-quality molecular spectroscopic parameters for remote sensing and radiative transfer modeling, CH3CN has been included in the HITRAN (Rothman et al., 2009) and GEISA (Jacquinet-Husson et al., 2011) databases. However, except for some experimental studies of line intensities, broadening and shifting coefficients (Rinsland et al., 2008) (see also references cited therein), the spectroscopic characteristics of this molecule, in particular line-shape parameters, remain very incomplete. HITRAN, for instance, provides information on one absorption band only. The listed self-broadening coefficients refer to the work of (Rinsland et al., 2008) for the measured lines and represent interpolated or average values for the transitions unstudied experimentally. No temperature dependence of acetonitrile self-broadening coefficients is given neither in HITRAN nor in GEISA databases. ⇑ Corresponding author at: V.E. Zuev Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences, 1 Akademishian Zuev Square, 634021 Tomsk, Russia. Fax: +7 3 822492086. E-mail address: [email protected] (A.S. Dudaryonok). http://dx.doi.org/10.1016/j.icarus.2014.11.020 0019-1035/Ó 2014 Elsevier Inc. All rights reserved.

The goal of the present work is to report first extensive theoretical data on CH3CN self-broadening coefficients and their temperature dependences for large intervals of rotational quantum numbers J and K (0 6 J 6 70, K 6 20) requested by spectroscopic databases. Despite quite low atmospheric concentrations of active molecules, the case of self-broadening is of interest because of the big value (3.913 D) of the CH3CN dipole moment (Colmont et al., 2006) and a non negligible expected self-absorption. Since the semi-classical approaches do not work well for the self-broadening of lines of molecules with large dipole moments (very deep isotropic potentials lead to a breakdown of the hypothesis on the small perturbation by molecular interactions), see e.g. CH3CN (Buffa et al., 1992), CH3Cl (Blanquet et al., 1995; Bray et al., 2013), CH3Br (Gomez et al., 2005), we use a semi-empirical (SE) method (Bykov et al., 2004a) which has proved its efficiency for highly polar molecules of atmospheric interest such as H2O (Bykov et al., 2004a), O3 (Buldyreva and Lavrentieva, 2009), CH3Cl (Dudaryonok et al., 2013). Implementation of the SE method requires an adjustment of model parameters on some experimental values, so that a short review of measurements available in the literature and of their quality is of interest. Acetonitrile self-broadening coefficients have been measured in the microwave (Srivastava et al., 1973), far-infrared (Buffa et al., 1981, 1988, 1989; Haekel and Mader, 1989; Buffa et al., 1992; Schwaab et al., 1993; Fabian et al., 1998), mid-infrared (Rinsland et al., 2008) and near-infrared (for one transition only) (O’Leary et al., 2012). Some of these studies (Buffa et al., 1981, 1989, 1992; Haekel and Mader, 1989; Schwaab et al., 1993) provide also theoretical values obtained with the Anderson–Tsao–Curnutte

