Maksim Koshelev

Ilya Vilkov

Oleg Egorov

Andrey Nikitin

Michäel Rey

High sensitive measurements of 12 CH3D pure rotational lines within ground and excited vibrational states in the subTHz region

Keywords: Methane, 12 CH3D, THz region, pure rotational lines, ground state parameters, GSCD

The pure rotational transitions of 12 CH3D having intensity down to 7.9•10 -28 cm/molec were studied by high sensitive spectrometer with radio-acoustic detection of absorption. Among the 14 measured spectral lines, 11 correspond to the rotational transitions within first three excited states of 12 CH3D.

A theoretical description was carried out by effective polyad model expressed in irreducible tensor form including the Triad of interacting bands. An accurate set of ground state rotational and centrifugal distortion constants was determined using a simultaneous weighted fit of experimental transitions available in literature together with the new subTHz measurements. Pressure broadening and shifting parameters of the JK=10-00 ground state rotational line were accurately measured and allowed estimating possible systematic errors in some previous studies.

Introduction

Deuterated chemical compounds are of significant interest for astronomical applications. A determination of the D/H ratio by spectral analyses is the subject of numerous works since this permits to test models of Galactic chemical evolution. Very contrasting D/H ratios in different parts of the Universe have been obtained that stimulated challenging cosmochemical studies ( [Owen 2015, Lindsky2006] and reference therein). Methane (CH4) is one of the most abundant gas in planetary atmospheres. CH4 and its monodeuterated isotopologue CH3D have been observed on the majority of the planets of the solar system and most of the larger moons, in particular, in Jupiter, Titan, Saturn, Uranus, and Neptune (see [Encrenaz1999, Penteado2005, Fletcher2009, Irwin2012, Irwin2014] and references therein).

Methane on Mars attracts much interest since it might be a sign of the microbial life or organic matter by analogy with the biological origin of methane in the Earth's atmosphere. Although the pure rotational transitions in CH4 are forbidden by symmetry in a rigid rotor approximation, a very weak absorption can be detected due to centrifugal distortions [Boudon2010]. Induced by isotopic substitution permanent electric dipole moment of CH3D is much larger than rotationally induced in CH4 but is still quite small (~ 0.006 D) [Ozier1969, Wofsy1970]. Therefore, investigation of CH3D spectra in THz region is a difficult/challenging task requiring a high sensitivity of the spectrometer.

First low resolution spectrum of 12 CH3D (hereafter CH3D) was recorded by Ozier et al. [Ozier1969] in the 40-120 cm -1 (1.2-3.6 THz) frequency range using grating spectrometer. Ten rotational lines identified as R(5) to R(14) transitions were observed. Despite no K-structure was observed, the values of the dipole moment and the spectroscopic molecular constants were determined. Later, the high resolution recordings of the JK = 10-00 line near 232.6 GHz were obtained by Pickett et al. Lantanzi et al. [Lattanzi2008] reported twelve new rotational transitions in the range of 697-1162 GHz which correspond to the next series with 3K-2K, 4K-3K, and 5K-4K. The spectral range was further extended in work of Drouin et al. [Drouin2009] where the 7K-6K series has been recorded. In Almost all the lines studied have intensity of about 10 -25 cm/molec or higher. However, many weaker lines of hot band transitions located in the range of the rotational spectra can validate the theory completeness and accuracy.

Note that the data sets for the ground state rotational transitions of CH3D in HITRAN [Gordon2017], GEISA [Jacquinet2016], JPL [Pearson2010] and Cologne databases [Christian2016] are quite different, whereas information concerning CH3D transitions in this range is not available in TDS [Tyuterev1994] or MeCaSDa [Ba2013] compilations. To our knowledge, the CH3D transitions in the subTHz region within excited vibrational states have not been included in existing databases.

In this work, we present the revised accurate measurements of the ground state transitions (10-00, 20-10, and 21-11) and the first measurements of the pure rotational transitions within 6, 3, and 5 excited states of CH3D. Lines were recorded in the frequency range up to 0.5 THz using a spectrometer with radio-acoustic detection of absorption (RAD spectrometer) [Tretyakov2008, Koshelev2017, Golubyatnikov_unpub]. The intensity of the studied lines varied from 10 -26 to 10 - 29 cm/molec. A new accurate set of rotational parameters of effective Hamiltonian expressed in irreducible tensors was determined by combining all measured in THz region transitions with those calculated by so called ground state combination differences (GSCD) method. Pressure broadening and shifting of the 10-00 ground state rotational line were accurately measured and allowed estimating possible systematic errors in some previous studies.

Experimental details

A spectrometer with radio-acoustic detection of absorption (RAD spectrometer) was used for recording the weak CH3D lines. A detailed description of the spectrometer can be found elsewhere [Tretyakov2008, Koshelev2017, Golubyatnikov_unpub]. Briefly, the method is based on registering a pressure variations induced in a gas due to molecular absorption of radiation modulated by frequency or amplitude. A significant improvement of the spectrometer sensitivity can be achieved by an increase of the radiation power. In this study, the spectrometer was equipped with two types of continuous wave radiation sources. The first one is a series of three backward wave oscillators (BWOs) covering a frequency range 179-535 GHz which output power varies from a few milliwatts to about 50 mW (see [Korolev2001] and references therein). The second source is a gyrotron operating in a narrow frequency interval of about 1 GHz around 263.5 GHz with the maximum power of 1 kW [Glyavin2015]. Both sources were frequency stabilized by the PLL system against a harmonic of a high stable signal of microwave synthesizer (Anritsu MG3692C) providing relative frequency stability of about 10 -10 and narrow spectrum bandwidth down to 1 Hz or less [Fokin2018].

Use of GPS Time and Frequency System (SR FS740) as a reference oscillator provided frequency setting accuracy and long term stability. Modulation of the radiation frequency by square-wave signal followed by demodulation at a synchronous detector was used for reducing the baseline effect when recording the weak lines. For this purpose, an arbitrary waveform generator (Tektronix AFG3101 and Rohde & Schwarz HFM2550), which permits modulating the radiation frequency with a preset modulation index, was employed in the PLL as the source of a reference signal for the phase detector.

Synchronous detection of the absorption signal was carried out both at the first (for BWO) and the second (for gyrotron) harmonics of the modulation frequency.

A single pass cell of 10 cm length and 2 cm diameter connected with a microphone was used.

The cell was equipped with the conical HDPE windows of 2 mm thickness. All spectra were recorded at room temperature 297 ± 1 K. For the line frequency measurements, the pressure of CH3D in the cell was about 0.4-0.5 Torr which seems to be the optimal compromise from the point of view of the RAD spectrometer sensitivity, line width and the baseline influence on the line shape. Gas pressure was measured using MKS Baratron (Type 626B) gauge having a declared accuracy of 0.25% of reading. A commercial methane gas, enriched with at least 90% of the 12 CH3D isotopologue was used in the study.

High stability of the experimental conditions (parameters of laboratory air, radiation and gas sample) allowed averaging a large number (up to 216) of repeated single scans without noticeable distortions in the observed spectra. The obtained signal-to-noise ratio (SNR) was sufficient (at least 10) for accurate determining the central frequencies of the weak CH3D lines. Acquisition parameters of the single scan were the following: 200 frequency points for a single line and 250 points for doublets, lock in time constant was 0.5 s. Thus, the accumulation time was up to 7.5 hours. Examples of experimental spectra of CH3D obtained using RAD spectrometer are shown in Fig. 1 for the BWO and in Fig. 2 for the gyrotron.

Spectra analysis

A model function based on the Voigt profile was fitted to the experimental spectra and the line shape parameters were derived. Measured central frequencies are presented in Table 1 along with the experimental details (number of averaged recordings and SNR) and spectroscopic information (calculated intensities and assignment) on the studied lines.

