N Komiya

K Hatada

F Ota

P Krüger

T Fujikawa

K Niki
email: niki@chiba-u.jp

Multiple scattering approach to photoemission from the highest occupied molecular orbital of pentacene

Keywords: ARPES, Multiple scattering 2010 MSC: 00-01, 99-00

Angle resolved photoemission spectroscopy (ARPES) gives detailed information about the surface electronic structures and oriented molecules. In the so-called orbital tomography method, the ARPES intensity is obtained by a simple Fourier transform of the initial state molecular orbital. While this method has given good results for a number of π-orbital systems, it is known to have strong limitations because the final state is approximated as a plane wave and thus photoelectron scattering is completely neglected. Here we propose an ARPES theory where the initial states are taken from a quantum chemistry method and the final states are calculated in multiple scattering theory. The initial molecular orbitals are reexpanded in a multi-site spherical wave basis and the multiple scattering potential is constructed from the ab initio charge density. These computations are performed algebraically using newly developed algorithms. The method is applied to pentance and the results are compared with the plane wave approximation.

Introduction

In the last decades, intensive research has been done on organic semiconductors composed of π conjugated organic molecules such as pentacence [1,2]. Compared to traditional inorganic materials, organic semiconductors are flexible, lightweight and cost-effective [START_REF] Loo | Proc. Natl. Acad. Sci[END_REF][START_REF] Forrest | [END_REF]. As organic semiconductors absorb light in visible region and often show electronic conductivity, they have potential for the applications such as organic light emitting diodes (OLEDs), organic solar cells (OSCs), and organic field effect transistors (OFETs) [START_REF] Forrest | [END_REF]5,6].

Angle resolved photoelectron spectroscopy (ARPES) is a powerful tool to investigate the electronic structure of surfaces. For photon energies of a few tens of eV, the photoelectron has a short inelastic mean free path and so the near surface region is probed.

Recently, P. Puschnig et al. [7] have developed the socalled orbital tomography method, by which the real space charge density of selected molecular orbitals can be reconstructed from the ARPES data. The orbital tomograph 20 method relies on the plane wave (PW) approximation for the final state. Since the photoelectron energy is fairly low in ARPES, electron scattering at the molecular potential is expected to be strong and the validity of the PW approximation is questionable [8]. One of the examples 25 where the PW approximation fails is circular dichroism in ARPES intensity [9]. Because the PW approximation gives exactly same intensity maps with a right and left handed light.

Photoelectron scattering effects can conveniently be 30 taken account for using multiple scattering (MS) theory [10,11,12]. Usually single atom data is used for the construction of the scattering potentials. However, such potentials are inconsistent with the molecular orbital electronic structure. Here we overcome this shortcoming by constructing 35 the MS potential from the electronic structure as given by a quantum chemistry method. For a gaussian-type orbital basis (as used, e.g. in the GAUSSIAN 09 code [START_REF] Frisch | Gaussian 09 Revision E.01[END_REF]). we have developed analytical formula and algorithms for mapping the molecular orbitals onto a MS spherical har-40 monics basis and have constructed the corresponding MS potential.

A c c e p t e d M a n u s c r i p t 2. Theory

The photoemission intensity

From Fermi's golden rule, the photoemission intensity becomes

I(k) ∝ f | ψ f |∆|ψ i | 2 δ( f -i + hω) , (1)
where, ψ i is the initial state and ψ f is the final state. ∆ is the electron-photon interaction operator and is expressed using the polarization vector ˆ , the momentum operator p and the position operator r

∆ ∝ ˆ • p ∝ ˆ • r . (2)
In the PW approximation, the final state in Eq.( 1) is a plane wave. Then, I(k) simply becomes proportional to the Fourier transform of the initial state φi (k)

I(k) ∝ |ˆ • k φi (k)| 2 . ( 3
)
If the energy of photoelectron is high enough, the scattering effects are not so strong and the PW approximation is justified to some extent. Also, scattering effects may be partly suppressed when the molecule is flat and the polarization vector is perpendicular to the molecular plane.