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(ATC) and Murphy–Boggs theories but highly overestimated (20%) with respect to the measurements. Namely, for rotational lines, a quite extensive experimental study of the J-dependence of acetonitrile halfwidths, for 21 6 J 6 68 and K = 3, 5, 8, was conducted by (Buffa et al., 1992); the authors performed ATC-calculations for the case of K = 0 too. K-dependences of CH3CN self-broadened rotational line-widths were considered by (Buffa et al., 1981; Schwaab et al., 1993; Fabian et al., 1998). Buffa and collaborators used an acoustic detection technique and reported values for J = 4 3 only and K = 0–3. Self-broadening coefficients for J = 43 42, J = 44 43, J = 56 55, J = 68 67 and 0 6 K 6 10 were measured by Schwaab and coworkers using a tunable diode-laser far-infrared spectrometer. A high-precision millimeterwave spectrometer was employed by Fabian et al. to measure the halfwidths of J = 6 5, 5 4 spectral lines for all possible K values. Collisional line-broadening and shifting coefficients for rotational lines J = 1 0, 2 1, 3 2, 4 3 demonstrating a hyperfine structure at pressures less than 10 mTorr were considered both experimentally and theoretically in the works (Buffa et al., 1988, 1989; Haekel and Mader, 1989). The authors claimed that the broadening and shifting coefficients are affected by the hyperfine splitting. The latest measurements of rovibrational methyl cyanide absorption lines, with the goal of future astrophysical observations of CH3CN in the near infrared, were carried out in the region 6000– 8000 cm1 by (O’Leary et al., 2012). More than 4500 absorption lines were identified but the self-broadened halfwidth (3.3(2)  103 cm1 mbar1) was obtained only for one line (at 7034.171 cm1) of the vibrational combination band 2m5 + m7. The most extensive data for vibrotational lines were obtained (Rinsland et al., 2008) with a high-resolution Fourier transform spectrometer. The authors reported experimental room-temperature self-broadening and shifting coefficients for over 700 transitions (J 6 48, K 6 10) in the P- and R-branches of the parallel (DK = 0) m4 band located near 920 cm1. These experimental results have been chosen for our work to fit the SE model parameters. Section 2 of this paper briefly reminds the salient features of the semi-empirical method and gives details of calculations. The next section presents the room-temperature results and their comparison with available experimental values as well as the temperature dependences for the Earth and Titan atmospheres conditions. The final section contains some concluding remarks and perspectives of future works. 2. Semi-empirical method and details of calculations 2.1. Outline of the method To calculate self-broadened halfwidths of CH3CN lines we apply the semi-empirical impact-approximation approach (Bykov et al., 2004a) which incorporates empirical corrections into the semiclassical Robert–Bonamy formalism (Robert and Bonamy, 1979) in order to simplify it to an Anderson-type (Anderson, 1949; Tsao and Curnutte, 1961) form. In the framework of the SE method the halfwidth associated with the radiative transition f i is defined by

cif ¼

nX qðrÞ c r

Z

1

tFðtÞdt 0

Z

1

bReSðbÞdb;

ð1Þ

0

where n and qðrÞ are the density and r-level rotational populations of the perturbing molecules, FðtÞ is the Maxwell–Boltzmann distribution over relative molecular velocities t, and SðbÞ is the interruption function determined by the impact parameter b. Dividing the inner integral over b into two parts (from 0 to the cut-off parameter b0 ðt; r; i; f Þ and from b0 ðt; r; i; f Þ to 1) and neglecting

the third and higher-order terms in the expansion of the scattering matrix, the expression (1) can be rewritten as

cif ¼

Z 1 X nX qðrÞ tFðtÞb20 ðt; r; i; f Þdt þ D2 ðii0 jlÞPl ðxii0 Þ c r 0 i0 l X 2 0 0 D ðff jlÞPl ðxff Þ: þ

ð2Þ

f 0l

In Eq. (2) the second and third terms depend on the transition 0 0 strengths (reduced matrix elements) D2 ðii jlÞ and D2 ðff jlÞ as well 0 0 as on the ‘‘efficiency functions’’ P l ðxii Þ and P l ðxff Þ corresponding to the scattering channels (i.e. non radiative transitions induced by collisions) i i, f f0 in the active molecule for the dipole (l = 1), quadrupole (l = 2), etc. interactions [more details can be found in (Bykov et al., 2004a)]. While the transition strengths are (well established) characteristics of the absorbing molecule only, the weighting coefficients P l ðxii0 Þ and Pl ðxff 0 Þ are defined by the properties of both colliding molecules and by their interaction (which is much less known):

Pl ðxii0 Þ ¼

X nX qðrÞ A0ll D2 ðrr0 jl0 ÞF ll0 ðkii0 rr0 Þ c r 0 0

ð3Þ

l ;r

(for the final state the corresponding expression is obtained by replacing the frequencies xii0 by xff 0 ). Here All0 are the normalization factors for the resonance functions f ll0 ðkii0 rr0 Þ at kii0 rr0 ¼ 0, F ll0 are specific functions dependent on the resonance parameter kii0 rr0 . Since the coefficients Pl are not known precisely, they are considered as products of the analytical efficiency functions P ATC of the ATC theory l and frequency-dependent empirical correction factors C l :