Self-broadening and self-shifting parameters of the rotational spectrum lines of CH3D were estimated on example of our best quality (in terms of SNR) ground state line JK = 10-00 near 232.644 GHz. For this, the line recordings were obtained at six pressures in a range 0.26 -1.04 Torr.

For each recording the modulation depth was preset approximately equal to the line half width at half maximum (HWHM) and this value was fixed in the model function. Both multispectra (Fig. 3) and single-spectra fitting procedures were applied and demonstrated similar results for the line shape parameters. SNR for the line recordings was 110-440. Pressure dependence of the line width and center position obtained from the single-spectra fitting is shown in Fig. 4.

Self-broadening and shifting parameters determined by both fitting procedures are 3.285(30) MHz/Torr and 0.085(25) MHz/Torr, respectively. Errors are threefold uncertainties obtained from the spectra fitting which seems to be reasonable estimate taking into account possible sources of inaccuracies (finite SNR, pressure and temperature measurement, gas impurities and others). Our measured self-broadening coefficient is about 4.5% less than the value tabulated in To the best of our knowledge, self-shifting has never been studied for the pure rotational lines of CH3D as opposed to the lines of the excited vibrational states, e.g., for 5 [M_Devi2002_v5], 6

[M_Devi2002_v6], 3 [M_Devi2002_v3], 2 [Predoi-Cross2005_v2] bands. Both positive and negative shifts were observed with values varying from line to line from -0.014 to 0.004 cm-1/atm (-0.55 to 0.2 MHz/Torr). Our self-broadening parameter is within this interval thus confirming its validity.

Pressure shifting if not taken into account causes systematic uncertainty in the line center determining. The higher the operating pressure the larger the error. Since the pressure shifting was not taken into account in all previous experimental studies [Pickett1980, Womac1996, Lattanzi2008, Drouin2009, Bray2016], the problem of corresponding systematic error seems to be common. As an estimate, operating pressures were 0.05 Torr in [Womac1996], 0.28 Torr in [Lattanzi2008] and 0.75 Torr in [Bray2016] that give center shifting as 4, 24 and 64 kHz, respectively, if our measured shift coefficient is used. Corresponding uncertainties should be taken into account in the error budget by its summing with the statistical one, because both positive and negative shifts are equally probable.

In our measurements we estimate the maximum value of the systematic error as 35 kHz, which is comparable with the statistical uncertainty.

Fitting of the center positions and comparison with previous works

As can be seen from Table 1, three measured frequencies of the ground state transitions of Womack et al [Womack1996] and Pickett et al [Pickett1980] agree with our results within the combined experimental uncertainties. However, the present values are more accurate. Weak lines of a series of the Q-branch pure rotational transitions with J ranging from 1 to 11 and ΔK= +1 belonging to the collisionally excited first vibrational state 6 (1161 cm -1 ) were also recorded. In the second vibrational state 3 (1306 cm -1 ) of A1 symmetry, three weak rotational transitions of the R branch were observed as well as one Q-branch rotational line within the third excited state 5 (1472 cm -1 ) of E symmetry.

To determine the parameters of the ground state, THz transitions from Table 1 were included into the fit together with those measured previously by [Pickett1980], [Womac1996] [Lattanzi2008],

[Drouin2009], [Bray2016] and collected in Table 1 of [Bray2016]. The pure rotational transitions in first three excited states were also fitted by our effective polyad model constructed for the ground state and Triad interacting bands. The effective Hamiltonian was expressed in terms of irreducible tensor operators adapted to symmetric top C3V molecules. This approach implemented in MIRS package [Nikitin2003, Nikitin2012] was previously applied for CH3D [Nikitin1997] [Nikitin2000]

[Nikitin2002] [Nikitin2013CH3D], PH3 [Nikitin2017PH3], and recently for NF3 [Rodina2019] [Egorov2019]. The initial values of the effective Hamiltonian parameters were obtained by the contact transformation method [Tyuterev1980, Tyuterev2013] from the molecular potential energy surface [Nikitin2011] similarly to the procedure previously applied for CH4 spectra analyses. The line intensities predicted [Rey2014, Rey2016] from the ab initio dipole moment surfaces [Nikitin2013CH4, Nikitin2017CH4] using variational method [Rey2013] were employed for the line searching and transition assignments. *see details in [Nikitin1997] The rotational constants of the ground vibrational state corresponding to the K-dependence cannot be extracted from the pure rotational transitions due to ΔK = 0 selection rule. Therefore, the GSCD method was applied to obtain pure rotational transitions from IR line positions of CH3D analyzed previously in Triad [Nikitin2000], Nonad [Nikitin2002], and Enneadecad [Nikitin2006]

[Nikitin2013CH3D] regions of interacting bands. Finally, we fitted more than 11900 rotational transitions including 77 known from THz measurements. Thirteen ground state parameters of the irreducible tensor operators were determined (Table 2) from the total number of 23 with the standard deviation of 5.70 MHz (0.19×10 -3 cm -1 ). Eleven rotational transitions within the Triad vibrational states measured in this work (Table 1)

were fitted with the IR transitions from [Nikitin2002] and experimental energy levels of Ulenikov et al. [Ulenikov2000]. For more than 3640 transitions and 680 levels, the achieved standard deviation of 15.59 MHz (0.52×10 -3 cm -1 ) corresponds to the accuracy of the majority of the experimental data from [Nikitin2002]. The detailed statistical information of the fit of the parameters of the ground and 6, 3, and 5 excited states is presented in Table 3. The determined ground state parameters reproduce in most cases (in 61 out of 77) the experimental THz transitions within their experimental uncertainty. Examples can be seen in Table 1 and Table 4 (a total list of the deviations is given in supplementary material I; supplementary material II contains rotational energy levels up to J = 20). The calculated rotational transitions within three excited states 6, 3, and 5 fall into experimental uncertainty in half of the cases. However the number of the transitions is not so much to make the conclusion on the quality of the corresponding parameters, taking into account the possible resonance interactions at higher J values.

Conclusion

New high sensitive measurements of pure rotational transitions of CH3D by radio-acoustic method are presented. Pressure broadening and shifting of the 10-00 ground state rotational line were accurately measured and allowed estimating the possible systematic errors in some previous studies.

Among the 14 measured transitions, 3 correspond to the ground vibrational state. Other 11 lines were assigned to rotational transitions within first three excited vibrational states: 6=1, 3=1 and 5=1.

Experimental frequencies of the ground state transitions agree with the previous experimental data but the present results are more accurate. These transitions together with those published previously were described in most cases within their experimental uncertainties using our effective Hamiltonian expressed in irreducible tensor operators. For determining the rotational parameters of the Hamiltonian, more than 11800 ground state combination differences were also calculated and included into the fit. The obtained parameters will be used in our future works devoted to describing experimental intensities of pure rotational lines of CH3D measured by various experimental groups including those measured in this work.

  [Pickett1980] and byWomack et al. [Womac1996], who also measured two lines JK = 20-10 and JK = 21-11 around 465.25 GHz to analyze the telescopic observation toward Orion-KL.

[

  photomixing CW-THz spectrometer provided a relatively broad spectral coverage from 7K-6K to 11K-10K series. As a result of these studies, line positions are known for 70 lines with the relative uncertainty of 10 -7 and an accurate set of ground state molecular spectroscopic constants was obtained from the global fit analysis [Bray2016]. Intensities of 51 transitions were measured in the work[Bray2016] with the estimated accuracy of 25% providing a set of the dipole moment components.

Fig. 1 .

 1 Fig. 1. Experimental spectra of CH3D obtained using RAD spectrometer with BWO are shown by red circles. Acquisition details (number of scans and approximate radiation power) and observed line parameters (approximate position and intensity) are presented near each spectrum. Solid lines are fitted model functions.

