Meriem Mouelhi

Arnaud Cuisset
email: arnaud.cuisset@univ-littoral.fr

C Jellali

S Galalou

H Aroui

Robin Bocquet

Gaël Mouret

F Rohart

Francis Hindle

Self and N2 broadening coefficients of H2S probed by submillimeter spectroscopy: Comparison with IR measurements and semi-classical calculations

Keywords: Broadening coefficient, H2S, submillimeter-wave spectroscopy, speed-dependence effects, semiclassical calculation, rotational dependencies

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

With its characteristic foul odor of rotten eggs, hydrogen sulfide (H2S) is a colorless, highly toxic, corrosive, and flammable gas, soluble in various liquids including water and alcohol. Most of the atmospheric H2S has natural origins. It is often produced from the microbial breakdown of organic matter in the absence of oxygen gas via anaerobic digestion. Therefore, H2S is a good marker of the food spoilage especially fish [START_REF] Hindle | Monitoring of food spoilage by high resolution THz analysis[END_REF]. Moreover, H2S is one of the main trace gases released from volcanoes and the emission ratio H2S:SO2 is an important geochemical probe. Some satellite instruments such as the Infrared Atmospheric Sounding Interferometer (IASI)/MetOp have observed large H2S plumes during explosive volcanic events [START_REF] Lieven | Infrared satellite observations of hydrogen sulfide in the volcanic plume of the August 2008 Kasatochi eruption[END_REF]. H2S is detected not only in the Earth's atmosphere but also in the atmospheres of Jupiter [START_REF] Zahnle | Atmospheric Sulfur Photochemistry on Hot Jupiters[END_REF] and of the ice giants Neptune and Uranus with the Gemini-North/NIFS H-band observations [START_REF] Irwin | Probable detection of hydrogen sulphide (H2S) in Neptune's atmosphere[END_REF]. Finally, due to its high toxicity and its very weak value of the low permissible concentration level which is equal to 0.008 mg/m 3 , the monitoring of anthropogenic H2S in industrial and urban atmospheres is very challenging. Continuous sensing has been performed by Raman lidar [START_REF] Privalov | Hydrogen Sulfide Molecules Lidar Sensing in the Atmosphere[END_REF].

Contrary to SO2, IR measurements of H2S are sparse and difficult [START_REF] Lieven | Infrared satellite observations of hydrogen sulfide in the volcanic plume of the August 2008 Kasatochi eruption[END_REF] and an accurate monitoring of atmospheric H2S at trace levels requires to fit the H2S atmospheric spectra with the best set of spectroscopic parameters and the most appropriate line profiles.

From a spectroscopic point of view, H2S is similar to H2O and represents a very light asymmetric top with a Ray parameter equal to 0.5234 [START_REF] Belov | Terahertz rotational spectrum of H2S[END_REF]. Due to its large asymmetry, the rotational spectrum of H2S shows no coherent line pattern. At room temperature, intense rotational lines are spread out over the complete submillimetre (smm)-wave regions. Numerous investigations have been performed on the pure rotational spectrum of H2S; most of them deal with line frequency analyses from the micro-wave (mw) [START_REF] Helminger | Pressure broadening of hydrogen sulfide[END_REF] to the far-IR regions [START_REF] Flaud | The far-infrared spectrum of hydrogen sulfide. The (000) rotational constants of H2 32 S, H2 33 S and H2 34 S[END_REF]. Ground state (GS) smm rotational line profile analyses and broadening parameter measurements are almost non-existent except the study of Helminger and De Lucia who determine the selfbroadening parameters for only four rotational transitions of H2S [START_REF] Helminger | Pressure broadening of hydrogen sulfide[END_REF]. The temperature dependences of these parameters were studied by Ball et al. in 1999 [9]. However, the ability of frequency-modulated rotational spectroscopy to perform quantitative analysis of gas phase molecular constituents has been demonstrated [START_REF] Minghe | Quantitative analysis of gas phase molecular constituents using frequency-modulated rotational spectroscopy[END_REF] and a systematic study of the broadening parameters and their rotational dependences is now possible even for asymmetric top molecules [START_REF] Tasinato | A complete listing of sulfur dioxide selfbroadening coefficients for atmospheric applications by coupling infrared and microwave spectroscopy to semiclassical calculations[END_REF]. Most of the broadening parameters of H2S have been measured in the IR region from rovibrational transitions belonging to fundamental and combination vibrational bands. Tan et al. [START_REF] Tan | The broadening coefficients of H2S[END_REF] have collected for HITRAN-2016 all the experimental self and air-broadening parameters of H2S provided from different experimental IR studies [START_REF] Waschull | Self-, Air, and Helium Broadening in the ν2 Band of H2S[END_REF][START_REF] Sumpf | Self-and Air-Broadening in the ν1 and ν3 bands of H2S[END_REF][START_REF] Kissel | Molecular-Gas-Pressure-Induced Line-Shift and Line-Broadening in the ν2-Band of H2S[END_REF][START_REF] Ciaffoni | Line strength and collisional broadening studies of hydrogen sulphide in the 1.58 μm region using diode laser spectroscopy[END_REF][START_REF] Sumpf | Experimental Investigation of the Self-Broadening Coefficients in the ν1+ ν3 band of SO2 and the 2ν2 band of H2S[END_REF]. A large variability of the IR data is observed and the vibrational dependence of the broadening parameters was neglected. Linear functions were used to describe the rotational dependences with a trend of the H2S self-and airbroadening parameters to decrease with J''+0.2Ka '' . For all these studies, Voigt line-shapes have been used to fit the measured line profiles. Yet a recent extended analysis of the high resolution FTIR spectra of H2S in the region of the ν2 bending fundamental band demonstrates that the lineshape fit could be significantly improved using the Hartman-Tran profile [START_REF] Tran | Efficient computation of some speed-dependent isolated line profiles[END_REF] with extra parameters taking into account the speed dependence of the relaxation. The half-widths analysis was made on the basis of the multi-spectrum fit procedure and the self-broadening coefficients were estimated for a few tens of lines for the three most abundant isotopologues [START_REF] Scherbakov | Extended analysis of the high resolution FTIR spectra of H2MS (M = 32, 33, 34, 36) in the region of the bending fundamental band: the ν2 and 2ν2ν2 bands: line positions, strengths, and pressure broadening widths[END_REF].

In this study, we report the first measurements of self-and N2-broadening coefficients of H2S rotational lines for various values of the rotational quantum numbers J'' and Ka '' in a large frequency range mainly in the Q branch with a frequency-multiplication chain. Owing to the high signal-to-noise ratio (SNR) achieved using the frequency modulation technics, speeddependence effects were systematically included in the fitting procedure of the observed lines.

In addition, semi-classical calculations using the Robert-Bonamy (RB) formalism have been performed to predict the broadening parameters. The experimental smm broadening parameters are compared to previous IR measurements and to the semi-classical calculations. A new insight of the rotational dependence of the self-and N2-broadening is finally provided.