Pl ðxii0 Þ ¼ PATC ðxii0 ÞC l ðxii0 Þ: l

ð4Þ

The correction factor is chosen in a convenient mathematical form (depending on the considered colliding pair) with a set of empirical parameters adjusted on available experimental data. This correction factor accounts for short-range forces, trajectory curvature and higher-order terms in the perturbation expansion of the scattering matrix and represents typically (Bykov et al., 2004a; Dudaryonok et al., 2013) a few-percent correction to P ATC . l 2.2. Choice of the correction factor and determination of the fitting parameters For the self-broadening of strongly polar symmetric tops which presents a characteristic local minimum on line-width J-dependences for some first low K-values (Gomez et al., 2005; Lerot et al., 2005; Bray et al., 2013) the correction factor is well represented (Dudaryonok et al., 2013) by a four-parameter expression

C l ðxii0 Þ ¼

c2

c1 1 pffiffiffi  J i þ 1 c3 ðJ i  c4 Þ2 þ 1

ð5Þ

with the adjustable parameters c1–c4 which are assumed to be the same for both dipole and quadrupole contributions to the efficiency functions. To fit c1–c4 for the CH3CN case, we chose the experimental values of (Rinsland et al., 2008) as the most complete available. Moreover, only R-branch experimental halfwidths were used, aiming to test further the validity of c1–c4 for the P-branch measurements (see Section 2.3). To model the intermolecular potential, besides the leading (more than 97%) dipole–dipole contribution to the line-width, we also took into account the orientation, induction and dispersion interactions. The methyl cyanide molecular parameters and multipole moments required for calculations of energy levels and reduced matrix elements are gathered in Table 1. The model parameters c1–c4 adjusted for rotational quantum numbers K 6 10 and extrapolated, using their obvious trends, for

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Table 1 Spectroscopic constants (in cm1) (Simeckova et al., 2004) and multiple moments (Colmont et al., 2006) for CH3CN in the ground state. Spectroscopic constants A 5.273615 B 0.306842 7 DJ  10 1.270030 6 DJK  10 5.917693 DK  105 9.439863 HJ  1015 8.806091 HJK  1011 3.410359

HKJ  1010 HK  109 LJJJJ  1020 LJJJK  1016 LJJKK  1015 LJKKK  1014

2.02103 4.4030 6.1709 2.3846 1.5811 1.5244

Table 3 Root-mean-square deviations (in cm1 atm1) of calculated values from experimental data (Rinsland et al., 2008; Schwaab et al., 1993). For the sake of testing, P-branch values are obtained with the semi-empirical parameters determined for the R-branch line-widths.

Multipole moments

H, D  Å

1.8

Table 2 SE-model fitting parameters deduced from the experimental values of R-branch CH3CN self-broadening coefficients (Rinsland et al., 2008) for K = 0–10 and extrapolated, on the basis of K = 3–10 trends, for K = 11–20. K

c1

c2

c3

c4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1.80 1.50 1.85 0.370 0.358 0.352 0.346 0.340 0.334 0.328 0.322 0.316 0.310 0.304 0.298 0.292 0.286 0.280 0.274 0.268 0.262

1.07 0.95 1.15 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0025 0.0025 0.0025 0.0006 0.0010 0.0014 0.0018 0.0022 0.0026 0.0030 0.0034 0.0038 0.0042 0.0046 0.0050 0.0054 0.0058 0.0062 0.0066 0.0070 0.0074

30 30 30 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28

11 6 K 6 20 are given in Table 2. Similarly to methyl chloride self-broadening (Dudaryonok et al., 2013), the parameters sets have different behaviors for K 6 2 and K P 3 because of the experimental halfwidth J-dependences that demonstrate, for K 6 2, local minima near small J-values. For K 6 2 only c1 and c2 are K-dependent whereas for higher K it is the case for c1 and c3. The root-mean-square (RMS) deviations for all experimentally accessible K in the R-branch (Rinsland et al., 2008) can be found in the second column of Table 3. For the sake of comparison, in the third column of this table, we show the RMS-values obtained with the use of less complete measurements of (Schwaab et al., 1993) which lead to slightly higher deviations.