On the other hand, photoelectron scattering can be fully included in MS theory. Here we employ the usual muffin-tin (MT) approximation where the scattering potential is divided into spherically symmetric potential regions (MT spheres) located at atoms and the remaining "interstitial" regions where the potential is constant. The final state is a solution of the Lippmann-Schwinger equation in this potential with appropriate boundary conditions. The photoemission intensity is written as [10]

I(k) ∝ | ψ - k |∆|φ i | 2 ≈ α e -ik•Rα AL1L2L3 Y L1 ( k) × [1 + X + X 2 + • • • ] αA L1L2 M A L2L3 2 . ( 4
)
The superscript of ψ - k indicates the imposed boundary 50 condition, where the wave function is formed by fully interacting incoming waves and a plane wave which describes electron into the detector. Y L ( k) is a spherical harmonics, and L ≡ (l, m). The matrix X αβ LL describes the propagation of photoelectron from atom β to atom α 55 and scattering at atom α, and M A LL are the optical transition matrix elements of atom A.

Algorithm for GAUSSIAN 09 output to MS calculations 2.2.1. Spherical averages of charge density and potential 60

We performed molecular orbital calculations by GAUS-SIAN 09 to construct the scattering potential from the charge density and to obtain the initial state molecular orbital.

As basis sets are composed of Gaussian type orbitals (GTOs) in GAUSSIAN, the electron density can be expanded by products of GTOs. Any product of GTOs can be expanded by Hermite Gaussian functions which are defined by partial derivatives of a Gaussian function [START_REF] Helgaker | Molecular Electronic-215 Structure Theory[END_REF] Λ

tuv (r p , p) = ∂ t ∂P t x ∂ u ∂P u y ∂ v ∂P v z e -pr 2 p , (5)
where t, u, v are orders of partial derivatives, r p = r-P, P is a point between two atomic sites, and the exponent p is determined by the exponents of two GTOs. The spherical averages of Hermite Gaussian functions in terms of a given center C are obtained by integrating Eq.( 5)

Λ tuv (r p , p)dr c = 2π pr c t u v t C t u C u v C v F t-t ,u-u ,v-v S t u v . (6)
Here, we introduced the following two terms

F tuv = ∂ t ∂P t x ∂ u ∂P u y ∂ v ∂P v z 1 R cp (7)
S tuv = ∂ t ∂P t x ∂ u ∂P u y ∂ v ∂P v z e -pR 2 cp sinh(2pr c R cp ) , (8)
where r c = r -C and R cp = C -P. To obtain the spher-65 ically averaged density, only a finite number of F tuv and S tuv term are needed. They can be calculated by using recurrence equations. Once the spherically averaged density is obtained, the spherically averaged scattering potential can be constructed using the local density approximation. 70

Angular momentum expansion of an initial state

In order to use an initial state molecular orbital in MS theory, we need its angular momentum expansion on the neighboring atomic sites. Any GTO has the following form

χ(r) = x l g y m g z n g e -αr 2 g = e -α(r 2 c +R 2 cg ) x l g y m g z n g e -2αrc•Rcg , (9)
where l, m, n are integers which determine the angular dependence of a GTO,

r g = r -G, R cg = C -G, G
is the center of a GTO, and C is the center of the angular momentum expansion. Then, the polynomial and the later exponential in Eq.( 9) depend on the direction from the center C. The polynomial can be expanded in spherical harmonics easily, and the exponential can also be expanded by using the analytic continuation of the Rayleigh expansion [START_REF] Stone | Mathematics for Physics: A Guided Tour for Graduate Students[END_REF] e

-2αrc•Rcg =4π L (-1) l × i l (2αr c R cg )Y L (r c )Y * L ( Rcg ) , (10)
where i l is a modified spherical Bessel function. So, we need to express products of spherical harmonics by a series of spherical harmonics.

A c c e p t e d

M a n u s c r i p t

Results and discussion

Computational details

We have applied the above theory to ARPES from the HOMO level of pentacene and compare the result with the PW approximation. A pentacene molecule consists of five linearly fused benzene rings. The calculations are performed according to the experimental conditions [7]. The photoelectron energy is 29.8 eV; the light is linearly ppolarized; the angle between the incident light q and the surface normal n is fixed to α = 40 • ; q, n and photoemission direction k lie in the same plane. The molecules lie essentially flat on the surface. The long molecular axis is in the surface plane while the short axis is tilted by β = ±25 •

Calculated ARPES intensity maps and photoelectron angular distributions over whole azumithal angles

The ARPES intensity maps calculated in the PW ap-95 proximation and in the MS theory are shown in Fig. 2. The result of the PW approximation (Fig. 2a) agrees well with experiment (Fig. 2c) for this π-conjugated orbital and the chosen experimental conditions [7]. The MS result (Fig. 2b) also agrees well with experiment, but shows a 100 more complex pattern, indicating additional scattering effects.