Fig. 2 .

 2 Fig. 2. Experimental spectra of CH3D obtained using RAD spectrometer with the gyrotron are shown by red circles. Line parameters (approximate position and intensity) and acquisition details (number of scans and approximate radiation power) are presented in the insets. Solid line is fitted model function.

  HITRAN [HITRAN] with 2-5% uncertainty on the base of IR measurements [M_Devi2002]. The only previous measurement of the self-broadening of the THz lines of CH3D was performed by Bray et al [Bray2016] for the Q R(7) multiplet. Experimental values obtained with total uncertainty of 25% for six K-structure lines are scattered in the interval 0.079-0.09 cm -1 /atm (3.11 -3.55 MHz/Torr) and no K-dependence was observed. Our accurate value of self-broadening coefficient confirms the results of Bray et al [Bray2016] demonstrating as well good general agreement with the IR measurements in several excited vibrational band (see, e.g., Fig. 5 in [Bray2016] and references therein).

Fig. 3 .

 3 Fig. 3. Experimental line recordings of the ground state rotational transition JK = 10-00 obtained at different pressures and the result of the multispectra fitting. Pressure values are presented for each recording. Magnified (x5) residuals are demonstrated in the lower part.

Fig. 4 .

 4 Fig. 4. Pressure dependence of the line shape parameters of the ground state rotational transition JK = 10-00: (a) HWHM and (b) relative center position shifted by the value 232644.26 MHz. Error bars are statistical uncertainties obtained from the spectra fitting.

  Womack et al [Womac1996]. 200 b result of Picket et al[Pickett1980]. 201 c difference between the observed and calculated wavenumbers in kHz. 202 d  = 0, 1, 2 and 3 corresponds to 000000(A1), 000001(E), 001000(A1), and 000010(E) vibrational states; A 203 means no information on A1-A2 splitting. 204 e SNR was determined as a ratio of peak-to-peak signal amplitude to the noise standard deviation. 205 f Pressure shifting is taken into account. 206 207

Table 1 .

 1 Measured pure rotational transition of CH3D in the ground and excited vibrational states.

	Errors are 1- fitting uncertainty. Intensities are presented for 100% of 12 CH3D.
	Wavenumber in MHz	Δ c	Intensity in 10 -28 cm/molec	averages Number of	SNR e	Assignment d
	196367.89(24)	265	0.715	50	12	1 -1	11 1 E -11 0 E

' -'' J' K' Γ' -J'' K'' Γ''

Table 2 .

 2 Ground State Effective Hamiltonian parameters of CH3D (in MHz)

	208
	No	Parameter, Tensorial Nomenclature*	Value
	1	R2(0, 0A1)	130021.9620(38)
	2	R2(2, 0A1)	8387.2084(23)
	3	R4(0, 0A1)	-2.368268(44)
	4	R4(2, 0A1)	1.55723(16)×10 -1
	5	R4(4, 0A1)	7.06776(61)×10 -2
	6	R4(4, 3A1)	-2.35(28)×10 -2
	7	R6(0, 0A1)	1.1961(19)×10 -4
	8	R6(2, 0A1)	6.298(32)×10 -6
	9	R6(4, 0A1)	3.168(18)×10 -6
	10	R6(6, 0A1)	-1.445(49)×10 -7
	11	R8(0, 0A1)	-1.009(40)×10 -8
	12	R8(2, 0A1)	4.41(25)×10 -10
	13	R8(6, 6A1)	-2.08(21)×10 -10

Table 3 .

 3 Statistical information of the fit of the parameters of the ground and Triad vibrational states

	of CH3D
	Vibrational state	Number of data: THz / IR / Levels	Sources*	Jmax	SD
	Ground	77 / 11828 / 0	[P] [W] [L] [D] [B] TH / GSCD	19	5.70(0.19)
	6	7 / 1575 / 290	TH / [Nikitin2002] /	20	14.69(0.49)
			[Ulenikov2000]
	3	3 / 641 / 121	TH / [Nikitin2002] /	18	16.19(0.54)
			[Ulenikov2000]
	5	1 / 1417 / 270	TH / [Nikitin2002] /	18	15.89(0.53)
			[Ulenikov2000]

*THthis work results; GSCDtransitions were determined by ground state combination differences method (see details in the text); SDstandard deviation of the difference between experimental and calculated frequencies in MHz (×10 -3 cm -1 )

Table 4 .

 4 Examples of the experimental transitions (in MHz) fitted in this work *Theoretical transitions were calculated on the basis of energy levels from Table6of Ulenikov et al.

	Exp.*	Exp.-Calc.(kHz) This work Ulenikov et al.**	Assignment*** J' K' Γ' -J'' K'' Γ''
	465235.553(13) a	-17	108	2 1 E -1 1 E

****Information on A1-A2 splitting is not presented in experimental works used in the fitting

Acknowledgements

Experimental activities using RAD spectrometer were supported by Russian Science Foundation (project No 17-19-01602). Data analysis was performed at the V.E. Zuev Institute of Atmospheric Optics under state program No АААА-А17-117021310147-0. O.E. thanks the supports from Academic D.I. Mendeleev program and International Competitiveness Enhancement programme of Tomsk State University.


L Thomas

L Manceron

M Daumont

K Rey

A E E Sung

S Protasevich

Andrei V Nikitin

A A Rodina

X Thomas

L Daumont

M Rey

K Sung

A E Protasevich

S A Tashkun

I S Chizhmakova

Vl G Tyuterev

Line list of 12 CH 4 in the 4300-4600 cm -1 region

Keywords: high resolution spectra, CH 4, methane, Octad, long path FTIR, vibration-rotation states, intensities, infrared absorption, effective Hamiltonian

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

The aim of the present work is to improve the line list and to extend the assignments of weak and hot band transitions of 12 CH 4 in the 4300 -4600 cm -1 region of the Octad [START_REF] Hilico | Analysis of the interacting octad system of 12CH4[END_REF] [2] [3] [4] [START_REF] Rodina | Improved line list of 12CH4 in the 3760-4100 cm-1 region[END_REF]. The Octad band system (24 upper state vibrational sublevels) has been first studied by Hilico et al. [START_REF] Hilico | Analysis of the interacting octad system of 12CH4[END_REF] who also considered some hot bands [START_REF] Hilico | New analysis of the pentad system of methane and prediction of the (pentad-pentad) spectrum[END_REF] [START_REF] Ouardi | The hot bands of methane between 5 and 10 µm[END_REF] for lower polyads of methane. The Octad assignments have been extended in Refs. [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm-1[END_REF] , [START_REF] Daumont | New assignments in the 2μm transparency window of the 12CH4 Octad band system[END_REF] and a list of strong lines in the 4300-4600 cm -1 range for atmospheric applications has been published in Ref [START_REF] Hashemi | Spectroscopic line parameters of 12CH4 for atmospheric composition retrievals in the 4300-4500 cm-1 region[END_REF]. The present analysis is a continuation of a series of works [START_REF] Daumont | New assignments in the 2μm transparency window of the 12CH4 Octad band system[END_REF], [START_REF] Rodina | Improved line list of 12CH4 in the 3760-4100 cm-1 region[END_REF] using Fourier Transform spectra with long optical paths and represents a considerable improvement over previous works [START_REF] Hilico | Analysis of the interacting octad system of 12CH4[END_REF], [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm-1[END_REF].

