Semi-empirical calculations of line-shape parameters and their temperature dependences for the ν6 band of CH3D perturbed by N2

Accepted Manuscript

Semi-empirical calculations of line-shape parameters and their temperature dependences for the ν 6 band of CH3 D perturbed by N2 A.S. Dudaryonok , N.N. Lavrentieva , J. Buldyreva PII: DOI: Reference:

S0022-4073(17)30889-0 10.1016/j.jqsrt.2018.03.006 JQSRT 6021

To appear in:

Journal of Quantitative Spectroscopy & Radiative Transfer

Received date: Revised date: Accepted date:

16 November 2017 8 March 2018 8 March 2018

Please cite this article as: A.S. Dudaryonok , N.N. Lavrentieva , J. Buldyreva , Semi-empirical calculations of line-shape parameters and their temperature dependences for the ν 6 band of CH3 D perturbed by N2 , Journal of Quantitative Spectroscopy & Radiative Transfer (2018), doi: 10.1016/j.jqsrt.2018.03.006

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ACCEPTED MANUSCRIPT 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

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Semi-empirical calculations of line-shape parameters and their temperature dependences for the ν6 band of CH3D perturbed by N2

A.S. Dudaryonoka, N.N. Lavrentievaa, J. Buldyrevab,*

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V.E. Zuev Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences, 1 Akademishian Zuev square, 634021 Tomsk, Russia Institut UTINAM, UMR 6213 CNRS, Université Bourgogne Franche-Comté, 16 Route de Gray, 25030 Besançon cedex, France

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Number of Figures: 10 Number of Tables: 8

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* Corresponding author. Fax: +33 (0)3 81 66 64 75 E-mail address: [email protected]

Keywords:

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Monodeuterated methane; N2-broadening coefficients; N2-induced shifts; J- and K-dependences; Perpendicular band; Temperature dependence; Semi-empirical calculation; Outer planets; Planetary atmosphere

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ACCEPTED MANUSCRIPT Abstract

(J, K)-line broadening and shift coefficients with their temperature-dependence characteristics are computed for the perpendicular (ΔK = ±1) ν6 band of the 12CH3D-N2 system. The computations are based on a semi-empirical approach which consists in the use of analytical Anderson-type expressions multiplied by a few-parameter correction factor to account for various deviations from Anderson’s theory approximations. A mathematically convenient form of the correction factor is chosen on the

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basis of experimental rotational dependencies of line widths, and its parameters are fitted on some experimental line widths at 296 K. To get the unknown CH3D polarizability in the excited vibrational state v6 for line-shift calculations, a parametric vibration-state-dependent expression is suggested, with two parameters adjusted on some room-temperature experimental values of line shifts. Having been validated by comparison with available in the literature experimental values for various sub-branches

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of the band, this approach is used to generate massive data of line-shape parameters for extended ranges of rotational quantum numbers (J up to 70 and K up to 20) typically requested for spectroscopic databases. To obtain the temperature-dependence characteristics of line widths and line shifts, computations are done for various temperatures in the range 200–400 K recommended for HITRAN and least-squares fit procedures are applied. For the case of line widths strong sub-branch dependence

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with increasing K is observed in the R- and P-branches; for the line shifts such dependence is stated for

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the Q-branch.

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ACCEPTED MANUSCRIPT 1. Introduction Monodeuteurated methane CH3D and its parent CH4 play important roles as greenhouse gases in the Earth’s atmosphere and influence radiative transfer in atmospheres of giant planets and their moons [1–9]. Their spectroscopic parameters are therefore necessary for remote sensing and climate modeling of these gaseous environments. In particular, since CH3D is characterized by strong absorption in CH4 transparency windows, isolated-line parameters such as line widths, line shifts and their temperature-dependence characteristics should be precisely known for perturbation by main

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atmospheric gases: N2, O2, H2, He, etc.

The CH3D-N2 system seems to be the most studied one from both experimental and theoretical points of view because of high abundance of atmospheric nitrogen. First measurements of N2broadening coefficients with Voigt-profile (VP) model concerned the parallel (ΔK = 0) ν3 [10] and perpendicular (ΔK = ±1) ν6 [11,12] bands at room temperature. Low-temperature measurements with

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extraction of temperature-dependence exponents were reported for 5 lines in the parallel ν2 band [13], 3 lines in the fundamental ν3 band and 4 lines in the ν6 band [14]. Blanquet and coauthors [15] employed Rautian profile to analyze 33 lines recorded at 296 K in the R- and P-branches of the ν3 band and concluded that this strong-collision model accounting for collisional narrowing leads to larger broadening coefficients than those obtained with VP approach. Later experimental studies of CH3D-N2

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line shapes were based on multi-spectrum analysis (spectra recorded at various pressures) aiming to reduce errors in parameters’ determination: line-broadening and line-shift coefficients were determined

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for 217 lines in the 3ν2 band presenting a particular interest in planetology [16], hundreds of lines in the ν3/ν5/ν6 triad [17–19] and 368 lines in the ν2 band [20]. The need of temperature-dependence

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characteristics of line widths and shifts for atmospheric applications initiated recently a series of measurements and multispectrum analyses of the ν3 (184 transitions), ν5 (205 transitions) and ν6 (about

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400 transitions) bands in the temperature range 79–296 K [21,22]. Theoretical studies of CH3D-N2 line-broadening coefficients were conducted first [23] in the

