Semi-empirical calculations of line-shape parameters and their temperature dependences for parallel bands of monodeuterated methane perturbed by nitrogen

https://doi.org/10.1016/j.jqsrt.2017.02.014Get rights and content

Highlights

  • Calculations of CH3D-N2 line widths and shifts for large ranges of quantum numbers.

  • Theoretical evaluation of temperature-dependence parameters for widths and shifts.

  • Theoretical line-lists for collisional widths, shifts and their temperature dependences.

Abstract

Theoretical nitrogen-pressure broadening and shift coefficients as well as their temperature-dependence characteristics for 12CH3D (J, K) lines in the parallel (ΔK=0) ν3 band are calculated by a semi-empirical approach based on analytical Anderson-type expressions corrected to account for the real curved trajectories. The parameters of the correction factor are adjusted on some recent experimental data for room-temperature line-broadening coefficients, and the unknown CH3D polarizability in the excited vibrational state is determined from a few measurements of room-temperature line-shifts. After validation by comparison with a set of measured values from the literature, this approach is employed for massive calculations of line-shape parameters for enlarged ranges of rotational quantum numbers (0 ≤ J ≤ 70, 0 ≤ K ≤ 20) requested by atmospheric/astrophysical applications and spectroscopic databases. The temperature-dependence characteristics are obtained for the range 200–400 K recommended for HITRAN. Given the negligible vibrational dependence of CH3D line-widths, our calculated broadening coefficients and their temperature-dependence exponents can be also used for other CH3D-N2 parallel bands.

Introduction

The important role of monodeuterated methane CH3D along with the parent methane molecule CH4 is widely recognized for physical and chemical processes occurring in the terrestrial atmosphere. Namely, they are known as greenhouse gases released by natural (wetlands, ocean) and anthropogenic (fossil fuel extraction) sources. They are also present in atmospheres of giant planets and their moons, in particular, those of Saturn, Jupiter [1], [2], [3], Uranus [4], [5], [6] and Titan [7], [8], [9] as well as in comets [10], [11].

Despite a low abundance of about 5×10−4, CH3D occupies a privileged place with respect to other CH4 isotopologues because of the possibility of D/H ratio determination which gives access to the past and present thermodynamic and kinetic processes, chemical reactions and evolution of planetary atmospheres, i.e. enables the development and validation of models for the origin and evolution of the Solar system. The D/H measurements from relative CH3D/CH4 line intensities are feasible owing to the fact that the isotopic substitution H→D changes significantly the stretching frequency ν2, so that the second overtone 3ν2 shifts to the 1.58 μm transparency window where CH4 absorption is extremely weak [12]. In such a way, the 3ν2 CH3D band has been used for determination of D/H ratios for Uranus [13], Neptune [14] and Titan [8], [15]. As CH3D strongly absorbs in CH4 transparency windows, reliable modeling (radiative transfer, climate changes, etc.) of CH4 reach atmospheres requires moreover a precise knowledge of its other line-shape parameters such as pressure-broadening and -shift coefficients as well as their temperature dependences for main atmospheric perturbers N2, O2, H2, He, etc.

The case of perturbation by nitrogen appears as the most important for remote sensing of planetary atmospheres, so that it benefited from a considerable attention of experimentalists and theoreticians. From the viewpoint of pressure-broadening and -shift parameters, the data were generally published for room temperature, only few works reported low-temperature measurements and calculations allowing evaluation of temperature dependences. So, N2-broadening coefficients at 296 K were retrieved with Voigt-profile (VP) model by Devi et al. [16] for seventeen 12CH3D lines in the P-, Q- and R-branches of the parallel (ΔK= 0) ν3 band (near 7.6 μm); similar measurements were performed by the same authors [17] for 24 RP and PP lines in the perpendicular (ΔK=±1) ν6 band (at 8.6 μm). The ν6 fundamental was also investigated at 296 K by Lacome et al. [18] who retrieved VP collisional widths for ten PP and RP lines. One of early experimental works by Chudamani and Varanasi [19] on the parallel ν2 band region (around 4.7 μm) provided CH3D-N2 broadening coefficients extracted with VP model for five P-branch lines P(5,2), P(5,3), P(7,2), P(7,3), P(8,3) at 94, 100, 146, 150, 197, 200, 248, 300 K and the deduced temperature-dependence exponents. Three lines P(4,2,E), P(5,3,A), P(7,3,A) in the fundamental ν3 band for 131, 228, 295 K and four lines PP(6,1,E), RP(5,0,A+), PP(5,1,E), PP(4,2,E) in the ν6 band for 123, 188, 295 K to get VP-broadening coefficients and their temperature exponents were analyzed later by the same authors [20]. Line-shape models going beyond the traditional Voigt profile were employed by Blanquet and collaborators [21] who analyzed 33 lines recorded at 296 K in the R- and P-branches of the ν3 band with Rautian profile and showed that this strong-collision model accounting for collisional narrowing yields naturally significantly larger broadening coefficients.