Experimental details and fitting methods

Experimental setup and experimental conditions

Self and N2-broadened H2S lines were recorded in the 160-850 GHz range using a frequency modulated smm-wave spectrometer. This spectrometer is composed by a frequency synthesizer operating in the range of 7-12 GHz and frequency referenced to a GPS timing signal. The microwave synthesizer is used to drive a frequency multiplication chain (Virginia diodes) covering 70 to 900 GHz as described previously [START_REF] Mouret | Versatile Sub-THz Spectrometer for Trace Gas Analysis[END_REF]. A frequency modulation (FM) was applied to the synthesizer. The FM was fixed at 13 kHz with a modulation depth m selected for each line in the range (0.3-4.5 MHz) according to the expected linewidth, see Fig. 1. Observed lineshapes were recorded using an InSb liquid He-cooled bolometer from QMC instrument up to 330 GHz and a zero bias Schottky detector at higher frequencies. Corresponding signals were demodulated thanks to a lock-in amplifier operating at a twice the modulation frequency. The data acquisition and operation of the smm spectrometer was computer controlled using a dedicated program. The gases H2S and N2 were introduced into an absorption cell with Teflon windows presenting a clear diameter of 56 mm. Cell lengths, 28 cm and 113 cm, were employed depending on the observed line strengths. The spectrometer is located in a temperature controlled (295±1 K) room. The H2S and N2 gases were purchased from Sigma Aldrich and Praxair respectively with claimed purities better than 99.5%. The gas pressures were measured with a vacuum gauge (Pfeiffer company, model CMR364) operating from 10 -3 to 1.1 mbar with a reading accuracy of 0.2%.

For self-broadening measurement, H2S pressures were chosen between 0.09 and 0.8 mbar. In the example spectrum shown in Fig. 1, the targeted frequency was swept using 50 kHz frequency steps of 300 ms duration, with a 100 ms time constant of the lock-in amplifier. Such conditions ensure negligible consequences of a limited detection bandwidth on observed lineshapes [START_REF] Rohart | Absorption line shape recovery beyond the detection bandwidth limit: application to the precision spectroscopic measurement of the Boltzmann constant[END_REF][START_REF] Rohart | Overcoming the detection bandwidth limit in precision spectroscopy: The analytical apparatus function for a stepped frequency scan[END_REF].

To measure the N2-broadening coefficients, the rotational lines were recorded using the following procedure: the cell was first filled with pure H2S at a fixed pressure about 0.1 mbar then about 6-8 lineshapes were recorded with increased N2 pressures up to about 0.8 mbar.

. Frequency-modulation submillimeter spectra

In case of a frequency modulated spectrometer with a lock-in detection operating at twice the modulation frequency νm, the line profile F(ν) has a W-shape which is given by the real part of the Fourier transform of [START_REF] Dore | Using Fast Fourier Transform to compute the line shape of frequency-modulated spectral profiles[END_REF]:

( ) ( ) ( ) [ ] ( ) ( )       - ℜ = ∫ ∞ t t i t t t m J t F m m d . 2 exp . 2 cos . sinc . 2 . 2 0 2 ν π ν π ν π π Φ ν (1)
where ν is the electromagnetic field frequency, 2 (x )

J
is the 2 nd order Bessel function, m is the modulation depth and Φ(t) is the molecular polarization correlation function, that is the gas pulse response which is null for t<0.

Let us first consider the usual Voigt profil FV(ν) which considers molecular displacements and molecular collisions as uncorrelated processes. It is simply given by the convolution of a Gaussian profile, related to the Doppler effect, and of a Lorentzian profile, related to collisional relaxation. So, its correlation function ΦV(t) is given by [START_REF] Dore | Using Fast Fourier Transform to compute the line shape of frequency-modulated spectral profiles[END_REF]:

( )                   - - = 2 0 , 0 0 2 2 2 exp t v k t t i t a V V Γ π ν π Φ (2)
where ν0 is the absorber line center frequency, Γ0,V is the collisional broadening, k=2πν0/c is the wavenumber with c the speed of light, and

B a0 a 2k T v m =
is the most probable value of the absorber speed defined by the Boltzmann constant kB, the temperature T and molecular mass ma of the absorber.

Due to the large intensities of H2S rotational lines, the Beer-Lambert law had to be considered.

This was done in the following way [START_REF] Buldyreva | Speed dependence of CH3 35 Cl-O2 line-broadening parameters probed on rotational transitions: Measurements and semi-classical calculations[END_REF][START_REF] Dudaryonok | Experimental studies, line-shape analysis and semi-empirical calculation of broadening coefficients for CH3 35 Cl-CO2 submillimeter transitions[END_REF]. The transmission of the gas T(ν) is given by:

= - ( 3
)
where S is the line intensity, Pa is the absorbing gas partial pressure, and l the cell length. So, the pulse response of the whole sample is given by:

for ≥ 0: ( ) ( ) ( ) ν ν π ν Θ d . 2 exp . t i T t + = ∫ +∞ ∞ - (4a)
for < 0: = 0 (4b)

In the case of frequency modulation with a 2f-detection, the detected signal D(ν) is simply proportional to the real part of the Fourier transform:

( ) ( ) ( ) [ ] ( ) ( )       - ℜ ∝ ∫ ∞ t t i t t t m J t D m m d . 2 exp . 2 cos . sinc . 2 . 2 0 2 ν π ν π ν π π Θ ν (5)
Since such a frequency modulated spectrometer does not allow to measure absolute transmissions, line intensities were fixed at the theoretical values given by HITRAN [START_REF] Hill | The HITRAN 2016 molecular spectroscopic database[END_REF].

Whereas ignoring the Beer-Lambert law leads to strongly erroneous relaxation rates, this approach remains quite reliable since a 25% error in line intensities leads to 1% deviation in retrieved relaxation parameters [START_REF] Dudaryonok | Experimental studies, line-shape analysis and semi-empirical calculation of broadening coefficients for CH3 35 Cl-CO2 submillimeter transitions[END_REF]. Note that the line profile detected by a frequency modulation spectrometer generally exhibits an asymmetry. This artifact may originate from baseline distortion and/or from the gas refractive index through residual standing waves [START_REF] Dore | Using Fast Fourier Transform to compute the line shape of frequency-modulated spectral profiles[END_REF]. It was taken into account by introducing an adjustable dispersion term chosen as proportional to the imaginary part of the Fourier transform of Eq. ( 5).