For a detailed discussion of these effects, we have plotted the photoelectron angular distribution over whole azimuthal angles while fixing the polar angle at 25 • and 75 • 105 in Fig. 3a and3b respectively.

In Fig. 3a the average angle between the photoemission direction and the normal of molecular plane is fairly small. (Note that the molecular plane is tilted by ±25 • .) Then electron scattering is should be relatively weak. Com-110 pared to the PW approximation, the MS calculation shows a somewhat more complex angular distribution, but the overall shape is the same. On the other hand, in grazing emission (Fig. 3b), stronger scattering is expected. Indeed, the MS calculation gives additional peaks, and the overall 115 shape is very different. We can therefore conclude that the importance of scattering effects considerably depends on the emission angle.

Multiple scattering theory fully accounts for the scattering of the photoelectron at the molecular potential, the 120 neglect of which is a main source of error of the PW approximation. However, the present implementation of MS theory also has possible shortcomings because the MT approximation is used for the final state calculation. The HOMO of pentacene (Fig. 4) is a π-orbital mainly con-125 sisting of carbon 2p orbitals. For the calculation of the transition matrix elements (M ) the delocalized nature of such molecular orbitals is taken into account by expanding them into spherical waves centered on all sites. However, the carbon 2p orbitals also extend into the so-called inter-130 stitial region, that is the space outside any atomic sphere. The contribution of this region is neglected in the calculation of the transition matrix elements. Second, the MT potential contains artificial jumps at the sphere boundaries which may cause spurious scattering effects. These ergy photoemission and should be corrected. This may be done by using the full-potential version of MS theory [START_REF] Hatada | [END_REF]. In full-potential MS theory, the MT spheres are replaced by space-filling atomic and empty cells. Thereby molecular potentials of any shape can be represented exactly.

As discussed before, some potential details are disregarded in the present calculation due to the MT approximation. However, it should be kept in mind that the PW approximation corresponds to the complete neglect of the 145 molecular potential for the final state.

Conclusion

In summary we have proposed an improved multiple scattering theory for ARPES of oriented molecules. For this purpose, we have developed new algorithms for obtain-150 ing the spherically averaged scattering potential and the angular momentum expansion of the initial state, which is taken from an ab initio molecular orbital calculation. We have tested the method on ARPES from the HOMO of pentacene and found good agreement with experiment.

Compared with the PW approximation, the ARPES maps obtained in MS theory display additional features which we attribute to final state photoelectron scattering. However, in the present system, which is a favorable case for the validity of the PW approximation, the overall difference between PW and MS results is rather small. Due to finite experimental resolution, both calculations fit the experimental data equally well. Other systems and experimental geometries will be investigated in the future for a more clearcut comparison between the two approaches. In 165 particular, large difference can be expected for molecules with appreciable emission perpendicular to the light polarization vector, because the PW approximation cannot account for this effect.

[ 7 ]

 7 , see Fig.1. We use the ground state wave function of the neutral molecule for both the PW and the MS calculations. For simplicity, scatterings off the substrate are 90 neglected and ARPES intensity maps of a single molecule are computed.

Figure 1 :

 1 Figure 1: Schematic diagram of ARPES experiment.

  135points might be important for the present case of low en-

Figure 2 :

 2 Figure 2: ARPES intensity map of pentacene. On the white solid and dashed line drawn in (a) and (b), the polar angles are fixed to 25 • and 75 • respectively. (a) PW calculation. (b) MS calculation. (c) Experimental data from Ref. [7], reprinted with permission.

Figure 4 :

 4 Figure 4: The HOMO of pentacene.


Koorosh Esteki

Adriana Predoi-Cross
email: adriana.predoicross@uleth.ca

Chad Povey

Sergey Ivanov

Aziz Ghoufi

Franck Thibault

Mary Ann

H Smith

Room Temperature Self-and H 2 -Broadened Line Parameters of Carbon Monoxide in the First Overtone Band: Theoretical and Revised Experimental Results

Keywords: carbon monoxide, CO widths, CO shifts, H 2, hydrogen, infrared spectra, line mixing, spectral line shapes, speed dependence 1

)) ro-vibrational transitions belonging to the first overtone (20) band of 12 C 16 O at room temperature. All spectra in the 4146 to 4332 cm -1 spectral interval were fitted simultaneously employing four line shape functions: the Voigt, Speed Dependent Voigt, Rautian and Speed Dependent Rautian profiles.