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framework of semi-classical (SC) Anderson theory, taking account of the dipole and octupole moments of CH3D and the quadrupole moment of N2. Line widths and averaged over K temperature exponents were reported for transitions in the pure rotational band, but the line broadening estimates were lower with respect to measurements [12]. Underestimates by 40 to 60% were obtained for the ν3 band [15] with the same electrostatic potential as in [23] but with a semi-classical treatment improved by an exponential representation of the scattering operator and curved trajectories governed by the isotropic potential. The atom-atom interactions of Lennard-Jones form were used later to complete the electrostatic terms for the ν2 band studies [20]. To this end, the authors considered CH3D as a linear molecule and adjusted the isotropic potential to a m-n Lennard-Jones form. Owing to these improvements, a 6.4% agreement with the measurements was achieved for lines with J below 14 4

ACCEPTED MANUSCRIPT (except for K = J or K = J - 1). An advanced semi-classical approach with exact trajectories and a rigorous treatment of the active molecule as a symmetric top was employed in the recent works [21,22] for broadening coefficients and temperature exponents of the lines in the ν3, ν5 and ν6 bands. Very realistic results for lines with K ≤ 7 were obtained, but for high values of K and J the broadening was clearly overestimated. To get reliable values of line-shape parameters for high values of rotational quantum numbers inaccessible experimentally, an alternative semi-empirical (SE) method [24] was applied very recently to calculate CH3D-N2 line-broadening and line-shift parameters with their temperature dependences

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for hundreds of lines (J ≤ 70, K ≤ 20) in the parallel ν3 band [25]. Together with analytical Andersontype line-width and line-shift expressions, this method uses a few-parameter empirical factor which accounts for deviations from the approximations of the Anderson theory. As soon as the model parameters are determined on some experimental line widths, SE calculations correctly reproduce all available experimental data on widths and shifts of lines in various branches and at various

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temperatures. Being performed for enlarged intervals of J and K, these calculations provide complete line-lists of broadening and shift coefficients with their temperature-dependence characteristics which are necessary for spectroscopic databases and atmospheric/astrophysical applications. In the present paper we complete our previous SE-calculations of line-shape parameters for the parallel ν3 band by similar computations for the perpendicular band ν6. The theoretical background of

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our approach is shortly presented in the following section. The parameterization of the correction

concluding remarks.

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factor for the CH3D-N2 system and SE results are discussed in Sec. 3. The final section contains the

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2. Outline of the semi-empirical approach The origins of the semi-empirical method [24] refer to the semi-classical formalism of Robert

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and Bonamy which line-width and line-shift expressions are factorized to isolate the transition strengths (generally well known for isolated active molecules) and the « efficiency functions » for the

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scattering channels (containing the influence of the interactions potential and, therefore, much more difficult to be evaluated). These efficiency functions are then seen as products of analytical Andersontheory functions and empirical correction factors for various l-th rank multipole moments of the active molecule responsible for long-range interactions. Usually, only one correction factor for the leading electrostatic interaction is needed: l = 1 (dipole) for the water vapor molecule, l = 2 (quadrupole) for the carbon dioxide molecule and so on. The complexity of the correction factor (mathematical form and number of fitting parameters) is determined by the experimentally observed dependence of line widths on the rotational quantum number J and depends on the molecular system under consideration. For instance, for highly polar active molecules like H2O and smoothly decreasing with increasing J line widths, a simple two-parameter correction factor is sufficient [24], whereas for self-perturbed 5

ACCEPTED MANUSCRIPT CH3Cl and CH3CN with line widths demonstrating a local minimum of J-dependences for small Kvalues the mathematical expression is more sophisticated and the number of model parameters equals four [26,27]. Independently from the considered molecular pair, no physical meaning is expected for the required model parameters; solely a convenient mathematical form is searched for. To get these parameters’ values, SE-computed line widths are fitted to some room-temperature experimental line widths (usually, from the R-branch characterized by a larger experimentally accessible range of rotational quantum numbers with respect to the other branches). Once the model parameters are determined, the semi-empirical method ensures reliable reproducing of line widths and shifts for all

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measured J and K and for all branches and sub-branches. In addition, it is characterized by a low CPU cost enabling rapid computations of line-shape parameters for thousands of lines, i.e. creation of linelists for spectroscopic databases.

More precisely, the working expressions for the SE collisional line half-width γif and shift δif (in cm-1) associated with the optical transition i → f in the absorbing molecule are written as [24]

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 if  A(i, f )   D 2 (ii  l ) Pl (ii )   D 2 ( ff  l ) Pl ( ff  ) , l ,i 

(1)

l, f 



 if  B(i, f )   D 2 ii  l Pl ii    D 2 ff  l Pl  ff   , l , i

l, f 

(2)

where the summations of the products D 2 (... l ) Pl (...) of the transition strengths (reduced matrix

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elements) Dii l  , D ff  l  and the efficiency functions Pl (ii ) , Pl ( ff  ) are made over the activemolecule multipole-moment ranks l and possible scattering channels i → i', f → f'. As mentioned

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above, Pl ( ) is viewed as the analytical efficiency function Pl A ) of the Anderson theory multiplied

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by the empirically adjustable factor Cl   :

Pl ω  Pl A ωCl ω .