In a preliminary step to the fitting procedure, the baseline perturbations caused by the instability of the smm-wave optical alignment in the cell are modeled with a 3 rd order polynomial function. Next the measured lines with corrected baseline are adjusted using a nonlinear least squares code based on the Eqs. [START_REF] Hindle | Monitoring of food spoilage by high resolution THz analysis[END_REF][START_REF] Lieven | Infrared satellite observations of hydrogen sulfide in the volcanic plume of the August 2008 Kasatochi eruption[END_REF][START_REF] Zahnle | Atmospheric Sulfur Photochemistry on Hot Jupiters[END_REF][START_REF] Irwin | Probable detection of hydrogen sulphide (H2S) in Neptune's atmosphere[END_REF][START_REF] Privalov | Hydrogen Sulfide Molecules Lidar Sensing in the Atmosphere[END_REF]. Signal amplitude, line center frequency, collisional parameters, as well dispersion term amplitude could be adjusted, whereas Doppler width, line intensities, as well as modulation depth and frequency, were kept fixed at the values corresponding to experimental conditions and tabulated parameters [START_REF] Hill | The HITRAN 2016 molecular spectroscopic database[END_REF]. An example is presented in the Fig. 2 for the 44,0 ← 43,1 rotational line of pure H2S measured at 295K. Using the Voigt profile and thanks to the good SNR obtained (≅ 900), one observes a remarkable difference between observed (orange curve) and fitted (black curve) profiles. Particularly, the observed profile has an amplitude greater than the fitted one and thus is narrower, the amplitude of the residual (black curve) is estimated to 3% of the line amplitude. Such a departure is characteristic of speed dependent and/or of Dicke narrowing effects [START_REF] Hartmann | Collisional effects on molecular spectra[END_REF].

Speed-dependence effects

Departures from the Voigt profiles can be related to a combined influence of velocity changing collisions (Dicke narrowing) [START_REF] Dicke | The Effect of Collisions upon the Doppler Width of Spectral Lines[END_REF] and of the speed dependence of relaxation rates [START_REF] Berman | Speed-dependent collisional width and shift parameters in spectral profiles[END_REF][START_REF] Pickett | Effects of velocity averaging on the shapes of absorption lines[END_REF]. To take into account these effects, the speed-dependent Galatry profile [START_REF] Ciuryło | Speed-dependent pressure broadening and shift in the soft collision approximation[END_REF] has been retained because the corresponding correlation function has an analytical form, that is more convenient in case of frequency modulated absorption lines. Of course, this profile reduces to the usual Galatry profile [START_REF] Galatry | Simultaneous effect of Doppler and foreign gas broadening on spectral lines[END_REF] if SD-effects are negligible, or to the SD-Voigt profile [START_REF] Berman | Speed-dependent collisional width and shift parameters in spectral profiles[END_REF][START_REF] Pickett | Effects of velocity averaging on the shapes of absorption lines[END_REF] if Dicke effect can be ignored.

Restricting to the velocity changing collisions only, the line narrowing can be modeled via the Galatry profile [START_REF] Galatry | Simultaneous effect of Doppler and foreign gas broadening on spectral lines[END_REF] whose correlation function is given by:

= 2 -2 , + " # $ %& '( #)* + , # 1 -2 . - -2 / 0 (6)
In this equation / is the narrowing parameter that can be considered as the optical diffusion rate related to velocity changing collisions. Since this process influences the Doppler contribution, the Galatry profile differs significantly from the Voigt profile in the Doppler regime, i.e. at low pressure, and coincide with the Voigt profile in the collisional regime.

Speed dependent effects can be considered separately by using the model first proposed by Berman [START_REF] Berman | Speed-dependent collisional width and shift parameters in spectral profiles[END_REF] and Pickett [START_REF] Pickett | Effects of velocity averaging on the shapes of absorption lines[END_REF] by assuming that collisional interaction is described by the empirical potential V(r) ∝ r -q , where r is the intermolecular distance and q an empirical parameter. This model leads to an hypergeometric dependence of the relaxation rate Γ 123 ν on the absorber speed va. However, this model requires rather long numerical calculations, so Rohart et al. [START_REF] Rohart | Speed dependence of rotational relaxation induced by foreign gas collisions: studies on CH3F by millimeter wave coherent transients[END_REF] have proposed the quadratic approximation:

( )

          -         + = 2 3 . 2 0 , 2 , 0 a a SDV Γ Γ Γ (7)
which leads to a simpler correlation function:

Φ 123 = 5678#9): ( ;<#)$= (,>?@ < A B = B,>?@ ,;C D"E#)= B,>?@ ;F A B G . I- %: '( ; B J.D"E#)= B,>?@ ;F K (8)
where

a v a SDV v ) ( , 0 Γ Γ =
is the mean relaxation rate over molecular speeds and Γ2,SDV is a pressure dependent parameter describing the speed dependence of relaxation rates. Although approximate, this quadratic model has been retained for the extension of data bases to non Voigt spectral lineshapes [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions[END_REF]. Indeed, this model has been shown to be actually an accurate approximation of the hypergeometric one, at least for SNR lower than several thousand [START_REF] Vizia | Investigation on speed-dependence of collision parameters in the H2 18 O near-IR spectrum: The quadratic model versus the hypergeometric one[END_REF].

Moreover, it can be easily connected to the hypergeometric model via [START_REF] Rohart | Lineshapes of the 172 and 602 GHz rotational transitions of HC 15 N[END_REF] ( )

      - - + = 2 3 ; 2 5 ; 2 1 M . 1 3 2 , 0 , 2 λ µ λ µ λ Γ Γ µ SDV SDV (9)
where λ=mb/ma is the mass ratio of buffer and absorbing molecules, µ=(q-3)/(q-1), and M[a;b;x] is the hypergeometric confluent function [START_REF] Abramowitz | Handbook of Mathematical Functions[END_REF].

Let us consider the recorded H2S self-broadened lineshape displayed in Fig. 2 for a given pressure. One observes the quality of fits is similar using either the Galatry or the SD-Voigt profiles. For both cases and on account of the fairly good SNR obtained, one gets a nearly perfect adjustment with residuals significantly smaller than those obtained with the Voigt profile. Note this lineshape corresponds to the Doppler regime, the collisional broadening rate being lower than the Doppler broadening. However, at much higher pressures corresponding to the collisional regime, and by contrast with the SD-Voigt profile, it was impossible to perform any fit using the Galatry profile. Let us consider the pressure dependences of the collisional relaxation rates ,3 L67 , ,123 L67 , #,123 L67 , as well as the Galatry optical diffusion rate .

L67

, as displayed on Fig. 3a. As expected for the binary collisional regime, Voigt and SD-Voigt relaxation rates behave linearly.

On the contrary, the Galatry optical diffusion rate . L67 exhibits a nonlinear pressure dependence for collisional broadenings larger than the Doppler width. Moreover, . L67 could not be determined for pressures above 0.5 mbar, corresponding fits being impossible. This feature, well explained in Ref. [START_REF] D'eu | Infrared HCN lineshapes as a test of Galatry and speed-dependent Voigt profiles[END_REF], shows that observed departures from the Voigt profile are mainly due to the speed dependence of relaxation rates and that the Dicke effect has a negligible role and can be disregarded in case of self H2S relaxation. Similar difficulties were also encountered in the case of N2-induced relaxation of H2S, as displayed on Fig. 3b. In this case, the non-linear pressure dependence of . L67 is also clearly evident, but occurs for pressures higher than in the pure H2S relaxation case (Fig. 3a), a feature due to the N2-H2S relaxation rate about twice smaller than the self H2S one, as explained in Ref. [START_REF] D'eu | Infrared HCN lineshapes as a test of Galatry and speed-dependent Voigt profiles[END_REF]. As a consequence, the role of velocity changing collisions has been disregarded and only the speed dependence of relaxation rates has been considered in the analysis of H2S collisional line shape.