The collisional line mixing effect has been observed and investigated as an asymmetry in the analyzed line profiles. A semi-empirical Exponential Power Gap Law method was used to estimate the self-and H 2 -broadening coefficients and the collisional line mixing parameters.

Additionally, a classical approach was applied to calculate the half-width coefficients of 2 transitions in the 20 band for carbon monoxide broadened by H 2 and for pure CO. The classical approach based on a simple computational method, ensures the molecular motion is correctly characterized in 3 dimensions. The calculations used vibrationally independent intermolecular interaction potentials. The variation of CO half-width coefficients with rotational quantum number J ≤ 24 was computed and compared with measurements. The agreement between the theoretical broadening coefficients is better for pure CO rather than for the CO-H 2 system.

Introduction

Carbon monoxide (CO) has been the subject of numerous investigations in recent decades due to its ability to offer insight into the evolution of galactic and extragalactic astrophysical entities [START_REF] Dickman | Carbon monoxide as an extragalactic mass tracer[END_REF]. The presence of CO in Jupiter's atmosphere was first reported in 1975 [START_REF] Beer | Detection of carbon monoxide in Jupiter[END_REF] and CO was later found in the atmospheres of the other giant planets, Saturn [START_REF] Noll | Detection of carbon monoxide in Saturn[END_REF], Neptune [START_REF] Rosenqvist | Millimeter-wave observations of Saturn, Uranus, and Neptune -CO and HCN on Neptune[END_REF][START_REF] Marten | First observations of CO and HCN on Neptune and Uranus at millimeter wavelengths and the implications for atmospheric chemistry[END_REF], and Uranus [START_REF] Encrenaz | First detection of CO in Uranus[END_REF] and in the atmosphere of Saturn's moon, Titan [START_REF] Lutz | Titan: Discovery of carbon monoxide in its atmosphere[END_REF]. The infrared lines of CO corresponding to the first overtone band were discovered in spectra of the predominantly CO 2rich atmospheres of Venus and Mars [START_REF] Young | Interpretation of high-resolution spectra of Mars: IV. New calculations of the CO abundance[END_REF][START_REF] Connes | Carbon monoxide in the Venus atmosphere[END_REF]. Moreover, CO is an attractive candidate for scientists to perform high signal-to-noise laboratory measurements (see, e.g. [START_REF] Seleznev | Shape of collision-broadened lines of carbon monoxide[END_REF]).

The upcoming missions such as the GEO stationary Coastal and Air Pollution Events (GEO-CAPE), Global Atmospheric Composition Mission (GACM) and Active Sensing of CO 2 absorption over Nights, Days and Seasons (ASCENDS) will map the spectral radiances located in the 2.3 m region to obtain distributions of concentrations for terrestrial atmospheric CO [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF].

Accurate retrievals of atmospheric composition from spectra recorded by remote sensing techniques rely on having access to highly accurate line parameters for both self-and foreign-gas broadening. While considerable progress has been made in improving self-and air-broadened line parameters in the 20 band of CO (see Ref. [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF]), our present study focuses on self-and H 2 -broadening in the same band, and in the following paragraphs we briefly review the previously available measurements.

Self-broadening parameters in the first overtone band of CO have been reported in numerous studies, while H 2 -broadened line shapes have been studied less often. The half-width coefficients of self-broadened transitions in the 20 and the 30 bands of CO have been measured by Plyler et al. [START_REF] Plyler | Self-broadening of carbon monoxide in the 2 and 3 bands[END_REF] using a high resolution grating spectrometer for 21 lines in the Rbranch over a range of pressures between 1.5 to 4 atm. James et al. [START_REF] James | Linewidths in the 2-0 band of carbon monoxide broadened by nitrogen and hydrogen[END_REF] have published measurements of pressure-broadened widths for 20 transitions in the 20 band of CO by hydrogen and nitrogen at 295 K for several pressures in the range of 10 to 35 Torr using a 1-m long gas cell attached to a Jarrel-Ash Ebert spectrometer. Hunt et al. [START_REF] Hunt | High-resolution determination of the widths of selfbroadened lines of carbon monoxide[END_REF] have reported the room temperature half width coefficients of 31 self-broadened lines in the first overtone band of CO in the pressure range of 1 to 2 atm with an estimated accuracy of ±3.0% employing a highresolution Littrow type grating spectrometer at a resolution of 0.045 cm -1 .