2.3. Comparison of pressure broadening for P- and R-branch lines The well-known empirical relation cP(J, K)  cR(J  1, K) enables estimates of halfwidths for R- (or P-) branch lines when the corresponding data for the other branch are available. However, for our purposes of high-precision spectra calculation, we preferred to perform independent computations for both branches. As mentioned above, the parameters c1–c4 were intentionally fitted on R-branch halfwidths only, so that their use for P-branch linewidth calculations furnished an excellent test of validity of the model parameters for other branches. The fourth column of Table 3 shows the RMS-deviations between calculated and measured halfwidths for the P-branch. In general, these deviations are even

a

R-branch (1993)

P-branch (2008)

0.075 0.048 0.033 0.060 0.048 0.044 0.052 0.123a 0.059 0.057 0.125

0.056 0.050 0.061 0.088 0.069 0.082 0.093 0.093 0.127 0.061 0.011

0.040 0.045 0.036 0.045 0.044 0.040 0.058 0.049 0.058 0.076 0.046

This value is reduced to 0.056 when the aberrant datum J = 38 is excluded.

2.0

Self-broadening coefficient, cm-1atm-1

3.913

R-branch (2008)

0 1 2 3 4 5 6 7 8 9 10

K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10

1.5

1.0

K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20

0.5

0.0 0

10

20

30

40

50

60

70

J Fig. 1. Calculated methyl cyanide self-broadening coefficients of R-branch lines at room temperature.

2.0

Self-broadening coefficient, cm-1atm-1

l, D

K

P-branch Expt 2008 Calc. R-branch Expt 1981 Expt 1993 Expt 1998 Expt 2008 Calc. Residuals: Expt 2008 Calc.

1.6

1.2

0.8

K=0

0.4

0.0 0

10

20

30

40

50

60

70

ImI Fig. 2. Measured (Buffa et al., 1981; Schwaab et al., 1993; Fabian et al., 1998; Rinsland et al., 2008) and calculated room-temperature self-broadening coefficients of methyl cyanide P- and R-branch lines for K = 0. The lower part of the figure shows the residuals between P- and R-branch values.

79

2.0

2.0

1.6

1.6

γ, cm-1atm-1

γ, cm-1atm-1

A.S. Dudaryonok et al. / Icarus 250 (2015) 76–82

1.2 0.8 0.4

K=1

0.0

Expt Expt Expt Expt Expt Calc

1.2 0.8 0.4

K=2

0.0 0

10

20

30

40

50

60

0

70

10

20

30

J

γ, cm-1atm-1

γ self, cm-1atm-1

1.2 0.8 0.4

K=3

60

70

40

50

60

70

40

50

60

70

40

50

60

70

40

50

60

70

1.6 1.2 0.8 0.4

K=4

0.0 0

10

20

30

40

50

60

70

0

10

20

30

J

J

2.0

2.0

1.6

γ, cm-1atm-1

γ, cm-1atm-1

50

2.0

1.6

0.0

1.2 0.8 0.4 0

10

1.6 1.2 0.8 0.4

K=5

0.0 20

30

40

50

60

K=6

0.0

70

0

10

20

30

J

J

2.0

2.0

1.6

γ, cm-1atm-1

γ, cm-1atm-1

40

J

2.0

1.2 0.8 0.4 0

10

1.6 1.2 0.8 0.4

K=7

0.0 20

30

40

50

60

K=8

0.0

70

0

10

20

30

J

J

2.0

2.0

1.6

γ, cm-1atm-1

γ, cm-1atm-1

1981 1992 1993 1998 2008

1.2 0.8 0.4

1.6 1.2 0.8 0.4

K=9

0.0

K = 10

0.0 0

10

20

30

40

50

60

70

0

10

20

30

J

J

Fig. 3. Comparison of experimental (Buffa et al., 1981, 1992; Schwaab et al., 1993; Fabian et al., 1998; Rinsland et al., 2008) and calculated room-temperature methyl cyanide self-broadening coefficients for R-branch lines at various K values.

smaller than for the R-branch lines (probably due to smoother experimental J-dependences). For the massive calculations of line broadening coefficients, we considered therefore the model parameters as completely independent from the branch type. 2.4. Temperature dependence of halfwidths All previous works reporting semi-empirical line-broadening coefficients for various molecular systems at various temperatures