The pressure dependence of the relaxation rate is obtained by linear least squares fittings as shown in Fig. 3a with their estimated uncertainties are listed in Tables 2 and4, respectively.

Formalism of the theoretical calculations

Since previous calculations of pressure broadening of H2S were performed in the # band and for rovibrational lines other than measured in this work, we decided to compute the self-and N2-brodening coefficients of H2S in the ground vibrational state in order to reproduce our measurements and to detect an eventual vibrational effect on the pressure broadening phenomena. The computations were performed using the semi-classical model based on the RB formalism. Within this formalism, the pressure broadening half-width Γ in the unit of Hz may be expressed as [START_REF] Robert | Short range force effects in semiclassical molecular line broadening calculations[END_REF][START_REF] Leavitt | Cutoff-free theory of impact broadening and shifting in microwave and infrared gas spectra[END_REF][START_REF] Buldyreva | Collisional line broadening and shifting of atmospheric gases[END_REF]: [START_REF] Minghe | Quantitative analysis of gas phase molecular constituents using frequency-modulated rotational spectroscopy[END_REF] where n is the number density of perturbing molecules, v is the relative velocity between the absorber and the perturber, ^ 6 ] is the Maxwell velocity distribution, the induction and the Tipping-Herman potential [START_REF] Tipping | Impact theory for the noble gas pressure-induced HCl vibration-rotation and pure rotation line widths -I[END_REF] expressed as:

= V #) W 8∑ Y Z B [ B \ ] ^ 6 ] _] \ 2 `a Eb c d ( $ & d e & , Eb Z B [ B `a, ] _`aC
f = f g h g B + f g h i B + f i h g B + f i h i B + 4k IW " $ l c d , "m -n " $ l c d , o K " pqr s + 4k IW # $ l c d , "# -n # $ l c d , t K # pqr s (12)
where P1 and P2 are the first-and second-order Legendre polynomials, θ is the angle between the axis of the absorbing molecule and the intermolecular axis, the indices 1 and 2 refer to the absorber and the perturber, ε and σ are the Lennard-Jones parameters. In this potential, R1, A1, R2 and A2

were chosen to obtain a reasonable agreement with the experimental values of the pressure broadening coefficients. The term due to the electrostatic interactions is a sum of dipole-dipole, dipole-quadrupole, quadrupole-dipole and quadrupole-quadrupole interactions, where µ and Q are the dipole and quadrupole moments of the molecules.

Computations of broadening coefficients

The collisional broadening coefficients of H2S self-and -N2 perturbed have been calculated using the above semiclassical RB formalism with the bi-resonance functions of Starikov [START_REF] Starikov | Bi-Resonance Functions in the Theory of Collisional Broadening of the Spectral Lines of Molecules[END_REF].

The computation has been performed at the experimental temperature T = 296 K for a complete set of rotational lines. The rotational constants, the electric multipole moments of H2S and N2

and the Lennard-Jones parameters are given in Table 1 with the associated references, as well as the A1, R1, A2 and R2 parameters varied manually until obtaining the best agreement between the measured and calculated broadening coefficients.

Results and discussion

Self-Broadening coefficients

Table 2 presents the self-broadening coefficients determined from 30 different rotational transitions of H2S in the 150 -850 GHz frequency range with 0 < J'' <12 and 0 < Ka '' <8. Due to the line narrowing, M ,123 L67 should be larger than M ,3 L67 . This assumption is systematically verified with the self-broadening coefficients. The averaged relative variation of the self-broadening coefficient due to the SD effect u (,>?@ PQR <u (,@ PQR u (,@ PQR is estimated to be in the 2% to 12% range with a mean value of about 7.3%. In Table 2 are also reported the

v w,xyz {|} v ~,xyz
{|} ratios which give an order of magnitude on speed dependent effects on relaxation. From the mean value of this ratio, about 0.15, and using Eq. ( 9), one obtains a q value of about 8.0, which corresponds to a rather hard sphere collision model for the Pickett empirical potential [START_REF] Pickett | Effects of velocity averaging on the shapes of absorption lines[END_REF]. Table 2 compared also experimental with the calculated self-broadening coefficients using the RB formalism. The mean square difference obtained between the calculated coefficients and the experimental ones adjusted with the Voigt profile is evaluated to 0.34 MHz/mbar. This difference, about 7% the mean value of self H2S broadening coefficients, shows the good quality of our theoretical broadening calculations.

In Fig. 4, the experimental and calculated self-broadening coefficients determined in this study are compared with previous measurements in the IR domain for different vibrational bands (Refs. [START_REF] Waschull | Self-, Air, and Helium Broadening in the ν2 Band of H2S[END_REF][START_REF] Sumpf | Experimental Investigation of the Self-Broadening Coefficients in the ν1+ ν3 band of SO2 and the 2ν2 band of H2S[END_REF][START_REF] Sumpf | Self-and Air-Broadening in the ν1 and ν3 bands of H2S[END_REF]), and for microwave rotational transitions by Helminger and De Lucia (Ref. [START_REF] Helminger | Pressure broadening of hydrogen sulfide[END_REF]). For all these references, the deviation from Voigt profile and the speed dependence effects were not taken into account. The comparison of the different datasets does not allow detect any vibrational dependence. A significant dispersion of the self-broadening coefficient between the different datasets is observed. Tan et al. in Ref. [START_REF] Tan | The broadening coefficients of H2S[END_REF] have performed a selection of the most reliable self-broadening and air-broadening coefficients of H2S for the HITRAN-2016 edition of the database from different IR datasets [START_REF] Hill | The HITRAN 2016 molecular spectroscopic database[END_REF]. This selection for the self-broadening is also plotted in Fig. 4. From 2016, a first order rotational dependence was considered in the HITRAN database with a linear fit of γself and γair versus J''+0.2 Ka '' reproducing the slight decreasing of the broadening coefficients observed in Fig. 4 from J''=2 to J''=11. For the self-broadening, the mean square difference between the M ,123 L67 determined in this study and the values tabulated in HITRAN-2016 is evaluated to 0.35 MHz/mbar, which is similar to the previous difference between our measurements and RB calculations. Microwave [START_REF] Helminger | Pressure broadening of hydrogen sulfide[END_REF] Hitran database [START_REF] Hill | The HITRAN 2016 molecular spectroscopic database[END_REF] γ Self (MHz/mbar) J'

Fig. 4: Self-broadening coefficients M 15•€ determined in this study compared to the previous IR (Refs. [START_REF] Waschull | Self-, Air, and Helium Broadening in the ν2 Band of H2S[END_REF][START_REF] Sumpf | Experimental Investigation of the Self-Broadening Coefficients in the ν1+ ν3 band of SO2 and the 2ν2 band of H2S[END_REF][START_REF] Sumpf | Self-and Air-Broadening in the ν1 and ν3 bands of H2S[END_REF][START_REF] Hill | The HITRAN 2016 molecular spectroscopic database[END_REF]) and mw (Ref. [START_REF] Helminger | Pressure broadening of hydrogen sulfide[END_REF]) studies.