Bouanich et al. [START_REF] Bouanich | Mesure des largeurs et des deplacements des raies de la bande 0 → 2 de CO autoperturbé et perturbé par N 2 , O 2 , H 2 , HCl, NO et CO 2[END_REF] have studied the self-and foreign-broadened widths of 22 transitions belonging to the first overtone band of CO perturbed by N 2 , H 2 , O 2 , NO, HCl, and CO 2 at 299 K and pressures ranging from 1 to 5 atm. Bouanich et al. [START_REF] Bouanich | On the temperature dependence of self-broadening in the first overtone band of CO[END_REF] also determined the self-broadened half-width coefficients of 22 lines in the P-and R-branches of CO at 298, 198, 131, and 85 K along with their temperature dependences.

Bouanich et al. [START_REF] Bouanich | Pressure-induced lineshifts in the 2 ← 0 band of CO self-perturbed and perturbed by He, Kr, O 2 , and N 2[END_REF] have used a tunable difference frequency laser spectrometer to measure the broadening and shift parameters in the 20 band of CO. They measured self-, He-, Kr-, O 2 -, and N 2 -broadened coefficients for several lines, and compared them with theoretical estimations based upon the semi-classical model by Robert-Bonamy and different interaction potentials.

Pressure broadening, pressure shift, and line mixing parameters of 42 lines of the first overtone band of pure CO and CO broadened by N 2 have been investigated by Predoi-Cross et al. [START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 2←0 band of CO and CO-N 2 : experimental results and theoretical calculations[END_REF] using spectra recorded with a Bomem DA8.003 Fourier transform spectrometer at 303 K at various gas sample pressures. The authors have used the Lorentz profile to retrieve spectral line parameters for pure carbon monoxide as well as a Voigt and an empirical line shape model (HC v ) which combines hard collision and speed-dependent Lorentz models to retrieve line parameters. They also compared the line broadening and pressure-shift coefficients with semi-classical computations. The measured line mixing parameters were compared with line mixing computations based upon an empirical energy corrected sudden scaling law.

Zou and Varanasi [START_REF] Zou | New laboratory data on the spectral line parameters in the 1-0 and 2-0 bands of 12 C 16 O relevant to atmospheric remote sensing[END_REF] have published self-and air-broadening coefficients, self-and airinduced shift parameters of the 10 and 20 bands of carbon monoxide for transitions between the P [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF] and R [START_REF] Hashemi | Line-shape models testing on six acetylene transitions in the 1 + 3 band broadened by N 2[END_REF] lines. The spectra were recorded at several temperatures ranging from 174 K to room temperature using a Bruker IFS-120HR Fourier transform spectrometer. In addition, they reported line positions and intensities, as well as the temperature dependences of the broadening and shift coefficients for each studied transition.

The line positions, intensities, broadening and pressure-induced shift parameters for pure CO and CO diluted in H 2 belonging to the first overtone band were reported by Devi et al. [START_REF] Devi | Determination of self-and H 2 -broadening and shift coefficients in the 2-0 band of 12 C 16 O using a multispectrum fitting procedure[END_REF] at 297 K for pressures between 3 and 507 Torr using the former Fourier transform spectrometer at the McMath-Pierce Solar Telescope, Kitt Peak National Observatory, AZ. Their measurements cover the 4130 to 4345 cm -1 region corresponding to transitions between P [START_REF] Berman | Speed-dependent collisional width and shift parameters in spectral line profiles[END_REF] and R [START_REF] Berman | Speed-dependent collisional width and shift parameters in spectral line profiles[END_REF]. The authors have studied the vibrational dependence of the self-shift parameters by comparing them with coefficients published in previous spectroscopic works on the fundamental band. Line mixing effects could not be quantified in their data analysis.

Brault et al. [START_REF] Brault | Selfbroadened 12 C 16 O line shapes in the =2←0 band[END_REF] studied line positions and intensities, self-broadened widths, pressureinduced shifts and line mixing parameters in the (20) band of CO for the P [START_REF] Devi | Self-and H 2 -broadened width and shift coefficients in the 2 ← 0 band of 12 C 16 O: revisited[END_REF] to R [START_REF] Devi | Self-and H 2 -broadened width and shift coefficients in the 2 ← 0 band of 12 C 16 O: revisited[END_REF] transitions at temperatures between 297.8 to 301.6 K and pressures from 200 to 600 Torr applying the Voigt and Speed Dependent Voigt (SDV) models. The authors have also calculated the transition dipole moments using the intensity information and compared them with the Herman-Wallis parameters for transitions in this band.