(see e.g., Tashkun et al., 2003; Bykov et al., 2008; Dudaryonok et al., 2013) show that the model parameters ci are temperatureindependent. It means that the SE calculations can be carried out for other temperatures around the room-temperature value and the temperature exponents N can be further deduced by a leastsquare-fit from the standard expression



cðTÞ ¼ cðT ref Þ

T T ref

N ð6Þ

A.S. Dudaryonok et al. / Icarus 250 (2015) 76–82

with the reference temperature Tref = 296 K. However, it should be kept in mind that Eq. (6) remains valid only for limited temperature ranges (typically 296 ± 50 K). Consequently, for the Earth and Titan atmospheres characterized by different temperature intervals [200–310 K (Keckhut et al., 2012) and 94–170 K (Fulchignoni et al., 2005), respectively] we calculated halfwidths for seven temperatures forming two separate sets: {250, 280, 310, 340 K} and {90, 130, 170 K}, and extracted two sets of temperature exponents. It is noteworthy that, given the depth of the isotropic interaction potential between two CH3CN molecules [about 180 K, as can be estimated by the common combination rules from the data of (Bouanich and Brodbeck, 1977; Colmont et al., 2006)], the calculations of semi-classical type are in principle not valid for the temperatures of the Titan atmosphere range. Nevertheless, since the quantum–mechanical calculations (that would be appropriate) are not currently feasible for the considered molecular system (too many relaxation channels and no refined potential energy surfaces available) and since the empirical correction factor is expected to compensate at least partially the inappropriateness of the SE method at so low temperatures, we report the ‘‘Titan’s set’’ too. 3. Results and discussion 3.1. Self-broadening coefficients at room temperature Self-broadening coefficients of methyl cyanide R-branch lines in parallel bands calculated for 296 K are shown in Fig. 1 as functions of J for fixed K values (the full set of data including the P-branch is given in Supplementary material). In agreement with the measurements (Rinsland et al., 2008) used for the model parameters fitting and observations made for the self-broadening of other symmetric tops [CH3Br (Gomez et al., 2005), CH3F (Lerot et al., 2005) CH3Cl (Bray et al., 2013)], these J-dependences have a maximum situated near the most populated rotational state (J  20 for small K and higher for higher K); the series of symbols corresponding to K = 0–2 have in addition a local minimum in vicinity of J = 1. The presence of maxima is due to the resonance dipole–dipole interactions [a detailed discussion of this perturber–absorber resonance effect can be found in (Buffa et al., 1992)]. The general decreasing of the broadening coefficient for very high J reflects the growing stability of a top rotating more and more rapidly. In order to look more attentively at the comparative broadening of R- and P-branch lines, we plotted in Fig. 2 the bulk of available experimental values (Buffa et al., 1981; Schwaab et al., 1993; Fabian et al., 1998; Rinsland et al., 2008) and our calculations as functions of the absolute value of the quantum number m (m = J + 1 for the R-branch and m = J for the P-branch), for the ‘‘linear-molecule limit’’ K = 0. The residuals between P- and Rbranch (both experimental and theoretical) values are given at the bottom of the figure. The difference between theoretical Pand R-branch line-widths has its maximum at |m| = 1 (6.1%) and decreases rapidly with increasing J (e.g., 0.4% only for |m| = 10). Similar analyses for other K show that the theoretical residuals also diminish quickly with increasing K: for example, for |m| = 10 but K = 3 the difference reduces to 0.3%. In such a way, from the theoretical point of view, the dependence of CH3CN self-broadening on the type of the branch can be considered as completely negligible, except for small J- and small K-values. To examine the vibrational dependence of CH3CN line-widths, we completed the m4 R-branch measurements [(Rinsland et al., 2008) for K = 0–10] by the data reported for the purely rotational band [(Buffa et al., 1981) for K = 0–4; (Buffa et al., 1992) for K = 3, 5, 8; (Schwaab et al., 1993) for K = 0–10; (Fabian et al., 1998) for K = 0–5] and plotted them in Fig. 3 together with our SE calculations (the case K = 0 is omitted since already considered in

Fig. 2). It is clearly seen from this figure that the experimental values associated with rotational transitions follow the same Jdependences as the measurements in the m4 band; moreover, for very high J these rotational data demonstrate a further smooth and continuous decrease of line broadening. This coherent rotational–vibrotational experimental behavior is very well reproduced by the SE calculations, even for the highest J values not included in the model parameters fitting. As a consequence, it can be concluded that the vibrational dependence is completely negligible for the self-broadening coefficients of CH3CN lines and that the SE results can be safely used for other parallel bands.