(3)

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The first term of Eq. (1)

A(i, f ) 

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  J  dvvf (v)b02 (v, J 2 , i, f ) 2

J2

(4)

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comes from the cut-off procedure of the Anderson theory [24] and the first term of Eq. (2)  3I I 2 ( f   i )  nb  2 2 3 B(i, f )  B1  2 (  f   i )     J 2  dvvf ( v)b0 ( v, J 2 , i, f ) c  2( I  I 2 )  J 2 0

(5)

represents the contribution from the isotropic part of the interaction potential responsible for the vibrational dependence of line shifts [28]. These terms depend on the numerical density of bath molecules nb, their rotational populations in the ground vibrational state  J 2 , velocities v of the relative molecular motion described by the Maxwell-Boltzmann distribution f(v) and the cut-off radius b0; c is the speed of light. B(i,f) is additionally determined by the constant B1 = -3π/(8ħv) and the mean 6

ACCEPTED MANUSCRIPT polarizability, dipole moment, and ionization potential of the active and perturbing molecules α, α2, μ, I, I2. To get the temperature-dependence characteristics of CH3D-N2 line-shape parameters, we assumed that the line widths at temperature T obey the standard relation  T  T    Tref    Tref

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N

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with the temperature-dependence exponents N and the reference temperature Tref = 296 K, whereas the line shifts follow the dependence

3. Application to CH3D-N2 and discussion of results 3.1. Interaction potential modeling and molecular constants

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 (T )   (Tref )    (T  Tref ) .

(7)

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In our semi-empirical calculations we assumed that the CH3D-N2 interaction potential includes the electrostatic dipole-quadrupole and octupole-quadrupole interactions as well as the induction, dispersion and short-range terms. The molecular rotational constants were taken as A0 = 5.2502 cm-1, B0 = 3.8800 cm-1 [29] for the ground state and A = 5.28744 cm-1, B = 3.87553 cm-1 [30] for the

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vibrationally excited ν6 state of the active molecule, B0 = 1.989622 cm-1 [31] for the ground state of the linear perturber (no vibrational transitions are induced by collisions). The multipole moments, mean

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polarizabilities and anisotropies for two colliding molecules were those given in Table 2 of Ref. [25]. 3.2. Determination of the SE model parameters

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For the CH3D-N2 system the leading electrostatic interaction is dipole-quadrupole but the CH3D dipole has a very small value (μ = 0.0057 D [32]). In this case, we found [25] that a four-

C1 ( JJ  ) 

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parameter expression

  c3 c1   1  2 1  c2 J  150  4J  c4  

(8)

enables very satisfactory fits of calculated line widths to some chosen experimental data [22] in the Rbranch of the ν3 band at 296 K and reproduces simultaneously the measured room-temperature values in the corresponding P-branch (the Q-branch was not considered because of the insufficient number of experimentally studied transitions). The deduced parameters c1–c4 were found to be K-dependent; for K = 13–20 inaccessible experimentally the model parameters’ values were extrapolated on the basis of K = 0–12 trend (see Table 1 of Ref. [25]). For the band ν6 considered here, we kept the same mathematical form of the correction factor, but performed c1–c4 fits for three branches R, P, Q independently, in order to see if these parameters 7

ACCEPTED MANUSCRIPT are branch-sensitive. Namely, we used some experimental data [21] for the RR, PP and RQ subbranches (these sub-branches were chosen because of the maximum number of data available for various K) and employed the deduced c1–c4 values (Tables 1–3) to get SE estimates for the subbranches PR,

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P and PQ. Uncertainties of parameters c1–c4 were determined from the fits to

experimental data.

c1 1.00(6) 1.00(5) 1.60(4) 1.35(8) 2.20(4)

c2 0.0001(1) 0.0002(1) 0.0020(2) 0.0005(2) -0.004+0.002K (2)

c3 0(1) -20(1) -75(1) -35(2) -90(2)

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K 0 1 2 3 4–20

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Table 1. Semi-empirical fitting parameters deduced from experimental values of room-temperature RR-subbranch CH3D-N2 broadening coefficients [21] for K ≤ 9 and extrapolated, on the basis of experimental trends, for higher K. Uncertainties given in the last line correspond to the experimentally observed 4 ≤ K ≤ 9. c4 0(2) 7(1) 8(1) 9(2) 6+K (2)

Table 2. Semi-empirical fitting parameters deduced from experimental values of room-temperature PP-subbranch CH3D-N2 broadening coefficients [21] for K ≤ 10 and extrapolated, on the basis of experimental trends, for higher K. Uncertainties given in the last line correspond to the experimentally observed 6 ≤ K ≤ 10. c2 0.0001(1) 0.0005(2) 0.001(2) 0.001(3) 0.006(1) 0.008(1) -0.002+0.002K (2)

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c1 1.00(3) 1.15(3) 1.40(4) 1.60(7) 2.30(3) 2.40(1) 2.60(3)

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K 0 1 2 3 4 5 6–20

c3 0(1) -30(1) -60(1) -50(2) -90(1) -90(1) -90(2)

c4 0(1) 5(2) 6(1) 7(2) 8(1) 9(1) 4+K (2)

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Table 3. Semi-empirical fitting parameters deduced from experimental values of room-temperature RQ-subbranch CH3D-N2 broadening coefficients [21] for K ≤ 9 and extrapolated, on the basis of experimental trends, for higher K. Uncertainties given in the last line correspond to the experimentally observed 6 ≤ K ≤ 9.

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K 0 1 2 3 4 5 6–20

c1 1.00(4) 1.15(5) 1.40(4) 2.00(5) 2.80(4) 3.10(4) 3.30(4)

c2 0.0002(2) 0.0005(2) 0.001(2) 0.002(1) 0.007(1) 0.010(1) -0.005+0.003K (2)

c3 0(1) -30(1) -60(1) -50(2) -95(1) -90(1) -90(2)

c4 0(2) 7(2) 8(2) 9(2) 10(1) 11(1) 6+K (2)

While computing line widths for T  296 K in the temperature interval 200–400 K recommended for HITRAN database [33], we introduced, like Ref. [25], a minor temperaturedependence correction for the parameter c1 which enables slightly lower root-mean-square deviations with respect to the low-temperature measurements:

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1.05

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For line shifts at T  296 K we used the same correction coefficient as for the ν3 band [25]:



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c1 (T )  c1 (Tref ) 1  0.009(T  Tref ) .