Using a Bruker IFS-120HR Fourier transform spectrometer Sung et al. [START_REF] Sung | Hydrogen-broadened half-widths and hydrogen-induced line shifts of 12 C 16 O relevant to the Jovian atmospheric spectra[END_REF] have measured H 2 -broadened half-widths and H 2 -induced pressure-shift coefficients and determined the temperature dependences for the fundamental (10), first overtone (20) and second overtone (30) bands over a temperature range between 83 and 302 K and pressures from 101.11 to 539.74 Torr.

Since there was considerable disagreement between the H 2 -broadened results of Devi et al. [START_REF] Devi | Determination of self-and H 2 -broadening and shift coefficients in the 2-0 band of 12 C 16 O using a multispectrum fitting procedure[END_REF] and those of Ref. [START_REF] Sung | Hydrogen-broadened half-widths and hydrogen-induced line shifts of 12 C 16 O relevant to the Jovian atmospheric spectra[END_REF], pressure-induced shift and half-width coefficients of pure CO and CO-H 2 mixtures were re-measured by Devi et al. [START_REF] Devi | Self-and H 2 -broadened width and shift coefficients in the 2 ← 0 band of 12 C 16 O: revisited[END_REF] employing the multispectrum nonlinear least squares method [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF] with a new set of H 2 -broadened spectra. The authors have analyzed 48 transitions between P(24) and R [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF] in the 20 band of CO at room temperature and pressure range from 3 to 643 Torr using a Voigt profile.

Regalia-Jarlot et al. [START_REF] Régalia-Jarlot | Pressure-broadened line widths and pressure-induced line shifts coefficients of the (1-0) and (2-0) bands of 12 C 16[END_REF] have studied the broadening and pressure-induced shift coefficients of CO diluted by air and H 2 in the 10 band as well as self-and H 2 -broadened line widths and shifts in the 20 band, analysing spectra recorded with a Fourier transform spectrometer operating in stepping mode.

Devi et al. [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF] have determined self-and air-broadened Lorentz half-width and pressureinduced shift coefficients and their temperature dependences of CO in the first overtone band using spectra recorded over the temperature and pressure ranges of 151.15 to 298 K and pressures of 5.11 to 699.14 Torr, respectively. Retrieving precise line positions and intensities enabled them to determine rovibrational constants (G, B, D etc.) employing a multispectrum nonlinear least squares spectrum fitting technique. The authors have reported the speeddependent line shape parameters along with collisional line mixing coefficients obtained by applying the off-diagonal relaxation matrix element (ORME) formalism to obtain best fit residuals.

Our review of the literature indicates that no studies have been reported for the spectral line parameters of carbon monoxide perturbed by hydrogen in the second overtone band since 2005.

In this study, we have re-analyzed the high-resolution spectra of self-broadened CO and CO broadened by hydrogen [START_REF] Devi | Determination of self-and H 2 -broadening and shift coefficients in the 2-0 band of 12 C 16 O using a multispectrum fitting procedure[END_REF][START_REF] Devi | Self-and H 2 -broadened width and shift coefficients in the 2 ← 0 band of 12 C 16 O: revisited[END_REF] recorded in the first overtone band. We have used four different line shapes in the multispectrum analysis (Voigt, speed dependent Voigt, Rautian, and Rautian with speed dependence) and compared the resulting line shape parameters with results available in the literature. These four models allowed us to investigate the contributions of Dicke narrowing and speed-dependence to the measured line shapes. Line mixing coefficients have been calculated using the Exponential Power Gap (EPG) law. A classical approach was applied to calculate CO line widths for collisions of pure carbon monoxide and of mixtures of carbon monoxide and hydrogen, both performed using simple interaction potentials.

Experimental description

Absorption spectra of high purity research-grade (99.999%) carbon monoxide ( 12 C 16 O) purchased from Matheson Inc. and samples of the same high-purity carbon monoxide mixed with dry, research grade hydrogen in the (20) band of CO were recorded at high resolution (0.0052 -0.0055 cm -1 ) using the former Fourier transform spectrometer situated on Kitt Peak, AZ.