3.2. Temperature exponents Two sets of temperature exponents N related to the temperature intervals 250–340 K (Earth) and 90–170 K (Titan) are shown in Fig. 4 for the R-branch case. The values range between 0.75 and 1.1, in a qualitative agreement with the range 0.52 to 1.07 obtained previously for the CH3Cl self-broadening (Dudaryonok et al., 2013). Again similarly to the methyl chloride case, the Kdependence of temperature exponents is practically negligible (the maximal difference for the studied K-values does not exceed 0.05) and their general behavior with increasing J exhibits the same features (a maximum near J 10, a rapid decrease to big negative values and finally a slower increase). The fact of negative temperature exponents deduced with the standard power law of Eq. (6) has been extensively reported and explained in the literature [see e.g., H2O–N2 (Bykov et al., 2004b) H2O–H2O (Wagner et al., 2005), CH3Cl–CH3Cl (Dudaryonok et al., 2013), CH3Cl–air (Buldyreva, 2013), HDO–CO2 (Lavrentieva et al., 2014)] on the basis of the theoretical developments suggested by Hartmann and collaborators (Hartmann et al., 1987). Indeed, for the CH3CN–CH3CN system with the leading dipole–dipole interaction, the negative resonance contribution to N dominates the positive terms coming from the ATC theory for middle J-values (a minimum observed on the temperature-exponent curves). For higher J, the dipole–dipole collisions become non-resonant and the temperature exponent increases again. The limited validity of the simple power law and the strong influence of the temperature interval choice on the extracted N-values are demonstrated by the shift of the temperature-exponent minimum: J  55 for the ‘‘terrestrial’’ set and J  45 for that of Titan. Globally, this shift can be attributed to the fact that for lower temperatures the maximum of rotational

1.2 90-170 K

1.0

K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10

0.8

Temperature exponent

80

0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8

250-340 K K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10

K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20

0

10

K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20

Expt (Mader et al., 1979) Expt (Derozier and Rohart, 1990)

-1.0 20

30

40

50

60

70

J Fig. 4. Calculated methyl cyanide temperature exponents of ‘‘Earth and Titan sets’’ as functions of rotational quantum number J for 0 6 K 6 20 and experimental value of (Mäder et al., 1979; Derozier and Rohart, 1990).

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Table 4 Example of SE-calculated CH3CN self-broadening coefficients c (in cm1 atm1) for K = 0, 5 at the reference temperature of 296 K and corresponding temperature exponents for the Earth’s and Titan’s temperature intervals. The quoted uncertainties correspond to one standar deviation. J

K

c

NEarth

NTitan

J

K

c

NEarth

NTitan

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1.836 1.213 1.165 1.185 1.230 1.287 1.349 1.413 1.477 1.540 1.599 1.655 1.706 1.752 1.793 1.827 1.854 1.874 1.886 1.891 1.888 1.878 1.860 1.834 1.801 1.762 1.716 1.664 1.607 1.547 1.482 1.416 1.347 1.278 1.208 1.139

0.854(9) 0.889(8) 0.943(9) 0.993(9) 1.029(8) 1.057(7) 1.074(6) 1.084(4) 1.087(3) 1.084(1) 1.076(1) 1.063(3) 1.046(5) 1.025(7) 1.001(9) 0.97(1) 0.94(1) 0.91(2) 0.87(2) 0.83(2) 0.79(2) 0.75(3) 0.67(3) 0.65(3) 0.60(3) 0.55(4) 0.50(4) 0.44(4) 0.39(5) 0.33(5) 0.27(5) 0.22(5) 0.16(5) 0.11(6) 0.05(6) 0.01(6)

0.93(2) 0.97(2) 1.02(2) 1.06(2) 1.09(1) 1.104(9) 1.105(4) 1.100(1) 1.085(6) 1.06(1) 1.04(2) 1.00(2) 0.96(3) 0.92(4) 0.87(4) 0.82(5) 0.76(6) 0.70(7) 0.64(7) 0.57(8) 0.51(9) 0.44(9) 0.4(1) 0.3(1) 0.2(1) 0.1(1) 0.1(1) 0.0(1) 0.1(1) 0.1(1) 0.2(1) 0.3(1) 0.3(1) 0.37(9) 0.42(8) 0.46(7)