In order to analyze more finely the rotational dependence of the H2S broadening coefficient, the empirical model of Starikov described in Refs. [START_REF] Starikov | Broadening of absorption lines of the ν2 band of the H2S molecule by the pressure of atmospheric gases[END_REF][START_REF] Starikov | Analytical Representation for Water Vapor Self-Broadening Coefficients[END_REF] for the measured broadening coefficients of C2v asymmetric top molecules such as H2O and H2S was adopted. The self-broadening coefficients for the

''

rotational transitions were fitted using the following empirical equation:

M " '' , " ' = M L…7 = " + # a † ‡ˆ‰6 Š D[ ' ee <[ ' e FD[ ' ee E[ ' e F‹ a † ‡ˆ‰6 A D[ ' e <6 OE F‹×a † ‡ˆ‰6 A D[ ' ee <6 OE F‹ (13)
where the J rotational dependence is included in an xk polynomial function (with k = 1, 2, 3, 4 and 5) given by:

% = % + %" • '' + • ' + %# • '' + • ' # (14)
The parameters xk0, xk1, and xk2 were obtained using a nonlinear least-square method that adjusts the equations ( 13) and ( 14) to the experimental values of self-broadening coefficients listed in Table 2

complemented with the calculated values

Cal RB γ for the non-measured transitions in the ranges 0 < J'' <12 and 0 < Ka '' <8. These fitted parameters are listed in Table 3 with their uncertainties estimated as the fit standard deviations. These uncertainties do not explicitly reveal the errors from the physical parameters intervening in the experiment, but implicit reflect the accuracy of linewidth measurements. The full set of parameters is included in our GS fit and, contrary to the ν2 fit of Ref. [START_REF] Starikov | Broadening of absorption lines of the ν2 band of the H2S molecule by the pressure of atmospheric gases[END_REF], all parameters are determined according to their accuracies.

The

Emp GS γ self-broadening coefficients determined in this study from Eq. ( 13) and Eq. ( 14) are listed in Table 2. For self-broadening, the comparison between the experimental M ,3 L67 and the empirical Emp GS γ provides a mean square difference evaluated to 0.16 MHz/mbar i.e two times smaller than those obtained with

Cal RB

γ . This result demonstrates the interest of the empirical modeling of Eq.( 13) for the interpolation of unmeasured (J,K) lines. The rotational dependences of the self-broadening coefficients in Ka '' and in J'' are presented in Fig. 5 which exhibits significant differences especially at low Ka '' and high J values with the empirical coefficients adjusted with our SMM measurements and those adjusted with the IR data (ν2 band) from Ref. [START_REF] Waschull | Self-, Air, and Helium Broadening in the ν2 Band of H2S[END_REF]. The increasing of γ0,self with J'' at low Ka '' for the R Q subbranch and the rapid decreasing with Ka '' at high J'' characteristic of the ν2 rovibrational transitions are not observed in the present study. In the GS, our γ0,self ( R Q) coefficients monotonically decreases with Ka '' and have a weaker variation with J'' at Ka '' =0.

N2-Broadening coefficients

The N2 -broadening coefficients measured for 27 rotational transitions of H2S in the GS with 0 < J'' < 12 and 0 < Ka '' < 8 using the frequency modulated spectrometer in the frequency range 350 -810 GHz are listed in Table 4. As for the self-broadening, the SD-Voigt profile provides the best adjustments of the N2-broadened rotational lines. The M ,123 L67 N2-broadening coefficients are greater than the M ,3 L67 coefficients for 70% of the measured lines. In Table 4 are also reported the ratios u B,>?@ PQR u (,>?@ PQR which give an order of magnitude of speed dependent effects on relaxation. From the mean value of this ratio, about 0.10, and using Eq. ( 9), one obtains a q value of about 6.0 for the Pickett empirical potential [START_REF] Pickett | Effects of velocity averaging on the shapes of absorption lines[END_REF], which corresponds approximately to a Van der Waals model, revealing lower speed dependent effects than for the self-broadening. γ is evaluated to 0.2 MHz/mbar, that about 8% of the mean value of H2S-N2 broadening coefficients. The figure 6 presents the experimental and calculated N2-broadening coefficients for all rotational transitions studied in this work compared with previous rotational GS (Ref. [START_REF] Ball | Variable-temperature pressure broadening of H2S by O2 and N2[END_REF]) and IR rovibrational measurements in the fundamentals bands ν1, ν2 and ν3 (Refs. [START_REF] Kissel | Molecular-Gas-Pressure-Induced Line-Shift and Line-Broadening in the ν2-Band of H2S[END_REF][START_REF] Meusel | Nitrogen Broadening of Absorption Lines in the ν1, ν2, and ν3 Bands of H2S Determined by Applying an IR Diode Laser Spectrometer[END_REF]). In these previous studies, only the Voigt profile was used. All datasets exhibit a monotonic decreasing of the N2-broadening coefficients with J'' but no vibrational dependence could be unambiguously extracted. Fig. 6: N2-broadening coefficients determined in this study compared to the previous IR (Ref. [START_REF] Kissel | Molecular-Gas-Pressure-Induced Line-Shift and Line-Broadening in the ν2-Band of H2S[END_REF][START_REF] Meusel | Nitrogen Broadening of Absorption Lines in the ν1, ν2, and ν3 Bands of H2S Determined by Applying an IR Diode Laser Spectrometer[END_REF]) and MW (Ref. [START_REF] Ball | Variable-temperature pressure broadening of H2S by O2 and N2[END_REF]) studies. The N2-broadening coefficients were also determined using the empirical model of Starikov (Eqs. ( 12) and ( 13)) with the same method applied to the self-broadening. The best parameters determined from the fit of our GS N2-broadening coefficients are listed in Table 5 with the parameters obtained in Ref. [START_REF] Starikov | Broadening of absorption lines of the ν2 band of the H2S molecule by the pressure of atmospheric gases[END_REF] with the coefficients measured in the ν2 band [START_REF] Kissel | Molecular-Gas-Pressure-Induced Line-Shift and Line-Broadening in the ν2-Band of H2S[END_REF]. In our study, the full set of xk parameters was adjusted and correctly determined contrary to those of Ref. [START_REF] Starikov | Broadening of absorption lines of the ν2 band of the H2S molecule by the pressure of atmospheric gases[END_REF] where some parameters were not include in the fit (e.g x1) and some parameters were not correctly determined (e.g x30 and x41). The empirical N2-broadening coefficients determined from our xk set of parameters are shown in The rotational dependences of the N2-broadening coefficients on Ka '' and on J'' are presented in Fig. 7. Compared to the self-broadening case (see Fig. 5), the differences between Emp GS γ determined in this study and Emp We can notice that for the N2-broadening, the rotational dependence is more significant on J'' than on Ka '' where a roughly linear decreasing of γ0,H2S-N2 for the R Q sub-branch is observed in agreement with previous studies shown in Fig. 6 and the air-broadening rotational dependence associated with the tabulated HITRAN-2016 parameters [START_REF] Tan | The broadening coefficients of H2S[END_REF][START_REF] Hill | The HITRAN 2016 molecular spectroscopic database[END_REF].