Over decades, a better knowledge of methane infrared spectra has been demanded for various atmospheric and astrophysical applications [START_REF] Brown | Methane line parameters in the HITRAN2012 database[END_REF], [START_REF] Bernath | Molecular opacities for exoplanets Phil[END_REF], [START_REF] Tinetti | Spectroscopy of planetary atmospheres in our Galaxy[END_REF]. This task was motivated by new challenges related to remote sensing of planetary atmospheres. Among them, many studies have been focused on the study of radiative properties of the Titan atmosphere (Saturn's largest satellite), which is composed of 98.6% nitrogen and 1.4% methane at temperatures ranging between 70 K and 200 K [START_REF] Fulchignoni | In situ measurements of the physical characteristics of Titan's environment[END_REF] [13] [START_REF] Bergh | Applications of a new set of methane line parameters to the modeling of Titan's spectrum in the 1.58 μm window Plan[END_REF] [15] [START_REF] Bezard | The methane mole fraction in Titan's stratosphere from DISR measurements during the Huygens probe's descent[END_REF] [START_REF] Rey | New accurate theoretical line lists of 12 CH 4 and 13 CH 4 in the 0-13400 cm-1 range: Application to the modeling of methane absorption in Titan's atmosphere[END_REF]. Reliable parameters of methane absorption and emission bands are essential for accurate interpretation of the IR spectra provided by orbiting and ground-based observatories [START_REF] Buchwitz | Atmospheric carbon gases retrieved from SCIAMACHY by WFM-DOAS: version 0.5 CO and CH4 and impact of calibration improvements on CO2 retrieval[END_REF], [START_REF] Frankenberg | Satellite chartography of atmospheric methane from SCIAMACHY on board ENVISAT: Analysis of the years 2003 and 2004[END_REF], [START_REF] Bergamaschi | Satellite chartography of atmospheric methane from SCIAMACHY on board ENVISAT: 2. Evaluation based on inverse model simulations[END_REF], [START_REF] Schneising | Three years of greenhouse gas column-averaged dry air mole fractions retrieved from satellite -Part 2: Methane[END_REF], [START_REF] Nisbet | Rising atmospheric methane: 2007-2014 growth[END_REF]. The insufficient coverage and accuracy of spectral data became a major issue for investigations of outer planets [START_REF] Sromovsky | Comparison of line-by-line and band models of near-IR methane absorption applied to outer planet atmospheres[END_REF] [14] [START_REF] Hirtzig | Titan's surface and atmosphere from Cassini/VIMS data with updated methane opacity[END_REF]. Despite recent progress [START_REF] Nikitin | High resolution spectroscopy and the first global analysis of the Tetradecad region of methane 12CH4[END_REF] [24] [START_REF] Campargue | The WKLMC empirical line lists (5852-7919 cm-1) for methane between 80 K and 296 K: "final" lists for atmospheric and planetary applications[END_REF] [8] [START_REF] Brown | Empirical line parameters of methane from 1.1 to 2[END_REF] [START_REF] Rey | Ab initio variational predictions for understanding highly congested spectra: Rovibrational assignment of 108 new methane sub-bands in the icosad range (6280-7800 cm-1)[END_REF] [4] [START_REF] Niederer | Analysis of the rovibrational spectrum of 13CH4 in the Octad range[END_REF] [START_REF] Rodina | Improved line list of 12CH4 in the 3760-4100 cm-1 region[END_REF] in the methane modeling, available line lists [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] [START_REF] Jacquinet | The 2015 edition of the GEISA spectroscopic database[END_REF] [31] [START_REF] Wenger | Spherical top data system (STDS) software for the simulation of spherical top spectra[END_REF] [START_REF] Ba | Methane and ethene calculated spectroscopic databases for the virtual atomic and molecular data centre[END_REF] [34] [35] based on laboratory measurements do not yet provide all necessary information to reproduce atmospheric methane spectra in the near infrared. This is particularly the case of relatively weak absorption bands that significantly contribute to the absorption at long optical paths of planetary atmospheres [START_REF] Toon | HITRAN spectroscopy evaluation using solar occultation FTIR spectra[END_REF].

Because of high tetrahedral symmetry, some normal modes of methane are doubly or triply degenerate in the harmonic approximation and fall within nearby intervals. Additionally, there are accidental resonances due to near coincidence of fundamental vibrational frequencies and of their combinations (  1   3  2 2  2 4 ) that results in grouping vibrational levels into so-called polyads (Dyad, Pentad, Octad, etc…) [START_REF] Champion | Spectroscopy of the Earth's Atmosphere and Interstellar Medium[END_REF]. The vibrational energy levels with the same polyad number calculated from the four vibrational quantum numbers fall within the same energy range. In this work, we study the methane spectra belonging to the Octad band system with P=3. The scheme of 12 CH 4 vibrational states is shown in Figure 1.

The blown-up scale at the right-hand side represents the sub-band centers with their symmetry types, which are studied in the present work.

At room temperature, our observed line positions and intensities agree with a series of experimental lines reported in [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm-1[END_REF] [4] within experimental accuracy and could be well reproduced by our theoretical model. However, in some intervals of the 12 CH 4 Octad , the calculated line lists included in the databases [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] [30] cannot be used for modeling spectra at temperatures that considerably differ from 296 K. In the nearby ranges 4600-4850 cm -1 and 3760-4100 cm -1 ranges, the accuracy of spectra modeling was considerably better than that in the 4100-4600 cm -1 range, which is the subject of the present work. Erratic behaviors of some line intensities at temperatures other than room temperature could be due to incorrect quantum assignments of experimental transitions in the past and to wrong lower level energy values. On the whole, in the Tetradecad range, the linelist was recently composed and updated simultaneously with the improved assignments [START_REF] Nikitin | GOSAT-2009 methane spectral line list in the 5550-6236 cm-1 range[END_REF] [39] [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF]. This was not the case of the Octad range, where the list of transitions had been compiled before high-accuracy effective models became available [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm-1[END_REF] [4] [START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF]. A lot of observed line positions and intensities have been reported in Ref. [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm-1[END_REF], but the authors did not aim at providing a complete list of the observed and assigned transitions.

Furthermore, the spectra of methane isotopologues and hot transitions of (Tetradecad -Dyad)

band system, which fall in the same range, had not been available at the time of previous publications. Without this information, the full assignment of weak 12 CH 4 cold band transitions was complicated. In the present work, we report an extensive list of assigned transitions in the 4300 -4600 cm -1 range using experimental spectra recorded at various temperatures and path lengths. This linelist provides a more accurate description of experimental spectra at room and cold temperatures in comparison with currently available databases. The paper is structured as follows. Experimental spectra recorded in GSMA (Reims) and SOLEIL (Paris) at 100, 113, 123 and 290 K are described in Sections 2a and 2b. Section 3 is devoted to the determination of line parameters and Section 4 to spectra assignments. Section 5

gives the information on newly assigned line lists provided in the Supplementary Materials.

Experiment

In this study, we used a large set of Fourier transform spectra (FTS) recorded in the GSMA Laboratory at Reims University. Some of the spectra have already been presented in former publications concerning specific studies [START_REF] Daumont | New assignments in the 2μm transparency window of the 12CH4 Octad band system[END_REF][START_REF] Nikitin | Measurements and modeling of long-path 12CH4 spectra in the 4800-5300 cm-1 region[END_REF][START_REF] Nikitin | Assignment and modelling of 12CH4 spectra in the 5550-5695, 5718-5725 and 5792-5814 cm-1 regions[END_REF][START_REF] Nikitin | First assignment of the 5v4 and v2+4v4 band systems of 12CH4 in the 6287-6550 cm-1 region[END_REF]. In the series of experimental studies, a 50 m base multipass cell of GSMA has been optically configured to high-resolution step-by-step spectrometer as first described in [START_REF] Daumont | New assignments in the 2μm transparency window of the 12CH4 Octad band system[END_REF] [5] [START_REF] Nikitin | Measurements and modeling of long-path 12CH4 spectra in the 4800-5300 cm-1 region[END_REF] [40] [START_REF] Nikitin | Assignment and modelling of 12CH4 spectra in the 5550-5695, 5718-5725 and 5792-5814 cm-1 regions[END_REF]. The absorption path lengths were set to 202, 602, 1603 meters by adjusting the number of the transverse beams inside the 50 meters based White-type gas cell. The methane gas used to fill the cell is a natural abundance sample, and the pressures varied from 1 to 25 Torr, as described in Table 1. The spectrometer is based on the Connes principle and its apparatus function is mainly determined by the maximal optical path difference (MOPD) and by the apperture chosen at the entrance of the spectrometer. During the experiment, the average cell temperature was controlled with fluctuations in time that did not exceed two degrees.