Details regarding the spectra and the data acquisition procedure are given in Refs. [START_REF] Devi | Determination of self-and H 2 -broadening and shift coefficients in the 2-0 band of 12 C 16 O using a multispectrum fitting procedure[END_REF][START_REF] Devi | Self-and H 2 -broadened width and shift coefficients in the 2 ← 0 band of 12 C 16 O: revisited[END_REF].

For the convenience of the reader, a brief summary of the experimental details is provided here. Ten pure CO and eight H 2 -broadened CO (CO+H 2 ) spectra with different mixing ratios were recorded at room (~297.90-298.20 K) temperature. The experimental setup consisted of a

Globar light source at 12 V and CaF 2 beam splitter. The experimental conditions of all the spectra analyzed in this work are given in Table 1. A LN 2 -cooled InSb detector was employed in recording the spectra. The signal to noise ratio (S/N) was estimated to be in the 200 to 500 range.

The entire spectral region extends between 4146 and 4332 cm -1 . Overlaid CO spectra used in the present study are shown in panel ( B) of Figure 1. The top panel presents the differences between observed and calculated spectra. The concentrations of the spectra studied in Ref. 20 have been re-calculated using the present line intensities for pure CO and we have entered the revised volume mixing ratios in Table 1.

Spectroscopic analysis

For remote sensing applications, the Voigt line shape model (VP) (see Eqs. (2-5) of Ref.

[26]) has been used for several decades. The line shape function known as the Speed Dependant

Voigt profile (SDV) (see Eq. ( 11) of Ref. [START_REF] Hashemi | Line-shape models testing on six acetylene transitions in the 1 + 3 band broadened by N 2[END_REF]) introduced first by Berman et al. [START_REF] Berman | Speed-dependent collisional width and shift parameters in spectral line profiles[END_REF] and later expanded by Pickett [START_REF] Pickett | Effects of velocity averaging on the shapes of absorption lines[END_REF] is a weighted summation of Lorentzian profiles according to different absorber speeds and incorporates the dependence of relaxation rates term on the speed of the absorber. The analysis software employed in this study uses the implementation of speeddependence introduced by Rohart et al. (see Eqs. [START_REF] Seleznev | Shape of collision-broadened lines of carbon monoxide[END_REF] Ref. [START_REF] Hashemi | Line-shape models testing on six acetylene transitions in the 1 + 3 band broadened by N 2[END_REF] and references therein).

The Voigt or speed dependent Voigt line shape functions is only satisfactory when it is assumed that the mean-free path of the molecule is much larger than the wavelength of the incident radiation. So, if this condition is not met, and if the memory about coherence with the radiation is preserved after collision, smaller broadening parameters would be expected. This phenomenon is known as the Dicke narrowing effect [START_REF] Galatry | Simultaneous effect of Doppler and foreign gas broadening on spectral lines[END_REF] and has to be taken into account by adopting appropriate model.

The Galatry profile (GP) [START_REF] Galatry | Simultaneous effect of Doppler and foreign gas broadening on spectral lines[END_REF] is used when the molecular collisions are assumed to be soft (i.e., a great number of collisions are needed to yield a noticeable change in velocity, meaning the effect of only one collision is small and can be ignored). The Rautian and Sobel'man line shape formulation (RP) ( [START_REF] Rautian | man II. The effect of collisions on the Doppler broadening of spectral lines[END_REF] or Eqs. (5-6) of Ref. [START_REF] Hashemi | Line-shape models testing on six acetylene transitions in the 1 + 3 band broadened by N 2[END_REF]) and the one of Nelkin-Ghatak [START_REF] Nelkin | Simple binary collision model for Van Hove's G s (r, t)[END_REF] have been introduced to account for hard collisions (i.e., for molecular systems where each collision randomizes the velocity, based upon a Maxwellian distribution [START_REF] Vizia | Speed-dependent effects in the near-infrared spectrum of self-colliding H 2 18 O molecules[END_REF], and thus the velocity memory is lost [START_REF] Hartmann | Collisional Effects on Molecular Spectra[END_REF]). Collisional narrowing was implemented assuming that it can be related to the molecular diffusion.