Conclusion

With the use of a frequency modulated THz spectrometer and of a dedicated fitting procedure, we have measured, in the 150 -850 GHz frequency range, a new set of precise selfand N2-broadening coefficients at T = 295 K for 30 and 27 GS rotational lines (mainly in the R Q sub-branch) of H2S, respectively. Benefiting from good S/N ratios (S/N>500) of the measured smm lines, systematic departures from the usual Voigt model have been stated for all the rotational lines studied in this work. The SD-Voigt profile yields to the best residuals and linear pressure dependences of the broadening and speed dependence parameters are observed in the 0.1 -0.8 mbar pressure range. In addition, the prediction of self-and N2-broadening coefficients using the RB formalism with bi-resonance functions leads to a reasonable agreement with the measured values and reproduces the observed rotational dependencies. The experimental broadenings show general consistency with the IR rovibrational measurements performed by other authors, with no evidence of systematic differences between the vibrational states. Using an empirical model developed by Starikov [START_REF] Starikov | Broadening of absorption lines of the ν2 band of the H2S molecule by the pressure of atmospheric gases[END_REF][START_REF] Starikov | Analytical Representation for Water Vapor Self-Broadening Coefficients[END_REF] and tested on H2S broadening coefficients determined in the ν2 fundamental band, the rotational dependences in J'' and Ka '' were analyzed with the self-and N2-broadening coefficients measured in this study. Some differences are observed compared to the IR results: (i) our γ0,self R Q coefficients monotonically decreases with Ka '' and have a weaker variation with J'' at Ka '' = 0; (ii) for the N2-broadening, the rotational dependence is more significant on J'' than on Ka '' with a roughly linear decreasing of γN2 in the R Q branch.

The present release of HITRAN does not account for branch and band type interactions, Dicke narrowing, speed dependence effects or line mixing. Such fine effects may be quantified in pure rotation provided sufficient SNR is available. In the case of line mixing higher pressures measurements are required and a specific baseline treatment. Our results suggest that the existing data base information may be extended with some confidence to the H2S rotational measurements considered in this work. To go further in this study, it will be interesting to introduce speeddependent collisional parameters in the semi-classical calculations [START_REF] Ngo | A pure H2O isolated line-shape model based on classical molecular dynamics simulations of velocity changes and semi-classical calculations of speed-dependent collisional parameters[END_REF].

Fig. 1 :

 1 Fig. 1: 44,0 ← 43,1 rotational line of pure H2S recorded at 424.315 GHz at different pressures. The modulation depth m is adjusted according to the estimated line width.

Fig. 2 :

 2 Fig. 2: Adjustments with Voigt, Galatry and SD-Voigt profiles and corresponding residuals enlarged by a factor of 10 for the 44,0 ← 43,1 rotational line of pure H2S. Experimental conditions: P= 0.1 mbar, T= 295K, modulation depth m = 540 kHz, modulation frequency νm = 13 kHz. Signal to noise ratio (SNR) is about 900. Doppler width= 482 kHz, Γ0,V Exp = 397(20) kHz, Γ0,SDV Exp = 469(10) kHz, Γ2,SDV Exp = 100(4) kHz, Γ0,G Exp = 446(20) kHz, ΒG Exp =315(10) kHz.

  and Fig. 3b for the self-broadened 44,0←43,1 and the N2-broadened 22,1←21,2 transitions. The slopes of the straight lines gives the relaxation coefficients M ,3 L67 , M ,123 L67 and M #,123 L67 , expressed in MHz/mbar and defined as M ,and ,123 L67 are the pressure broadenings, #,123 L67 is the relaxation speed dependence parameter and P is the gas pressure. The measured values of self-and N2-broadening coefficients M ,3 L67 , M ,123 L67 and M #,123 L67

Fig. 3 :

 3 Fig. 3: Pressure dependence of the relaxation rates of H2S measured at room temperature (T = 295 K). The relaxation coefficients are derived from weighted linear least squares: (a) Self-broadened 44,0←43,1 transition: M ,3 L67 = 4.59(9) MHz/mbar, M ,123 L67 = 4.74(3) MHz/mbar, M #,123 L67 = 0.66(3) MHz/mbar. (b) N2-broadened 22,1← 21,2 transition for T B 1 = 0.01 mbar: M ,3 L67 = 2.89(2) MHz/mbar, M ,123 L67 = 2.941(6) MHz/mbar, M #,123 L67 = 0.292(3) MHz/mbar. The error bars correspond to one standard deviation (SD); they take into account the different experimental uncertainties: fitting standard deviation (<1%), cell length (0.7%), temperature(0.34%), pressure (0.4%) and the systematic errors linked to detector and electronic nonlinearity (2%).

S

  perturber, rc and ' c ν are position and velocity parameters related to the relative trajectories model and rc0 is the distance of closest approach[START_REF] Robert | Short range force effects in semiclassical molecular line broadening calculations[END_REF]. The differential broadening cross section ( ) are the second-order terms of the perturbation development of the differential cross section[START_REF] Robert | Short range force effects in semiclassical molecular line broadening calculations[END_REF][START_REF] Leavitt | Cutoff-free theory of impact broadening and shifting in microwave and infrared gas spectra[END_REF][START_REF] Tsao | Line-widths of pressure-broadened spectral lines[END_REF]. To calculate the self-and N2-broadening coefficients, we have considered the intermolecular potential involving the electrostatic interactions as well as

Fig. 5 : 2 υγ

 52 Fig. 5: Examples of Ka '' and J rotational dependences of the H2S self-broadening coefficients: Ka '' dependence for J '' =8 (top) and J '' dependence for Ka '' =0 (bottom). 3 sets of data are compared: the calculated coefficients with the RB formalism Cal RB γ and the empirical coefficients Emp GS γ

2 υγ

 2 are less pronounced especially for the dependence on J''.