(10)

The small values of these corrections confirm the generally negligible dependence of SE model parameters on temperature observed previously for various molecular systems with the leading dipolequadrupole, dipole-dipole and quadrupole-quadrupole interactions (see, e.g., [24] for H2O-N2, [27] for

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CH3CN-CH3CN and [34] for C2H2-CO2). It means that the semi-empirical computations for various temperatures are expected to furnish very realistic estimates of temperature exponents and temperature-dependence shift parameters.

3.3. Room-temperature line widths

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Semi-empirical CH3D-N2 line-broadening coefficients computed for 296 K are plotted in comparison with measurements [21] (2015), [35] (2002) and semi-classical calculations [21] in Figs. 1–3 for RR-, PP- and PQ-sub-branches, respectively; for the other sub-brunches the results are very similar and are not shown. As can be seen from these figures, owing to the correction factor the SE approach, contrary to the SC values, ensures very faithful reproducing of experimental J-

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dependences for all values of the quantum number K. This fact guarantees to some extent the

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reliability of SE computations for high J and K given in our line-lists. The general behavior of semi-empirical line widths computed in the full intervals 0  J  70, K  20 is visualized in Fig. 4. It can be noted that, except for the Q-branch case, the semi-empirical

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values demonstrate clear sub-branch dependences with opposite low-J-trends for increasing K.

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Fig. 1. J-dependences of semi-empirical (SE) CH3D-N2 broadening coefficients calculated for the RR-sub-branch lines in the ν6 band at 296 K in comparison with various sets of experimental data (2015 [21], 2002 [35]) and semi-classical (SC) calculations [21] for some given values of K.

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Fig. 2. Same as Fig. 1 but for the PP-sub-branch lines.

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50

70

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

0.07 0.06

65

55

60

65

70

M

0.04

0

70

d

0.08

0.01

5

0.08

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

0.01

0

Broadening coefficient, cm-1atm-1

Broadening coefficient, cm-1atm-1

70

R

b

0.08

Broadening coefficient, cm-1atm-1

65

P

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

CR IP T

0.01

0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00

AN US

Broadening coefficient, cm-1atm-1

0.07

Broadening coefficient, cm-1atm-1

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

0.08

40

45

50

55

60

65

70

CE

PT

Fig. 4. Room-temperature SE-calculated CH3D-N2 broadening coefficients as functions of the rotational quantum number J for various fixed K-values and different sub-branches of the ν6 band (values in the RQ and PQ sub-branches are identical).

3.4. Temperature-dependence of line widths

AC

The extracted SE temperature exponents are compared in Fig. 5 to the experimental data and SC results [21] for the RR-sub-branch and two particular K values, K = 0 and 4, for which a large number of transitions with various J is available. The semi-empirical N values show a very good agreement with measurements. The bulk of temperature exponents computed for the RR-sub-branch is shown in Fig. 6. For the other sub-branches the obtained N-values are identical to those of the RR-sub-branch. It can be noted that in comparison with the temperature exponents in the ν3 band (Fig. 5 of [25]) stronger Kdependence is observed for low J. The main features of N dependence on J can be interpreted with a rough theoretical expression [36] N  0.5  (n  1) 1  N kin  N nres , where the first two contributions (n = 4 for the dipole-quadrupole interactions) provide the resonance term of Anderson theory 13

ACCEPTED MANUSCRIPT A N res  0.83 (which corresponds to the temperature exponents computed for low J). The term N kin is

due to velocity changes resulting from collisions and is negative for weakly interacting molecular systems. The last term N nres comes from the resonance effects and may take negative values (“resonance overtaking”) which are as more pronounced as n is small. This last effect is well known for self-broadened (n = 3) H2O (N < 0) and, in contrast, is very weak for quadrupole-quadrupole (n = 5) interactions [36], as confirmed by our own SE computations for CH3CN-CH3CN [27] and C2H2-CO2 [34]. For the CH3D-N2 system with n = 4 the situation is intermediate: the resonance

values for high J are much lower than 0.83 but remain positive.

0.9

CR IP T

A overtaking is important but not sufficient to balance completely the N res resonant term, so that N-

expt K=0 expt K=4

SC calc. K=0 SC calc. K=4

0.7

AN US

SE calc. K=0 SE calc. K=4

0.6 0.5 0.4 0.3

M

Temperature exponent

0.8

0.2

0

5

10

15

ED

0.1 20

25

30

35

J

40

45

50

55

60

65

70

AC

CE

PT

Fig. 5. Semi-empirical temperature-dependence exponents as functions of the rotational quantum number J in comparison with measurements and calculations of Ref. [21] for RR(J,0), RR(J,4) lines in the ν6 band.

14

ACCEPTED MANUSCRIPT 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

0.90

0.80

0.60 0.50 0.40 0.30

ν6 band 0.20

0.10 0

5

10

15

20

25

30

35

40

45

J

50

55

CR IP T

Temperature exponent

0.70

60

65

70

AN US

Fig. 6. Set of calculated semi-empirical temperature-dependence exponents as functions of the rotational quantum number J for R(J,K) lines in the ν6 band.