The first series of spectra with 1600 m absorption path-length in the 1.6 µm window of methane (e.g., H-band) has been explored [START_REF] Nikitin | First assignment of the 5v4 and v2+4v4 band systems of 12CH4 in the 6287-6550 cm-1 region[END_REF] for the Titan atmospheric spectra analysis [START_REF] Hirtzig | Titan's surface and atmosphere from Cassini/VIMS data with updated methane opacity[END_REF]. In this work, most of the measured lines were obtained from E, F, H, I spectra (see Table 1). G and J spectra were only used to check the intensities of the weak lines. F and I spectra recorded at a pressure of 5 Torr were used to determine the positions and check the intensities of the weak lines in the 4300-4500 cm -1 range and to determine the positions and check the intensities of some strong lines in the 4500-4600 cm -1 range. The spectra E and H were only used to check the positions and intensities of the strongest lines in the region. Because of significant spatial temperature grаdients within the cell for low-T conditions , the Reims spectra A, B, C were used to determine positions of weak lines only at the initial stage of work. Six spectra were recorded at low temperature at Synchrotron SOLEIL using the long path cryogenic cell described in reference [START_REF] Tchana | low temperature long-pass cell for mid-infrared to terahertz spectroscopy and synchrotron radiation use[END_REF] and the Bruker 125 HR interferometer. The optical path length in the cell was set to 93.14(1) meters for all these recordings. Such a long path length would make the strong lines in the region easily being saturated and subject to unwanted nonlinearity effects unless the sample pressure was used sufficiently low. At the low sample pressure, however, the pressure readings of the cold cell become uncertain due to thermomolecular effects, especially when the pressure sensor is placed outside the cell, as was the case for our setup. To avoid these possible issues, the methane sample was diluted in pure nitrogen gas in a 3L container at a 0.100(1)% mixing ratio and precisely measurable amounts (0.917 to 2.52 mbar) were introduced in the cell [START_REF] Lago | A rugged, high precision capacitance diaphragm low pressure gauge for cryogenic use[END_REF]. The mixing ratio was chosen so that nitrogen pressure broadening is not an issue here. The relative uncertainty on the methane pressure is estimated to be about 1.5%. The spectra were recorded using a Si/CaF 2 beamsplitter, a scanner optical velocity of 5.06 cm/s, a low pass filter with 40 kHz cut-off and a 120 cm maximum optical path difference. This corresponds to 0.0075 cm -1 resolution, according to Bruker"s definition, which is about the Doppler linewidth at this temperature. The spectra were obtained with no apodization and 2400 scans were averaged for each of them. Wavenumber calibration was carried out using both weak residual water lines and CO lines resulting from a special spectrum recording. For this spectrum, a separate mixture containing 0.0053 torr of CO with a trace amount of methane was used. For spectra M-Q, an agreement within 3% (1σ) for the CO intensities available in HITRAN-2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] was obtained. The average temperature was measured in two ways: a value T= 100 ± 3 K was obtained using 12 different temperature sensors along the optical path giving about 3 K uncertainty (1σ) [START_REF] Tchana | low temperature long-pass cell for mid-infrared to terahertz spectroscopy and synchrotron radiation use[END_REF]. Secondly, using the CO 2-0 line intensities of the calibration spectrum, an average temperature of 99 ± 3K was obtained, consistent with the sensor's direct temperature measurement. In the 4300-4600 cm -1 range, S and T spectra recorded at 112 and 123 K were used to determine line positions and intensities for low J values mostly for weak lines. The same setup as for spectra M-Q was used for spectra R-T.

Line parameters in the 4300 -4600 cm-1 region

All positions and intensities have been obtained using the SpectraPlot software [START_REF] Nikitin | Visualization and identification of spectra by the SpectraPlot, Visualization and identification of spectra by the SpectraPlot program[END_REF] from spectra recorded in Reims and Paris. All spectral features with intensities > 1.0×10 -25 cm - 1 /(molecule•cm -2 ) and many of the lines with intensities between 1.0×10 -25 and 2.0×10 -26 cm - 1 /(molecule•cm -2 ) were retrieved. At the first stage, we used the same technique as described in [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF]. Line parameters of low J values were obtained from Spectrum S and T at 112 and 123 K, respectively. Then, we used the fixed parameters determined from the low J lines to obtain the parameters of strong lines from the spectra recorded with the optical path L = 201.84 meters. At the next stage, we fitted weak lines using the spectra E, F, G, I, and J. The final fit was made using the six room-temperature spectra E -J and spectrum T recorded at 123 K. In this case, some positions of the low J lines were set to values previously obtained from cold spectra.

Calibration of spectra A, B, and C was carried out in the similar way as in Ref. [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF]. The previously observed methane lines and CO 2 transitions were used to calibrate the spectra E, F, G, H, I, and J. The CO transitions were used to calibrate the spectra K and L. For spectra A, B and C, the calibration was checked for selected residual water transitions from the HITRAN-2016 database. The average shift of these transitions was 5.0 × 10 -6 cm -1 . When the spectra with different pressures were used for a simultaneous fitting, the self-pressure-induced line shift parameter was assumed to be the same for all lines equal to -0.013 cm -1 /atm [START_REF] Devi | Self-and air-broadened line shape parameters in the ν2+ν3 band of 12CH4: 4500-4630 cm-1[END_REF].

The strongest lines of 12 CH 4 (with intensities > 3.×10 -23 cm -1 /(molecule•cm -2 )) were almost saturated in several spectra (1 Torr, 201 meters ) in the 4300-4600 cm -1 range. For these few transitions the previously observed lines of Ref. [START_REF] Hilico | Analysis of the interacting octad system of 12CH4[END_REF] or HITRAN-2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] These comparisons show that HITRAN-2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] provides correct integrated methane absorption on the entire scale, but the line-by-line list fails to reproduce spectra at low temperatures in the considered range under high resolution. It would not provide reliable simulations of methane absorption for some spectral features when the temperature conditions significantly differ from 296 K. Furthermore, Figure 7 illustrates that, in some cases, previously available line lists inaccurately describe observed spectra in some intervals even at 296 K. As many other empirical compilations, it comprised a mixture of quite accurate laboratory measurements and extrapolations using the effective Hamiltonian and effective dipole moment models. Figures 5 and7 illustrate that HITRAN-2016 database (and other empirical compilations as well) contains some transitions in this range, for which line positions and intensities have significant errors beyond their reported uncertainties. This mostly concerns several series of weak and medium lines with intensities in the range 3×10 -23 -1×10 -24 cm -1 /(molecule•cm -2 ). An invalid assignment of transitions could lead to errors in the temperature dependence and to inaccurate interpretation of the observed transmittance in terrestrial and planetary atmospheric for some spectral intervals.