Fig. 7 2 υγ

 72 Fig. 7Examples of Ka '' and J'' rotational dependences of the H2S N2-broadening coefficients: Ka '' dependence for J '' =8 (top) and J '' dependence for Ka '' =0 (bottom). 3 sets of data are compared: the calculated coefficients with theRB formalismCal RB γ and the empirical coefficients Emp GS γ

Table 1

 1 Molecular parameters used in the calculations of the self-and N2-broadening coefficients of H2S in the GS.

		H2S	N2
	M (g.mol -1 )	34.08	28.0134
	A (cm -1 )	10.35995 a	-
	B (cm -1 )	9.018496 a	1.989622 d
	C (cm -1 )	4.730608 a	-
	µ (D)	0.974 b	0
	Q (DǺ)	0.71 b	-1.4 e
	ε (K)	309.6 c	92.91 f
	σ (Ǻ)	3.509 c	3.816 f
			Ajustable parameters
	Molecular system	A1	R1	A2	R2
	H2S -H2S	0.08	1	0.6	0.6
	H2S -N2	0.5	5	0.08	0.08

a Ref.

[START_REF] Azzam | Terahertz spectroscopy of hydrogen sulfide[END_REF]

, b Ref.

[START_REF] Starikov | Broadening of absorption lines of the ν2 band of the H2S molecule by the pressure of atmospheric gases[END_REF]

, c Ref.

[47]

, d Ref.

[START_REF] Reuter | The v=1←0 quadrupole spectrum of N2[END_REF]

, e Ref.

[START_REF] Gray | Theory of Molecular Fluids[END_REF]

, f Ref.

[START_REF] Bouanich | Theoretical O2-and N2-broadening coefficients of CH3Cl spectral lines[END_REF]

Table 2 .

 2 Self-broadening coefficients of H2S in MHz/mbar determined in this study. Frequencies are given in GHz.

	J', Ka', Kc', J'' , Ka '' , Kc'' are the upper and lower state quantum numbers. M ,3 L67 , M ,123 L67 and M #,123 L67 are the experimental coefficients fitted with Voigt and SD-Voigt profiles. The ratio v w,xyz {|} {|} gives the magnitude of the speed v ~,xyz dependence. Cal RB γ are the calculated coefficients with the RB formalism. Emp GS γ are the empirical coefficients based
	on the Starikov model adjusted with the GS self-broadening coefficients determined in this study (see Section 4).
	Last digit quoted errors in parentheses are equal to one standard deviation (1 SD).
	Frequency	J '	Ka '	Kc '	J ''	Ka '' Kc ''	M ,3 L67	M ,123 L67	M #,123 L67	M #,123 L67 M ,123 L67	γ	Cal RB	γ	Emp GS
	168.762	1	1	0	1	0	1	4.52(7)	4.84(4)	0.63(2)	0.130(5)	4.61	4.36
	216.710	2	2	0	2	1	1	4.91(7)	5.40(2)	0.69(1)	0.128(2)	5.02	5.03
	300.505	3	3	0	3	2	1	3.98 (8)	4.34(3)	1.04(2)	0.240(6)	4.80	4.64
	369.101	3	2	1	3	1	2	5.39(9)	5.67(3)	1.36(3)	0.240(7)	4.75	5.04
	369.127	4	3	1	4	2	2	4.4(1)	4.75(2)	0.74(2)	0.156(5)	4.55	4.66
	393.450	2	1	1	2	0	2	5.62(9)	6.08(1)	1.39(6)	0.23(1)	4.99	5.06
	407.675	5	4	1	5	3	2	4.08(8)	4.34(2)	0.93(4)	0.21(1)	4.36	4.58
	424.314	4	4	0	4	3	1	4.59(9)	4.74(6)	0.66(3)	0.139(8)	4.56	4.47
	493.362	6	5	1	6	4	2	4.56(7)	4.74(1)	0.64(2)	0.135(5)	4.17	4.61
	505.564	2	2	1	2	1	2	5.09(5)	5.34(1)	1.26(6)	0.24(1)	5.02	5.03
	555.254	7	5	2	7	4	3	4.54(9)	4.89(3)	0.84(3)	0.172(7)	4.28	4.54
	567.078	6	4	2	6	3	3	4.30 (6)	4.53(2)	0.53(1)	0.117(3)	4.50	4.63
	568.049	3	3	1	3	2	2	4.36(7)	4.67(2)	0.93(2)	0.199(5)	4.80	4.64
	579.798	5	5	0	5	4	1	4.97(9)	5.15(3)	1.12(3)	0.218(7)	4.33	4.61
	593.169	8	6	2	8	5	3	4.17(5)	4.48(3)	0.66(4)	0.15(1)	4.08	4.30
	626.473	7	6	1	7	5	2	4.90(9)	5.31(2)	1.19(1)	0.224(3)	3.96	4.46
	665.395	4	2	2	4	1	3	5.23(7)	5.60(4)	1.01(5)	0.18(1)	4.96	4.94
	687.304	2	0	2	1	1	1	4.01(6)	4.41(3)	0.99(5)	0.23(1)	4.75	4.76
	689.121	9	7	2	9	6	3	4.03(9)	4.20(3)	0.52(3)	0.124(8)	3.91	4.05
	733.025	10	7	3	10	6	4	4.55(9)	4.90(5)	0.59(3)	0.120(7)	4.03	4.15
	746.720	9	6	3	9	5	4	4.34(9)	4.78(2)	0.74(2)	0.155(5)	4.20	4.25
	747.301	3	2	2	3	1	3	5.49(8)	5.68 (5)	0.82(3)	0.144(7)	4.75	5.04
	748.240	6	6	0	6	5	1	4.44(7)	4.58(3)	0.58(2)	0.127(5)	4.10	4.67
	749.433	5	5	1	5	4	2	4.87(6)	5.12(1)	0.71(2)	0.139(4)	4.33	4.61
	782.344	11	8	3	11	7	4	4.35(9)	4.79(2)	0.75(4)	0.157(9)	3.91	4.29
	794.222	8	7	1	8	6	2	4.54(6)	4.74(4)	0.52(3)	0.110(7)	3.80	4.13
	800.850	5	4	2	5	3	3	4.27(5)	4.53(2)	0.68(3)	0.150(7)	4.36	4.58
	804.729	8	5	3	8	4	4	4.61(7)	4.80(4)	0.54(2)	0.113(5)	4.39	4.48
	839.140	10	8	2	10	7	3	3.64(5)	4.89(3)	0.57(3)	0.117(7)	3.75	3.99
	841.280	8	3	6	7	4	3	4.91(6)	5.12(3)	0.83(3)	0.162(7)	4.58	4.51

  • [ ' e ,[ d e

' ← • [ ' ee ,[ d ee

Table 3 :

 3 Parameters adjusted in the Starikov model using Eqs. 13 and 14 for the empirical determination of the selfbroadening coefficients. x1k and x2k are in unit of cm -1 .atm -1 , x3k, x4k and x5k are unitless. Last digit quoted errors in parentheses are equal to one standard deviation (1 SD).