3.5. Room-temperature line shifts

According to Eq. (5), line-shift calculations require the mean dipole polarizabilities of the CH3D molecule in the initial and final vibrational states. Whereas the αi value can be found in the

M

literature (see Table 2 of [25]), no such data are currently available, to the best of our knowledge, for

ED

the αf value corresponding to the v6 = 1 state. Consequently, like Ref. [25], we approximated αf by

 f   f 0 (1  a J J f )

(11)

with the adjustable parameters αf 0 denoting the effective polarizability for the final state with Jf = 0

PT

and aJ characterizing the rotational dependence. This formula was used for calculations with low Jvalues (e.g. in the R-branch: for J < 12 at K = 0, for J < 14 at K = 7, for J < 25 at K = 18), for which

CE

experimental data were available for fitting; for higher J the shifts were approximated by slowly decreasing straight lines. Moreover, since the asymptotic high-J behavior of line shifts must be

AC

identical for all sub-branches but the experimentally observed in the R-branch values are essentially bigger that those in the other sub-branches, independent fits were performed to smooth the Jdependences in the middle-J region via specific for each sub-branch parameters’ sets:

C1 ( JJ  ) 

c1 1  c2 J

  c3   1  2      c  4 J  c 4 5  

(12)

(for simplicity, c'1 was fixed to one and c'2 was fixed to zero). The obtained values of c'3–c'5 parameters are collected in Tables 4–7.

15

ACCEPTED MANUSCRIPT Table 4. SE fitting parameters for calculations of room-temperature line shifts in the RR- and PR-sub-branches (deduced from experimental values [21] for K ≤ 8 and extrapolated, on the basis of experimental trends, for higher K). Uncertainties given in the last line correspond to the experimentally observed K = 8. c'3 0 0 0 0 0 0 0 0 0

c'4 -

c'5 -

af0 2.600(2) 2.583(1) 2.592(2) 2.596(2) 2.612(1) 2.615(1) 2.6221(9) 2.622(4) 2.609+0.001K (5)

aJ 0.0010(2) 0.0033(1) 0.0019(1) 0.0015(2) -0.0007(2) -0.0006(2) -0.0010(1) -0.0014(3) -0.0014(4)

CR IP T

K 0 1 2 3 4 5 6 7 8–20

Table 5. SE fitting parameters for calculations of room-temperature line shifts in the RP- and PP-sub-branches (deduced from experimental values [21] for K ≤ 7 and extrapolated, on the basis of experimental trends, for higher K). Uncertainties given in the last line correspond to the experimentally observed K = 7. c'4 60(1) 50(1) 50(1) 20(2) 25(2)

c'5 5(1) 8.5(7) 11(1) 10(1) 8.5+0.5K (7)

af0 2.646(2) 2.624(2) 2.617(1) 2.624(1) 2.608(2) 2.603(2) 2.615(2) 2.618-0.001K (5)

AN US

c'3 0 0 -16(2) 0 -18(1) -18(2) -10(1) 21-K (2)

aJ -0.0040(3) 0.0015(2) 0.0005(1) 0.0014(2) 0.0012(2) 0.0012(2) 0.0000(1) -0.0012+0.0002K (2)

M

K 0 1 2 3 4 5 6 7–20

c'4 6.0(2) 6.5(2) 7.0(4) 7.5(2) 8.0(3) 5.5+0.5K (5)

PT

c'3 0 7(1) 7(2) 7(2) 7(1) 7(2) 7(3)

CE

K 0 1 2 3 4 5 6–20

ED

Table 6. SE fitting parameters for calculations of room-temperature line shifts in the RQ-sub-branch (deduced from experimental values [21] for K ≤ 6 and extrapolated, on the basis of experimental trends, for higher K). Uncertainties given in the last line correspond to the experimentally observed K = 6. c'5 10(1) 10(2) 10(1) 10(1) 10(1) 10(2)

af0 2.624(3) 2.630(2) 2.609(2) 2.606(6) 2.607(4) 2.608(4) 2.608(7)

aJ -0.0025(3) -0.0027(3) 0.0002(1) 0.0004(1) 0.0006(1) 0.0008(1) -0.002+0.0002K (2)

AC

Table 7. SE fitting parameters for calculations of room-temperature line shifts in the PQ-sub-branch (deduced from experimental values [21] for K ≤ 6 and extrapolated, on the basis of experimental trends, for higher K). Uncertainties given in the last line correspond to the experimentally observed K = 6. K 1 2 3 4 5 6–20

c'3 - 30(2) -100(2) - 90(3) - 95(2) - 90(3) - 90(3)

c'4 150(1) 150(1) 150(1) 150(2) 150(1) 150(1)

c'5 7(1) 6(1) 6(1) 9(2) 9.5(1) 4+K (3)

af0 2.624(1) 2.609(2) 2.606(2) 2.607(2) 2.608(2) 2.608(2)

aJ -0.0025(3) 0.0002(1) 0.0004(1) 0.0006(1) 0.0008(1) -0.0002+0.0002K (2)

16

ACCEPTED MANUSCRIPT Comparisons of SE shifts with available experimental data [21, 34] are shown in Fig. 7 for lines with some selected values of K (K = 0, 2, 4, 6, 8, 10) in the RR- and PR-sub-branches. It is clearly seen from this figure that the semi-empirical values reproduce very well the measurements of Ref. [21] deduced from multi-temperature multi-spectrum fits. This agreement allows expecting the validity of our values for the extended ranges of quantum numbers. Measurements in the PR-sub-branch are scarce and characterized by very large dispersions. It is for this reason that we did not perform separate fits of model parameters for this sub-branch and assumed that its SE shifts are identical to those in the R

R-sub-branch. Similar situation occurs for the line shifts in the RP- and PP-sub-branches (the same SE

CR IP T

values are used for both sub-branches). For the Q-branch, where experimental sets of RQ- and PQ-shifts are quite complete, independent fits of SE parameters reproduce well the measured J-dependences for various K (for the sake of brevity, we do not show corresponding figures). The full set of roomtemperature line-shifting coefficients computed semi-empirically up to J = 70 and K ≤ 20 is plotted in

AC

CE

PT

ED

M

AN US

Fig. 8.