Further CH3D-N2 line-shape studies privileged simultaneous analysis of spectra recorded at various pressures in order to reduce errors in parameters’ determination. For instance, a very detailed room-temperature (294 K) study of N2-pressure-broadening and -shift coefficients with a multispectrum fitting technique [22] was done for 217 lines in the P-, Q- and R-branches (0 ≤ K ≤ 6 and J ≤ 14, J ≤ 13 and J ≤ 12, respectively) in the 3ν2 band presenting a particular interest in planetology. The authors also demonstrated the negligible vibrational dependence of CH3D-N2 broadening coefficients in the A1-type bands from comparison of ν2, ν3, ν6 and 3ν2 P-line data. Devi et al. [23], [24], [25] extended multispectrum line-shape analysis to the ν356 triad bands with a report on broadening, shifting and line-mixing coefficients at 296 K for hundreds of lines. For the ν2 band at the same temperature, measurements of N2-broadening and N2-shift coefficients extracted by a multispectrum approach for 368 lines were published by Predoi-Cross and coauthors [26]. The need of spectroscopic databases such as HITRAN [27] and GEISA [28] for temperature-dependence characteristics of both CH3D-N2 line-broadening and shifting initiated very recently a series of measurements and multispectrum analyses of the bands from the ν356 triad in the temperature range 79–296 K [29], [30]. The reference-temperature (296 K) line-broadening and line-shift coefficients as well as the corresponding temperature exponents and temperature-dependence shift parameters were deduced for 184 transitions (0 ≤ J ≤ 22, K ≤ 14) in the ν3 band, 205 transitions (0 ≤ J ≤ 17, K ≤ 11) in the ν5 band [30] and about 400 transitions (0 ≤ J ≤ 19, K ≤ 16) in the ν6 band [29].

From the theoretical point of view, N2-broadening of CH3D lines have been evaluated first [31] with the use of the Anderson-Tsao-Curnutte theory, accounting for the dipole and octupole moments of CH3D and the quadrupole moment of N2. The authors reported the room-temperature (300 K) line-widths for the transitions K=0–10, J=0–20 in the pure rotational band and the (averaged over K) temperature exponents up to J=25 for the range 100–300 K. Their estimates of line broadening were about 13% lower with respect to later measurements by Lacome et al. [18]. Much lower results (by 40 to 60%) were obtained for the ν3 band [21] with the same electrostatic potential as in [31] but with an improved semi-classical treatment based on an exponential representation of the scattering operator and including the influence of the isotropic potential in the trajectory model. Since adding induction and dispersion forces did not furnish satisfactory results [21], the atom-atom interactions of Lennard-Jones form were used later to complete the electrostatic terms for the ν2 band studies [26]; to account for these short-range terms, the authors approximated CH3D by a “linear” molecule “3HCD” with three H atoms projected on the molecular symmetry axis. Moreover, the isotropic potential was adjusted on a m-n Lennard-Jones potential form. All these improvements allowed the authors getting a 6.4% agreement with their measurements for J below 14 (except for K=J or K=J−1). A semi-classical approach based on the exponential form of the scattering operator, a rigorous treatment of the active molecule as a symmetric top, an intermolecular potential comprising both long- and short- range interaction and exact classical trajectories was used in the recent woks [29], [30] to evaluate theoretically the line-broadening coefficients and the temperature exponents in the ν3, ν5 and ν6 bands. While comparing very favorably with measurements at K ≤ 7, this approach seemed to overestimate the broadening for high values of K and J.

As the theoretical estimates are of crucial importance for lines with high values of rotational quantum numbers which are inaccessible experimentally, in the present paper we apply an alternative semi-empirical (SE) method [32] for calculating CH3D-N2 line-broadening and line-shift parameters with their temperature dependences. This method employs analytical Anderson-type line-width and line-shift expressions corrected by a few-parameter empirical factor to account for the real trajectory curvature, vibrational effects, and corrections to the scattering matrix. Once the model parameters are determined on some experimental line-widths, extensive and reliable computations can be performed for wide ranges of J and K requested by spectroscopic databases and atmospheric/astrophysical applications. The next section describes briefly the theoretical background of our approach and provides some details of correction-factor parameterization for the particular CH3D-N2 case. Presentation of our results and their comparison with available in the literature experimental and theoretical data are given in Section 3. The final section summarizes concluding remarks and perspectives.

Section snippets

Theoretical background and details of calculations for CH3D-N2

The semi-empirical method [32] employed in the present work was initially proposed for molecular systems with quite strong electrostatic interactions (H2O-N2, CO2-N2, etc.), to which the Anderson theory is applicable and the empirical correcting factor does introduce a small correction. However, further studies showed that this method works sufficiently well even for slightly polar (O3-N2, O3-O2 [33], [34]) and non polar (C2H2-CO2 [35]) active molecules. We decided therefore to test the

Room-temperature line-widths

Semi-empirical CH3D-N2 R-branch line-broadening coefficients computed for the reference temperature of 296 K are compared to the measurements and semi-classical (SC) calculations of Ref. [30] in Fig. 1. It can be seen that contrary to the SC results which furnish very realistic J-dependences solely for K up to 7 (see Refs. [29], [30] for more details), the SE predictions remain perfectly coherent with measurements even for the highest experimentally accessible value K=12. Fig. 2 enlarges this

Conclusions and perspectives

In the present work we have tested the semi-empirical approach developed for polar molecules and molecules with quite strong electrostatic interactions for the case of monodeuterated methane colliding with nitrogen. This colliding pair is of great importance for remote sensing of N2-rich planetary atmospheres containing methane and its isotopologues. Because of the very small CH3D dipole moment and significant contributions from the short-range forces to line-broadening and line-shifting,

Acknowledgements

This work has been supported by the LIA SAMIA (Laboratoire International Associé “Spectroscopie d’Absorption de Molécules d’Intérêt Atmosphérique et planétologique: de l’innovation instrumentale à la modélisation globales et aux bases de données”). NNL thanks the Region of Franche-Comte for a financial support of her stay in Besancon as Invited Researcher.

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