A sample of seventeen isolated lines observed in this work (TW) with intensities in the range [1×10 -24 -3×10 -23 ] cm -1 /(molecule•cm -2 ) is listed in Table 2. The third column shows the intensities ratio from HITRAN-2016 line list, ratioed to the corresponding intensities of this work in the third column. The fourth column gives the ratio of ab initio line intensity to that measured in this work. Initially, these theoretical predictions were obtained using ab initio ACVQZ dipole moment surface [START_REF] Nikitin | New dipole moment surfaces of methane[END_REF] and global variational calculations [START_REF] Rey | First principles intensity calculations of the methane rovibrational spectra in the infrared up to 9300 cm-1[END_REF] [52] [START_REF] Rey | Complete nuclear motion Hamiltonian in the irreducible normal mode tensor operator formalism for the methane molecule[END_REF] as included in the TheoReTS information system [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF]. Some lines listed in Table 2 were considered "unstable" in terms of the classification described in Ref [START_REF] Nikitin | Accurate line intensities of methane from first-principles calculations[END_REF] due to sharp accidental resonances. In the last column of Table 2, the corresponding outliers of variational calculations were smoothed using accurate wavefunctions of the optimaised EH. Table 2 shows that the intensities obtained in this work for the seventeen relatively strong lines listed are much closer to the best available ab initio intensities [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF] and 7% higher than those HITRAN-2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] [1]. The integrated intensities (obtained by summation of intensities of all lines) in the range 4300-4600 cm -1 are shown in Table 3. The integrated intensities of our observed line list are close to the integrated intensities of HITRAN-2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. The integrated intensities of [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF] and GEISA [START_REF] Jacquinet | The 2015 edition of the GEISA spectroscopic database[END_REF] appear to be larger by 5-7% than those of this work. There are two factors contributing to this difference: greater intensities of the strong and intermediately strong lines and much larger number of weak lines incorperated in full variational calculations [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF]. The average absolute uncertainty of the intensities measured in this work is estimated as 5-10%. The factors influencing the accuracy include temperature fluctuations of ~ 1.5 degrees and a large aperture of 3-5 mm for the Reims spectrum sets. Considerable numbers of transitions with intensities below 1 × 10 -24 cm -1 / (molecule • cm -2 ) are found to be blended, and an empirical determination of transition intensity strongly depends on the neighboring lines. In many cases, the lower J was not known, and a default lower state energy value of 814.6 cm -1 was used. Since the Reims spectra were recorded at a temperature of T = 291 K, recalculation of the intensities of such transitions at T = 296 K could be incorrect for the unassigned lines. Note, that the 113 K spectrum was particularly useful for transitions blended by higher J lines in the room temperature spectra.

However, for more accurate measurement of intensities, further extension of assignments and recording of spectra with a shorter optical path and better temperature stabilization is necessary.

Spectra assignment

The line-by-line assignment of spectra relies on a comparison of calculated lists that contain complete quantum identifications with observed spectra. Previous works on the assignment of crowded methane spectra in the range of Octad [1] [9] have not been sufficiently complete to cover transitions of all sub-bands.

The traditional approach for spectral analyses based on effective Hamiltonian (EH) and effective dipole moment (EDM) models ( see for example [START_REF] Champion | Spectroscopy of the Earth's Atmosphere and Interstellar Medium[END_REF] [56] [35] and refs therein) had faced the well-known issues related to rapidly increasing number of adjustable parameters.

Thanks to improved ab initio calculations of the potential energy surfaces (PES) and of dipole moment surfaces (DMS) [START_REF] Nikitin | First fully ab initio potential energy surface of methane with a spectroscopic accuracy[END_REF], [START_REF] Nikitin | New dipole moment surfaces of methane[END_REF], [START_REF] Cassam-Chenai | Ab initio calculation of the rotational spectrum of methane vibrational ground state[END_REF], [START_REF] Cassam-Chenaï | An improved third order dipole moment surface for methane[END_REF], [START_REF] Owens | A highly accurate ab initio potential energy surface for methane[END_REF], [START_REF] Majumder | Explicitly correlated MRCI-F12 potential energy surfaces for methane fit with several permutation invariant schemes and full-dimensional vibrational calculations[END_REF] and to global variational calculations [START_REF] Rey | First principles intensity calculations of the methane rovibrational spectra in the infrared up to 9300 cm-1[END_REF] [52] , a better understanding of absorption bands in spectra of methane isotopologues has become posssible [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF] [62] [START_REF] Rey | First Predictions of Rotationally Resolved Infrared Spectra of Di-Deuteromethane (12CH2D2) From Potential Energy and Dipole Moment Surfaces[END_REF] [64] [START_REF] Starikova | Assignment and modeling of the absorption spectrum of 13CH4 at 80K in the region of the 2v3 band (5853-6201cm-1)[END_REF] . In particular, global theoretical line lists [START_REF] Rey | New accurate theoretical line lists of 12 CH 4 and 13 CH 4 in the 0-13400 cm-1 range: Application to the modeling of methane absorption in Titan's atmosphere[END_REF], [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF] for astrophysical applications [66] [67] [START_REF] Yurchenko | ExoMol line lists-IV. The rotation-vibration spectrum of methane up to 1500[END_REF] [69] [START_REF] Hargreaves | An Accurate, Extensive, and Practical Line List of Methane for the HITEMP Database The[END_REF] had been generated at various temperature conditions from 50 K up to 3000 K. These theoretical studies cited above have permitted a qualitative agreement of band intensities with experiments and an improvement of predictions for the band centers [START_REF] Nikitin | First fully ab initio potential energy surface of methane with a spectroscopic accuracy[END_REF] [60], however the accuracy of purely ab initio line positions is not yet sufficient for high-resolution atmospheric applications.

A recent progress in methane spectra analyses [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF] [71] [START_REF] Ghysels | The methane absorption spectrum near 1.73 μm (5695-5850 cm -1 ): Empirical line lists at 80 K and 296 K and rovibrational assignments[END_REF] was due to a "combined approach" [START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF] that comprised three steps. First, the ab initio based effective EH polyad models were derived from the molecular PES via a high order Contact Transformation (CT) method [START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF]. This provided realistic estimations for the coupling parameters between various rovibrational bands and for related resonance perturbations in the observed spectra. Finally, a fine tuning of a reduced set of empirically adjusted parameters permitted to extend the number of assigned lines. The formalism of irreducible tensor operators (ITO) [START_REF] Zhilinskii | Method of Irreducible Tensorial Operators in the Theory of Molecular Spectra[END_REF] [37], implemented in the MIRS computational code [START_REF] Nikitin | Extension of the MIRS computer package for modeling of molecular spectra: from effective to full ab initio ro-vibrational hamiltonians in irreducible tensor form[END_REF], was used for a full account of tetrahedral symmetry properties of the methane molecule.

A more detailed discussion can be found in refs [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF] [71] [START_REF] Nikitin | Measurements and modeling of long-path 12CH4 spectra in the 4800-5300 cm-1 region[END_REF] devoted to assignments of different parts of the Tetradecad [START_REF] Nikitin | Measurements and modeling of long-path 12CH4 spectra in the 4800-5300 cm-1 region[END_REF] [71] [START_REF] Ghysels | The methane absorption spectrum near 1.73 μm (5695-5850 cm -1 ): Empirical line lists at 80 K and 296 K and rovibrational assignments[END_REF] in previous analyses. In this work, we used the most recent EH of [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF] obtained via the "combined approach" [START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF] as an initial model to extend assignments in the present spectral range. Exact KEO * , Ref [START_REF] Nikitin | An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: tetrahedral molecules[END_REF], PES [START_REF] Nikitin | First fully ab initio potential energy surface of methane with a spectroscopic accuracy[END_REF] CT # Ref [START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF], PES [START_REF] Nikitin | Rotational and vibrational energy levels of methane calculated from a new potential energy surface[END_REF]

Number

Fitted lines RMS (10 Notes:

In total, 886 EH parameters were adjusted to fit more than 34000 measured 12 CH 4 line positions from the Dyad up to the lower edge of the Icosad range. It was necessary to include all this data because the parameters of low lying polyads contribute to higher polyads according to the EH polyad extrapolation scheme [37] [42] . Ten ground state 6 th -order parameters were fixed to the values of Ref. [START_REF] Champion | The vibrational ground state of 12CH4 and 13CH4[END_REF], and 62 parameters of the Dyad were empirically optimized. Of the total number of symmetry-allowed 382, 1202, and 2539 EH 6 th -order parameters specific to the Pentad, Octad, and Tetradecad, only a restricted set of 211, 279, and 329 parameters were adjusted. These samples of adjusted EH parameters correspond to the choise of our previous works [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF] [72] [START_REF] Nikitin | Assignment and modelling of 12CH4 spectra in the 5550-5695, 5718-5725 and 5792-5814 cm-1 regions[END_REF]. The major sets of remaining parameters were held fixed to the theoretical predictions from the molecular PES via the CT method [START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF] . The obtained RMS (calculatedobserved) deviation for line positions 0.0014 cm -1 is closed to the average descrepancies of combination differences for the upper level energy ~ 0.001cm -1 , obtained using several transitions .