17

ACCEPTED MANUSCRIPT

-0.002 -0.004 -0.006 -0.008

K=0

-0.002 -0.004 -0.006 -0.008

K=2

-0.010

-0.010 0

2

4

6

8

10

J

12

14

16

18

0

20

2

4

6

8

10

J

12

14

0.002

Shifting coefficient, cm-1atm-1

0.002 0.000 -0.002 -0.004 -0.006

expt RR 2015 expt RR 2002

-0.008

expt PR 2015 expt PR 2002

K=4

SE calc. RR=PR

-0.010 0

2

4

6

8

10

J

12

14

16

18

-0.002 -0.004 -0.006 -0.008

K=6

-0.010

20

0

expt RR 2015

0.002

0.000

AN US

Shifting coefficient, cm-1atm-1

0.000

CR IP T

Shifting coefficient, cm-1atm-1

0.000

expt RR 2015 expt RR 2002 expt PR 2015 expt PR 2002 SE calc. RR=PR

0.002

Shifting coefficient, cm-1atm-1

expt RR 2015 expt RR 2002 SE calc. RR=PR

0.002

2

4

6

8

10

J

12

14

M

-0.004

-0.008

K=8

-0.010 0

2

4

6

8

10

ED

-0.006

J

12

14

16

18

Shifting coefficient, cm-1atm-1

-0.002

20

expt RR 2015 expt RR 2002 expt PR 2002 SE calc. RR=PR

16

18

20

expt RR 2002 SE calc. RR=PR

0.000

-0.002 -0.004 -0.006 -0.008

K=10

-0.010 20

0

2

4

6

8

10

J

12

14

16

18

20

CE

PT

Fig. 7. Semi-empirical line-shift coefficients as functions of the rotational quantum number J compared to measurements (2015 [21], 2002 [34]) in the RR- and PR-sub-branches of the ν6 band at 296 K.

AC

Shifting coefficient, cm-1atm-1

0.000

18

expt RR 2015

0.002

expt RR 2002

SE calc. RR=PR

16

18

ACCEPTED MANUSCRIPT K=2 K=5 K=8 K=11 K=14 K=17 K=20

-0.002 -0.003 -0.004 -0.005 -0.006

R

P

R, R

-0.007

-0.001

K=1 K=4 K=7 K=10 K=13 K=16 K=19

K=2 K=5 K=8 K=11 K=14 K=17 K=20

-0.002 -0.003 -0.004 -0.005 -0.006

R

P, PP

-0.007 0

5

10

15 20

25 30

a

35

J

40 45

50 55

60 65

70

0

5

10

Shifting coefficient, cm-1atm-1

0.000

-0.001 -0.002 -0.003

-0.005 -0.006

R

Q

-0.007 0

5

10

K=1 K=4 K=7 K=10 K=13 K=16 K=19

15 20

K=2 K=5 K=8 K=11 K=14 K=17 K=20

25 30

c

-0.001 -0.002 -0.003 -0.004 -0.005 P

-0.006

25 30

35

40 45

J

50 55

K=1 K=4 K=7 K=10 K=13 K=16 K=19

60 65

70

K=2 K=5 K=8 K=11 K=14 K=17 K=20

K=3 K=6 K=9 K=12 K=15 K=18

Q

AN US

-0.004 K=0 K=3 K=6 K=9 K=12 K=15 K=18

15 20

b

0.000

Shifting coefficient, cm-1atm-1

K=0 K=3 K=6 K=9 K=12 K=15 K=18

0.000

CR IP T

Shifting coefficient, cm-1atm-1

-0.001

K=1 K=4 K=7 K=10 K=13 K=16 K=19

Shifting coefficient, cm-1atm-1

K=0 K=3 K=6 K=9 K=12 K=15 K=18

0.000

-0.007

35

J

40 45

50 55

60 65

70

0

5

10

15 20

25 30

35

J

d

40 45

50 55

60 65

M

Fig. 8. Room-temperature SE-calculated CH3D-N2 line-shift coefficients as functions of the rotational quantum number J for various fixed K-values and different sub-branches of the ν6 band (values in the RR and PR sub-branches are identical, those in the RP and PP sub-branches are identical too).

ED

3.6. Temperature-dependence line-shift parameters The temperature-dependence parameters for line shifts were deduced on the basis of additional

the

R

R- and

P

PT

semi-empirical calculations for 200 and 400 K. Their comparison with the experimental values [21] for R-sub-branch lines is presented in Fig. 9. The general increasing of measured

CE

temperature-dependence parameters with increasing J is faithfully reproduced by the SE computations. For high experimentally accessible K-values the dispersion of measured data is significant, and large

AC

discrepancies between measurements and calculations are observed for some J. Nevertheless, given the excellent agreement of SE room-temperature shifts with experimental data and the practically negligible dependence of SE model parameters on temperature, we believe our values to be good estimates, even in the extended ranges of quantum numbers. Figure 10 gathers the plots of all SE-

20.