36 37 38 39 40 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

0 0 0 0 0 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

1.072 1.019 0.968 0.918 0.869 1.000 1.081 1.163 1.243 1.320 1.394 1.463 1.528 1.586 1.638 1.682 1.719 1.749 1.770 1.783 1.787 1.784 1.773 1.755 1.729 1.697 1.659 1.615 1.567 1.515 1.460 1.404 1.348 1.290 1.233 1.177

0.06(6) 0.11(6) 0.17(6) 0.22(6) 0.27(6) 1.039(7) 1.060(6) 1.073(4) 1.079(3) 1.078(1) 1.071(1) 1.060(3) 1.044(5) 1.024(7) 1.00(1) 0.97(1) 0.94(1) 0.91(2) 0.87(2) 0.83(2) 0.79(2) 0.75(3) 0.70(3) 0.65(3) 0.60(3) 0.55(4) 0.50(4) 0.44(4) 0.39(5) 0.33(5) 0.28(5) 0.22(5) 0.16(5) 0.10(6) 0.05(6) 0.01(6)

0.50(6) 0.53(5) 0.57(4) 0.59(3) 0.61(2) 1.084(8) 1.090(3) 1.088(1) 1.076(5) 1.06(1) 1.03(2) 1.00(2) 0.96(3) 0.92(4) 0.87(4) 0.82(5) 0.76(6) 0.70(6) 0.64(7) 0.58(8) 0.51(8) 0.44(9) 0.4(1) 0.3(1) 0.2(1) 0.1(1) 0.1(1) 0.0(1) 0.1(1) 0.1(1) 0.2(1) 0.3(1) 0.3(1) 0.37(9) 0.42(8) 0.47(8)

populations (and, as a consequence, the maximal influence of the resonant collisions) shifts to lower J. Fig. 4 shows also the data reported by other authors (Mäder et al., 1979; Derozier and Rohart, 1990) for some low J and K-values [0.70(6) for J = 0, K = 0; 0.76(3) for J = 1, K = 1; and 0.69(5) for J = 4, K = 3] for 14N and 15N CH3CN isotopologues. These data are lower than our results. Buffa and coworkers (Buffa et al., 1992) have also extracted CH3CN–CH3CN temperature exponent J-dependences, which demonstrate (their Fig. 7) the same positions of minima and maxima as our plots in Fig. 4 but a larger (10%) amplitude of temperature exponent variations. These authors mention however that their temperature dependence ‘‘should be a little less pronounced’’. The full sets of room-temperature self-broadening coefficients and associated temperature exponents for both P- and R-branches of parallel bands and for both considered intervals are provided in Supplementary material. Table 4 gives an example of these data for some first J- and K-values.

4. Conclusions and perspectives Methyl cyanide self-broadening coefficients of P- and R-branch lines in parallel bands have been calculated for wide ranges of rotational quantum numbers and temperature intervals relevant to the Earth and Titan atmospheres. These calculations, performed by the appropriate for CH3CN–CH3CN semi-empirical method, demonstrate an excellent agreement with the bulk of available room-temperature experimental data for rovibrational and pure rotational lines as well as a reasonable agreement with a few

temperature exponent values reported in the literature. They provide, for the first time, extensive sets of line-shape characteristics for both Earth and Titan atmospheres applications. It should be underlined that the temperature exponents for the Titan atmosphere conditions have been obtained outside the domain of validity of semi-classical approaches and these data must be used with care. To test unambiguously their suitability, low-temperature measurements bellow 170 K would be particularly worthy. The model parameters deduced from self-broadening coefficients in parallel bands and the branch-type independence of CH3 CN line broadening enable similar calculations for P-, Q-, R-branch lines in perpendicular (DK = ±1) bands for which no measurements are currently available. This work is in progress and will form the subject of a separate communication. Acknowledgments The work was supported by RAS Program ‘‘Optical Spectroscopy and Frequency Standards’’ and by the LIA SAMIA (Laboratoire International Associé ‘‘Spectroscopie d’Absorption de Molécules d’Intérêt Atmosphérique et planétologique: de l’innovation instrumentale à la modélisation globale et aux bases de données’’). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.icarus.2014.11. 020.

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