The methane line list with assignments

In the Supplementary Materials of this work, we provide the line list compiled at 296 K, including quantum assignments. Table 5 shows a sample of this list . It includes the observed positions and intensities (at 296 K), the quantum assignments following the notations described in Ref [START_REF] Nikitin | Measurements and modeling of long-path 12 CH 4 spectra in the 5300-5550 cm -1 region[END_REF], and lower state energies. Self-broadening and air-broadening coefficients obtained from Refs. [76] [77] were added to our final line list. More recent values of self-broadening and air-broadening coefficients in the Octad region have also been obtained in Ref. [START_REF] Devi | Self-and air-broadened line shape parameters in the ν2+ν3 band of 12CH4: 4500-4630 cm-1[END_REF] (see Refs.

[78] [79] [START_REF] Kochanov | Methane line shapes and spectral line parameters in the 5647 - 6164 cm-1 region[END_REF] for the tetradecad region). Isotopic lines were identified using the line list of 13 CH 4 obtained from the spectrum of enriched 13 CH 4 [START_REF] Brown | Measurements and modeling of cold 13CH4 spectra in the 3750-4700 cm-1 region[END_REF] . -1 ]. Order of priority: exact assignment, lower J, observed E lower, default E lower corresponded to J=12 (see Text). f Self-Broadening coefficient obtained from [START_REF] Lyulin | Measurements of selfbroadening and self-pressure-induced shift parameters of the methane spectral lines in the 5556-6166 cm-1 range[END_REF].

g Air-Broadening coefficient obtained from [START_REF] Lyulin | Measurements of N2-and O2-broadening and shifting parameters of methane spectral lines in the 5550-6236 cm-1 region[END_REF] An overall comparison of 12 CH 4 line-stick diagrams in the considered spectral range 4300-4600 cm -1 from the three line list is shown in Fig. 8. This includes HITRAN2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF], experimental list of the present work, and the ab initio born list of TheoReTS database [START_REF] Cassam-Chenai | Ab initio calculation of the rotational spectrum of methane vibrational ground state[END_REF] produced by variational calculations. At this large scale of Fig. 8, all line lists look similar. However, the detailed comparisons of observed and calculated spectra shown in Fig. 5 -7 reveals considerable differences for medium and weak lines between the HITRAN2016 list and this work. TheoReTS [START_REF] Rey | TheoReTS -An information system for theoretical spectra based on variational predictions from molecular potential energy and dipole moment surfaces[END_REF] based on ab initio dipole moment [START_REF] Nikitin | Accurate line intensities of methane from first-principles calculations[END_REF].

Conclusion

The main results of the present spectrum analysis in the 4300-4600 cm -1 region are the extended assignments and improved line lists provided in the Supplementary Materials. More than 7000 new lines of 12 CH 4 up to J = 21 were assigned in experimental FTS spectra recorded at various temperatures using a combined approach involving ab initio calculations with subsequent empirical optimization of the effective model. Upper state energy levels were obtained using empirical adjustment of a restricted subset of EH parameters, which were statistically welldetermined in the fit. This approach allowed us to find our several significant outliers in available compilations of methane line lists in this range based on previous empirical extrapolations. These results will permit including new assignments in a forthcoming updates of HITRAN [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] and GEISA [START_REF] Jacquinet | The 2015 edition of the GEISA spectroscopic database[END_REF] spectroscopic databases.

Fig. 1 .

 1 Fig. 1. Vibrational levels of the 12 CH 4 polyads (left side) and the vibrational sublevels of a part of Octad (right side) corresponding to rovibrational bands analyzed in this work. The right hand side panel displays the principal vibration quantum numbers (υ 1 υ 2 υ 3 υ), symmetry types of vibration sublevels, and vibrational ranking numbers within the Octad. The symmetry types correspond to irreducible representations of the T d point group [42] [37].

Fig. 2 .

 2 Fig. 2. Example of quantum number assignments in the 12 CH 4 spectra. The upper panel shows residuals (obs-calc) for three spectra (orange 602 m at 289 K and green Reims 201 meter spectra at 291 K, blue S, T cold spectra). Next panel below shows 602 meter (black) and two calculated spectra (orange). Next panel below shows the 201 meter observed spectrum in black, two calculated 201 m spectra (green). Next panel S, T shows observed spectra and two corresponding calculated spectra. Next panel shows assigned experimental line sticks and the lowest panelour calculated intensity sticks at 296 K.

Fig. 3 . 1 Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .

 314567 Fig. 3. The same as in Fig. 2, except for the spectral region of 4402.4-4403.4 cm -1

Fig. 8

 8 Fig. 8 Line stick diagrams obtained from four line lists in the 4300-4600 cm -1 range. From top downward: HITRAN2016; This work (observed line list); Variational calculations from

Table 1 . Experimental conditions for the series of CH 4 spectra in the Octad range. Spectrum ID Iris Diameter, Focal length (mm)

 1

					Absorption
			Pressure (Torr)	Temperature (K)	path
					(m)
		GSMA FTS spectra recorded in Reims
	A		3.43	110	8.52
	B	4.5, 1040	4.17	113	32.52
	C		3.28	113	80.52
	E		1.06	292
	F	4, 1040	5.03	291	201.84
	G		25.98	289
	H		1.05	289
	I	4, 1040	5.08	290	602.32
	J		25.11	289
	K		1.065	289
		3.5, 1040			1603
	L		4.070	288
		SOLEIL FTS spectra recorded in Paris
	M		0.0073
	N		0.0019
	O P	1.5, 418	0.00159 0.00155	100	93.14
	Q		0.00068
	R		0.00094	102
	S		0.03	112
	T		1.16	123

  values were incorporated in our final line list. The corresponding 209 lines are flagged with H. Some 8619 12 CH 4 transitions are now assigned in the 4300-4600 cm -1 region that is to compare with 2834 experimental transitions assigned in Refs [2] [3]. Detailed examples of newly measured and assigned transitions are shown in Figs. 2-4 for the 4308-4513 cm -1 region. A comparison of observed and calculated spectra at 123 K using both the present work and HITRAN-2016 [29] line lists is shown in Figs 5-6 for the 4338-4443 cm -1 range. In these examples, we compare new data with HITRAN-2016, which is the most frequently used database for atmospheric applications, but the general conclusions are also valid for other existing empirically fitted line lists. HITRAN-2016 spectroscopic database [29] contains 29009 transitions of 12 CH 4 in this range with the intensity cutoff 1×10 -29 cm -1 /(molecule•cm -2 ), only about 10% of these lines being measured and assigned in laboratory spectra [2] [3].

Table 2 . Example of intensities for seventeen isolated lines in the 4300 -4600 cm -1 region.