Temper. prameter, cm-1atm-1K-1

computed δ' values as functions of J for K = 0– expt RR 2015

0.00004

K=2

expt PR 2015 SE calc. RR=PR

0.00003

0.00002

0.00001

19 0.00000 0

2

4

6

8

10

J

12

14

16

18

20

70

Temper. parameter, cm-1atm-1K-1

ACCEPTED MANUSCRIPT expt RR 2015

0.00004

K=0

SE calc. RR=PR

0.00003

0.00002

0.00001

0.00000 4

6

8

10

J

12

14

16

18

20

expt RR 2015 expt PR 2015 SE calc. RR=PR

K=4

0.00003

0.00002

0.00001

0.00000

K=6

0.00003

0.00002

0.00001

0.00000 2

4

6

8

10

J

12

14

16

18

20

0

expt PR 2015 SE calc. RR=PR

2

4

AN US

0

6

8

10

J

12

14

16

18

20

expt RR 2015

0.00004

K=8

SE calc. RR=PR

Fig. 9. J-dependences of semi-empirical CH3D-N2 temperature-dependence shift parameters calculated for the R-branch lines in the ν6 band in comparison with measurements [21].

0.00003

M

0.00002

0.00000 2

4

6

8

10

J

12

14

16

18

20

CE

PT

0

ED

0.00001

AC

Temper. parameter, cm-1atm-1K-1

expt RR 2015

0.00004

CR IP T

0.00004

2

Temper. parameter, cm-1atm-1K-1

Temper. parameter, cm-1atm-1K-1

0

20

ACCEPTED MANUSCRIPT

0.00005 P

R, R

0.00004

0.00003

K=0 K=2 K=4 K=6 K=8 K=10 K=12 K=14 K=16 K=18 K=20

0.00002

0.00001

0.00000 0

5

K=1 K=3 K=5 K=7 K=9 K=11 K=13 K=15 K=17 K=19

J

0.00004

0.00003

0.00002 K=0 K=3 K=6 K=9 K=12 K=15 K=18

0.00001

0

Q

0.00004

0.00003

K=0 K=3 K=6 K=9 K=12 K=15 K=18

0.00001

0.00000 0

5

K=1 K=4 K=7 K=10 K=13 K=16 K=19

K=2 K=5 K=8 K=11 K=14 K=17 K=20

10 15 20 25 30 35 40 45 50 55 60 65 70

J

c

5

P

Q

0.00004

0.00003

0.00002

J

K=1 K=4 K=7 K=10 K=13 K=16 K=19

0.00001

0.00000

0

d

K=2 K=5 K=8 K=11 K=14 K=17 K=20

10 15 20 25 30 35 40 45 50 55 60 65 70

AN US

0.00002

Temper. parameter, cm-1atm-1K-1

0.00005 R

K=1 K=4 K=7 K=10 K=13 K=16 K=19

0.00000

b

0.00005

P

P, P

10 15 20 25 30 35 40 45 50 55 60 65 70

a

Temper. parameter, cm-1atm-1K-1

R

CR IP T

R

Temper. parameter, cm-1atm-1K-1

Temper. parameter, cm-1atm-1K-1

0.00005

5

K=2 K=5 K=8 K=11 K=14 K=17 K=20

K=3 K=6 K=9 K=12 K=15 K=18

10 15 20 25 30 35 40 45 50 55 60 65 70

J

AC

CE

PT

ED

M

Fig. 10. Set of calculated semi-empirical temperature-dependence shift parameters as functions of the rotational quantum number J for various fixed K-values and different sub-branches of the ν6 band (values in the RR and PR sub-branches are identical, those in the RP and PP sub-branches are identical too).

21

ACCEPTED MANUSCRIPT The bulk of line-shape parameters calculated in the present work can be found in Supplementary material. Table 8 gives examples of RR-branch values for J  40 and K = 0, 5. Table 8. Example of semi-empirical CH3D-N2 broadening coefficients  and shifting coefficients δ (both in cm-1atm-1) at the reference temperature of 296 K together with associated temperature exponents N (unitless) and temperature-dependence shift parameters δ' (in cm-1atm-1K-1) for RR-sub-branch lines with K = 0 and 5 in the ν6 band. J and K stand for the initial values of the rotational quantum numbers. The quoted uncertainties correspond to one standard deviation. γ

N

δ

CR IP T

K 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 5 5 5 5 5 5 5 5 5 5

0.0544 0.0601 0.0604 0.0582 0.0560 0.0541 0.0528 0.0522 0.0520 0.0516 0.0508 0.0497 0.0483 0.0467 0.0450 0.0432 0.0415 0.0398 0.0381 0.0365 0.0350 0.0336 0.0322 0.0310 0.0298 0.0287 0.0276 0.0267 0.0257 0.0249 0.0241 0.0233 0.0226 0.0219 0.0213 0.0207

0.791(16) 0.790(16) 0.786(18) 0.779(20) 0.765(22) 0.746(26) 0.721(30) 0.690(35) 0.655(39) 0.618(42) 0.577(43) 0.538(45) 0.500(45) 0.464(46) 0.431(45) 0.400(43) 0.373(42) 0.349(41) 0.328(41) 0.310(38) 0.295(37) 0.282(33) 0.271(32) 0.262(29) 0.253(28) 0.246(27) 0.241(24) 0.236(25) 0.232(25) 0.228(23) 0.226(23) 0.223(21) 0.220(19) 0.219(19) 0.215(18) 0.215(20)

AN US

δ' 0.0000110(4) 0.0000105(4) 0.0000108(4) 0.0000110(4) 0.0000118(4) 0.0000131(4) 0.0000144(5) 0.0000153(5) 0.0000160(5) 0.0000166(5) 0.0000169(5) 0.0000173(5) 0.0000176(5) 0.0000177(5) 0.0000177(5) 0.0000178(5) 0.0000179(5) 0.0000180(5) 0.0000181(5) 0.0000182(5) 0.0000183(5) 0.0000184(5) 0.0000185(5) 0.0000186(5) 0.0000187(5) 0.0000188(5) 0.0000189(5) 0.0000190(5) 0.0000191(5) 0.0000192(5) 0.0000193(5) 0.0000194(5) 0.0000195(5) 0.0000196(5) 0.0000197(5) 0.0000198(5) 0.0000199(5) 0.0000200(5) 0.0000201(5) 0.0000202(5) 0.0000203(5)