	Parameter	This study (GS)	Ref. [46] (ν2)
	x10	-5.676(3)	-
	x11	0.468(3)	0.00275(5)
	x12	-0.00942(1)	-
	x20	5.81(4)	0.194(1)
	x21	-0.45762(5)	-0.00484(7)
	x22	0.00906(2)	-
	x30	-0.114(2)	0.107(7)
	x31	0.01022(2)	0.00306(4)
	x32	-0.000290(2)	-
	x40	0.821(4)	5.2(2)
	x41	0.04542(3)	-0.50(2)
	x42	-0.03610(3)	0.0215(7)
	x50	0.0363(4)	0.011(4)
	x51	0.00194(2)	-
	x52	-0.0001899(4)	-

Table 4

 4 present the calculated N2-broadening coefficients with the Voigt and SD-Voigt profiles, the adjusted ones and the calculated values using the RB formalism. The mean square

	difference between M ,3 L67 and	Cal RB

Table 4 .

 4 N2-broadening coefficients of H2S in MHz/mbar determined in this study. Frequencies are given in GHz. M ,3 L67 , M ,123 L67 and M #,123 L67 are the experimental coefficients fitted with Voigt and SD-Voigt profiles. The ratio Cal RB γ are the calculated coefficients with the RB formalism. are the empirical coefficients based on the Starikov model adjusted with the GS self-broadening coefficients determined in this study (see Section 4). Last digit quoted errors in parentheses are equal to one standard deviation (1 SD).

		v w,xyz {|} {|} v ~,xyz Emp GS γ	gives the magnitude of the speed dependence.
	Frequency	J '	Ka '	Kc '	J ''	Ka ''	Kc ''	M ,3 L67	M ,123 L67	M #,123 L67	M #,123 L67 M ,123 L67	γ	Cal RB	γ	Emp GS
	369.101	3	2	1	3	1	2	2.99(4)	2.87 (1)	0.24 (1)	0.084(4)	2.75	2.81
	369.127	4	3	1	4	2	2	2.81(5)	2.809 (6)	0.266(4)	0.095(2)	2.65	2.66
	393.450	2	1	1	2	0	2	3.05(5)	2.972(6)	0.256(3)	0.086(1)	2.99	2.71
	407.675	5	4	1	5	3	2	2.75(3)	2.65(2)	0.213(6)	0.080(3)	2.56	2.52
	424.314	4	4	0	4	3	1	2.84(3)	2.68(1)	0.197(4)	0.074(2)	2.86	2.74
	493.362	6	5	1	6	4	2	2.72(7)	2.57(2)	0.263(9)	0.102(4)	2.48	2.51
	505.564	2	2	1	2	1	2	2.89(4)	2.941 (6)	0.292(3)	0.099(1)	3.13	2.79
	555.254	7	5	2	7	4	3 2.41(5)	2.50(1)	0.27(2)	0.108(8)	2.27	2.35
	567.078	6	4	2	6	3	3	2.50(6)	2.54(1)	0.23(1)	0.091(4)	2.34	2.39
	568.049	3	3	1	3	2	2	2.79(6)	2.85(4)	0.25(2)	0.088(8)	2.95	2.89
	579.798	5	5	0	5	4	1	2.46(5)	2.45(1)	0.29(2)	0.118(9)	2.74	2.63
	593.169	8	6	2	8	5	3	2.32(4)	2.42 (1)	0.267(9)	0.110(4)	2.19	2.22
	626.473	7	6	1	7	5	2	2.56(5)	2.690(8)	0.43(4)	0.16(2)	2.42	2.51
	650.376	4	4	1	4	3	2	2.52(4)	2.63(4)	0.18(2)	0.068(9)	2.86	2.74
	665.395	4	2	2	4	1	3	2.67(3)	2.766(3)	0.237(2)	0.0857(8)	2.56	2.60
	687.304	2	0	2	1	1	1	2.77(5)	2.847(7)	0.24(1)	0.084(4)	3.13	2.72
	689.121	9	7	2	9	6	3	2.10(3)	2.240(9)	0.19(1)	0.085(5)	2.10	2.07
	733.025	10	7	3	10	6	4	2.07(4)	2.36(3)	0.31(3)	0.13(1)	1.83	1.92
	736.033	2	1	2	1	0	1	2.84(5)	2.71(4)	0.208(6)	0.077(3)	3.01	2.72
	746.72	9	6	3	9	5	4	2.21(4)	2.27(2)	0.246(1)	0.108(1)	1.96	1.96
	747.301	3	2	2	3	1	3	3.20(3)	2.760(9)	0.224(1)	0.0812(6)	2.75	2.81
	748.240	6	6	0	6	5	1	2.27(3)	2.36(1)	0.162(4)	0.069(2)	2.64	2.67
	749.433	5	5	1	5	4	2	2.47(2)	2.478(8)	0.174(5)	0.070(2)	2.74	2.63
	782.344	11	8	3	11	7	4	2.07(4)	2.11(2)	0.189(9)	0.090(5)	1.71	1.94
	794.222	8	7	1	8	6	2	2.17(5)	2.21(4)	0.139(3)	0.063(3)	2.34	2.39
	800.850	5	4	2	5	3	3	2.61(4)	2.66(2)	0.18 (1)	0.068(4)	2.56	2.52
	804.729	8	5	3	8	4	4	2.32(5)	2.220(9)	0.158(9)	0.071(4)	2.03	2.10

Table 4

 4

	(column Emp GS γ ). For N2-broadening, the mean

Table 5 .

 5 Parameters adjusted with the Starikov model (Eqs. (12) and (13)) for the empirical determination of the N2-broadening coefficients. x1k and x2k are in unit of cm -1 .atm -1 , x3k, x4k and x5k are unitless. Quoted errors in parentheses are in the last digit given and are equal to one standard deviation (1 SD).

	Parameter	This study (GS)	Ref. [46] (ν2)
	x10	-0.10262(2)	-
	x11	0.01778(4)	-
	x12	-0.000505732(3)	-
	x20	0.21667(4)	0.096(2)
	x21	-0.02119(2)	-0.0014(2)
	x22	0.0005253(2)	-
	x30	0.04042(3)	0.1 (4)
	x31	-0.00496(2)	-0.0007(2)
	x32	0.00014697(3)	-
	x40	-6.499(4)	-1.32(8)
	x41	9.688(2)	0.3(4)
	x42	-1.2698(1)	-
	x50	-0.061(2)	-0.016(2)
	x51	0.0047421(7)	0.00096(7)
	x52	-0.00052909(5)	-

SDV a SDV v v v

Acknowledgements

This study was undertaken as part of the Terafood project, which is financially supported by the European Regional Development Fund and the province Oost-Vlaanderen (1.2.11). It was also supported by the CaPPA project (Chemical and Physical Properties of the Atmosphere) and CPER-ClimiBio that are funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissement d'Avenir) under contract "ANR-11-LABX-0005-01", by the Regional Council "Nord-Pas de Calais" and by the "European Funds for Regional Economic Development" (FEDER).