 2

	Line	Line intensity	Intensity ratio to TW
	position a	This work b	HITRAN-2016	Ab initio c
	4309.370639	15.61	0.86	0.98
	4338.140149	6.999	0.54	0.99
	4353.040613	17.28	1.06	0.88
	4391.662283	4.798	0.93	0.91
	4415.850673	15.57	0.59	0.96
	4418.536734	19.12	0.86	1.00
	4425.295494	18.67	0.83	0.98
	4455.944122	63.21	1.20	1.06
	4502.424255	62.86	1.00	1.01
	4508.039449	22.22	0.96	0.98
	4508.413075	41.06	0.98	1.02
	4560.096669	2.887	0.74	1.05
	4560.374781	21.53	1.28	0.97
	4569.715772	16.46	0.99	1.00
	4577.868249	46.67	1.08	1.04
	4588.477338	13.37	0.98	1.02
	4588.704137	11.74	0.96	0.97
	Average ratio	0.93	0.99
	Notes:

a wavenumber measured in this work [cm

-1

]. b intensity measured in this work in 10 -24 cm -1 /(molecule•cm -2 ) c with corrected outliers of "unstable lines " ( see the text )

Table 3 .

 3 Integrated methane intensities in the range 4300-4600 cm-1

	Source	#lines	S Int*
	This work : observed intensities	14151	3.98***
	This work : calculated from empirically	24221	3.90
	fitted EDM model
	This work: calculated from ab initio based	23812	4.21
	EDM intensities (EDM fitted to variational
	intensities [54] computed using ACVQZ
	dipole moment)
	Full variational ab initio based list [54] ** 286635	4.20
	HITRAN-2016 [29] ( 12 CH 4 only)	29009	4.09
	GEISA-2015 [30]	22127	4.18
	* Sums of line intensities (10 -19 cm/molecule)
	** Ab initio intensities computed with ACVQZ DMS [55], see TheoReTS [54] including hot
	bands (for natural 12 CH 4 abundance)
	*** contains 13 CH 4

Table 4 . Line position and intensity statistics for 12 CH 4 transitions at 296 K corresponding to the studied range 364

 4

	357
	358
	359
	360
	361
	362
	Vibration upper state symmetry levels,	This work Energy cm -1 Vibration	Calculated from PES	Line positions	Line intensities

-3 cm -1 ) JMin JMax

								Number
								Fitted	RMS %
								Transit.
	(0003) F2	3870.485238	3870.506	3870.839	2	1.68	17	0
	(0102) E	4101.391836	4101.426	4102.026	4	2.47	15	2	4.19
	(0102) F1	4128.763930	4128.744	4129.233	63	2.28	8	46	1.04
	(0102) A1	4132.863475	4132.874	4133.553	27	1.60	8	17	9.46
	(0102) F2	4142.861828	4142.810	4143.119	48	1.55	8	33	8.98
	(0102 ) E	4151.202962	4151.164	4151.558	38	2.36	8	20	9.43
	(0102) A2	4161.840387	4161.793	4162.141	61	1.71	8	40	8.48
	(1001) F2	4223.460976	4223.566	4223.569	283	1.73	6	207	9.43
	(0011) F2	4319.208149	4318.958	4319.412	772	1.61	0	607	9.91
	(0011) E	4322.188360	4321.946	4322.485	598	1.43	1	466	1.08
	(0011) F1	4322.590936	4322.351	4322.744	1090	1.45	1	829	1.02
	(0011) A1	4322.691766	4322.429	4323.024	449	1.52	1	357	9.73
	(0201) F2	4348.718167	4348.742	4349.458	744	1.61	0	423	9.75
	(0201) F1	4363.607752	4363.608	4364.108	653	1.40	1	391	9.97
	(0201) F2	4378.948765	4378.943	4379.351	693	1.49	1	376	1.06
	(1100) E	4435.125649	4435.277	4435.232	750	1.41	1	436	9.29
	(0110) F1	4537.550360	4537.353	4537.746	998	9.89	1	479	9.59
	(0110) F2	4543.760944	4543.574	4544.081	1117	9.49	0	569	1.02
	(0300) E	4592.036524	4592.117	4592.830	124	1.46	1	59	8.17
	(0300) A2	4595.278804	4595.276	4595.667	47	1.04	1	17	8.00
	(0300) A1	4595.515674	4595.544	4595.976	44	1.17	2	28	4.85
				Total	8605	1.386		5402	9.9

Table 5 .

 5 Sample of Electronic Supplementary data. Methane at 296 K with assignments in the 3760-4100 cm -1 region.

	Key	positions	Intensity cm -1	Rotational assignment d	E low estimates
	a	 0 (cm -1 ) b	2 ) /(molec•cm -		(cm -

1 ) e Self HW f (cm -1 /atm) Air HW g (cm -1 /atm) Lower state Upper state

  + assigned line, -unassigned line, 3 corresponds to13 CH 4 , Hline from HITRAN b measured line positions. Lower and upper state rovibrational assignments are given by the vibrational polyad number P, the rotational quantum number J, the rovibrational symmetry type C (T d irreducible representation) and the rovibration ranking index α.

	+	4300.386978 1.892e-23 0 14 A1 1 3 14 A2 35 1095.828 0.061	0.0416
	+	4300.390664 7.933e-25 0 16 F1 3 3 17 F2 76 1417.807 0.054	0.0316
	-	4300.395409 2.357e-24	814.646	0.066	0.0499
	+	4300.408638 5.657e-24 0 10 E 2 3 10 E 51 575.271	0.071	0.0565
	+	4300.450200 3.049e-23 0 11 F2 2 3 11 F1 84 689.876	0.069	0.0534
	+	4300.456513 2.247e-23 0 11 E 1 3 11 E 55 689.886	0.069	0.0534
	H 4300.459438 1.063e-22 0 12 F1 2 3 12 F2 94 814.884	0.066	0.0499
	+	4300.461964 3.824e-25 1 7 F2 4 4 7 F1 120 1631.804 0.076	0.0630
	+	4300.501773 2.576e-24 1 3 A1 1 4 3 A2 17 1369.017 0.079	0.0657
	+	4300.502860 1.440e-24 0 16 F1 2 3 16 F2 129 1417.129 0.054	0.0316
	+	4300.310020 1.726e-24 0 11 F2 3 3 11 F1 84 690.017	0.069	0.0534
	Notes:
	+	4300.310020 1.726e-24 0 11 F2 3 3 11 F1 84 690.017	0.069	0.0534
	+	4300.320078 2.460e-25 0 16 F2 3 3 16 F1 126 1417.753 0.054	0.0316
	+	4300.347522 6.940e-25 0 16 F2 4 3 16 F1 127 1418.137 0.054	0.0316
	H 4300.365965 1.732e-21 0 3 A2 1 3 2 A1 8	62.878	0.079	0.0656

a c I(296 K): measured line intensities in cm/molecule. d e E low : recommended value for the lower state energy [in cm

*) using exact kinetic energy operator (KEO) in internal curvilinear coordinates[START_REF] Nikitin | An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: tetrahedral molecules[END_REF]

#) using contact transformation (CT) method in normal coordinated[START_REF] Vl | Accurate spectroscopic models for methane polyads derived from a potential energy surface using highorder contact transformations[END_REF]

Acknowledgments

The supports of the CNRS (France) in the frame of "Laboratoire International Associé SAMIA", of the French ANR project e-PYTHEAS (ref: ANR-16-CE31-0005), of the ROMEO computer center Reims-Champagne-Ardenne and of Academic D.Mendeleev program of Tomsk State University ( Russia) are acknowledged. Part of the research was performed at Institute of Monitoring of Climatic and Ecological Systems under contract of Russian Science Foundation (RSF), grant No. 19-77-10046. Part of the research was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Part of the research was performed at Synchrotron SOLEIL (Project 99180032).