M

δ -0.00105 -0.00101 -0.00111 -0.00117 -0.00124 -0.00135 -0.00148 -0.00161 -0.00173 -0.00184 -0.00192 -0.00198 -0.00202 -0.00203 -0.00204 -0.00205 -0.00206 -0.00207 -0.00208 -0.00209 -0.00210 -0.00211 -0.00212 -0.00213 -0.00214 -0.00215 -0.00216 -0.00217 -0.00218 -0.00219 -0.00220 -0.00221 -0.00222 -0.00223 -0.00224 -0.00225 -0.00226 -0.00227 -0.00228 -0.00229 -0.00230

ED

N 0.874(17) 0.863(18) 0.846(20) 0.832(19) 0.823(18) 0.820(16) 0.819(16) 0.816(17) 0.808(20) 0.792(22) 0.770(27) 0.741(32) 0.708(36) 0.670(40) 0.629(43) 0.588(46) 0.546(47) 0.506(48) 0.468(47) 0.433(47) 0.400(46) 0.370(44) 0.344(42) 0.320(39) 0.300(36) 0.284(35) 0.269(33) 0.255(31) 0.245(28) 0.235(26) 0.228(24) 0.221(23) 0.215(22) 0.210(22) 0.207(21) 0.204(19) 0.201(19) 0.197(20) 0.195(17) 0.193(15) 0.191(14)

PT

γ 0.0656 0.0672 0.0676 0.0677 0.0672 0.0664 0.0655 0.0645 0.0634 0.0624 0.0615 0.0606 0.0594 0.0580 0.0564 0.0547 0.0530 0.0511 0.0493 0.0475 0.0456 0.0439 0.0422 0.0405 0.0390 0.0375 0.0361 0.0348 0.0336 0.0324 0.0313 0.0303 0.0293 0.0284 0.0275 0.0267 0.0260 0.0253 0.0246 0.0239 0.0233

CE

K 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 0 0 0 0

AC

J 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 36 37 38 39 40

-0.00125 -0.00153 -0.00162 -0.00172 -0.00179 -0.00186 -0.00186 -0.00194 -0.00210 -0.00234 -0.00257 -0.00281 -0.00300 -0.00310 -0.00316 -0.00321 -0.00325 -0.00329 -0.00332 -0.00335 -0.00337 -0.00339 -0.00340 -0.00341 -0.00342 -0.00343 -0.00344 -0.00345 -0.00346 -0.00347 -0.00348 -0.00349 -0.00350 -0.00351 -0.00352 -0.00353

δ'

0.0000187(6) 0.0000177(6) 0.0000173(6) 0.0000176(6) 0.0000177(6) 0.0000178(5) 0.0000173(5) 0.0000178(5) 0.0000191(6) 0.0000211(6) 0.0000230(7) 0.0000251(8) 0.0000267(8) 0.0000274(8) 0.0000277(8) 0.0000280(8) 0.0000281(8) 0.0000282(8) 0.0000281(8) 0.0000282(8) 0.0000281(8) 0.0000281(8) 0.0000282(8) 0.0000283(8) 0.0000284(8) 0.0000285(8) 0.0000286(8) 0.0000287(8) 0.0000288(8) 0.0000289(8) 0.0000290(8) 0.0000291(8) 0.0000292(8) 0.0000293(8) 0.0000294(8) 0.0000295(8)

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ACCEPTED MANUSCRIPT 4. Conclusions In the present work we continued our semi-classical computations of line-shape parameters for the CH3D-N2 molecular system involved in modeling of N2-rich planetary atmospheres containing methane traces. These computations, performed for the perpendicular band ν6, encountered more difficulties than in the previously considered ν3-band case. Besides the quite complex form of the correction factor needed for CH3D-N2, to get coherent with measurements values of line shifts and, simultaneously, physically correct asymptotic behavior in various sub-branches, we were obliged to re-

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adjust our sets of SE-model parameters for middle-J regions for each sub-branch. Significant subbranch dependences were stated for line widths in the R- and P-branches, contrary to the case of line shifts which showed this strong dependence in the Q-branch.

Line-broadening and line-shift coefficients together with their associated temperaturedependence characteristics were obtained for the temperature interval 200–400 K recommended for

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HITRAN and for a large amount of rovibrational transitions 0  J  70, 0  K  20 requested by spectroscopic databases. These new data complete the previously obtained results for the ν3 fundamental and enable accurate theoretical modeling of collisional line-broadening for both (parallel and perpendicular) kinds of CH3D-N2 absorption bands. Since the line shifts are essentially banddependent, our shifting coefficients and their temperature-dependence parameters remain valid solely

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for the considered ν6 (previously – ν3) band.

The capacity of the semi-empirical approach to reproduce available measurements of line-

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shape parameters and to extrapolate their values to higher J and K inaccessible experimentally can be also exploited to get line-shape characteristics for similar molecular systems, e.g. CH3D-H2 which is of

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study in future.

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great interest for astrophysicists and planetary scientists. Such calculations can be the subject of a new

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Acknowledgements

This work was 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”) and by the Russian Foundation of Fundamental Research (grant n° 17-52-16022 НЦНИЛ_а).

Appendix: Supplementary material Supplementary data associated with this article can be found in the online version at http://...

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