Practically, the speed dependence of the velocity changing collisions and relaxation rates turn up simultaneously. Ciurylo and Szudy [START_REF] Ciuryło | Speed-dependent pressure broadening and shift in the soft collision approximation[END_REF] described the collisional broadening applying the classical shift theory by Anderson [START_REF] Anderson | A method of synthesis of the statistical and impact theories of pressure broadening[END_REF] and the thermal motion of absorbing molecules by the Galatry model and introduced the speed dependent Galatry (SDG) line shape profile. By integrating the speed dependence relaxation rate in Rohart's approximation (see Eqs. [START_REF] Seleznev | Shape of collision-broadened lines of carbon monoxide[END_REF] Ref.

[26] and references therein) in the Rautian and Sobel'man formulation [START_REF] Hartmann | Collisional Effects on Molecular Spectra[END_REF], we can obtain the speed dependent Rautian (SDR) profile.

To obtain the self-and air-broadened half-width and pressure-induced shift parameters, the following two equations are needed:

( ) [ ( )( ) [ ] ( ) [ ] ] (1)
( ) [ ( )( ) ( ) ] (2)
where and represent the retrieved pressure-shift and Lorentzian half-width coefficients (in cm -1 atm -1 ) at the reference pressure (p 0 = 1 atm) and temperature (T 0 = 296 K), respectively.

( ) expressed in cm -1 is the Lorentzian half-width of the line at the pressure p (

) and temperature T. n 1 and n 2 are the temperature dependence exponents of half-width coefficients and is the volume mixing ratio of CO in the pressure-broadened spectra.

The transition intensity between each two rovibrational states of any molecule possessing electrical dipole moment for a pure gas can be described by the following expression [START_REF] Šimečková | Einstein Acoefficients and statistical weights for molecular absorption transitions in the HITRAN database[END_REF]:

( ) ⁄ ( ( ) ⁄ ) ( ) (3)
In the equation above, is the weighted spectral line intensity based upon the natural terrestrial isotopologue abundances, I a (for 12 C 16 O is equal to 0.986544), introduced with the unit of (cm -1 / (molecule. cm -2 )) to describe it as the wavenumber per column density. h is Planck's constant, c

is the speed of light, T is the temperature (K) and is the transition wavenumber (cm -1 ). is the Einstein coefficient in s -1 , is the lower state energy (cm -1 ) and is the is the upper state statistical weight which can be estimated by ( ) ( stands for total degeneracy yielding from the product of vibrational and electronic statistical weight, and and are the state-independent and state-dependent nuclear spin statistical weights, respectively (in the case of carbon monoxide, ). Double prime and prime (′′ and ′) correspond as usual to the lower and upper states, respectively. ( ) is the total internal partition function and is the Boltzman constant. Note that equation (3) can only be applied for those molecules that have electrical transition dipole moments.

A dispersion parameter is required to be implemented in the line shape function of interest when a weak asymmetry is observed in the spectral lines that is characteristic to line mixing effects [START_REF] Rosenkranz | Shape of the 5 mm oxygen band in the atmosphere[END_REF]. We least squared fitted the spectral interval (4146-4332 cm -1 ) corresponding to the entire band, all at once, rather than analyze the transitions one by one, and we used the ORME formalism [START_REF] Levy | Spectroscopy of the Earth's atmosphere and of the interstellar medium[END_REF]. The pressure broadening and the pressure shift coefficients come from the real and imaginary parts of the diagonal relaxation matrix elements, as shown in the following expression:

The off-diagonal elements of the relaxation matrix are labeled . These elements cause mixing of the lines l and k. For a given line interacting with all the other lines, the coefficient which realizes that effect can be represented as follows [START_REF] Rosenkranz | Shape of the 5 mm oxygen band in the atmosphere[END_REF]:

( ) ∑ . (5)
( ) are the first order, Rosenkranz [START_REF] Rosenkranz | Shape of the 5 mm oxygen band in the atmosphere[END_REF], line mixing coefficients, and this theory works well if the spectral lines are separated well enough. In Eq. ( 5) and are the dipole moments of the optical transitions, and are the line centers of the transitions at zero pressure. Finally, the off-diagonal matrix elements are approximated by (minus) state-to-state rotational transfer rates (see [START_REF] Hartmann | Collisional Effects on Molecular Spectra[END_REF][START_REF] Levy | Spectroscopy of the Earth's atmosphere and of the interstellar medium[END_REF] for a review). With the help of the Rosenkranz [START_REF] Rosenkranz | Shape of the 5 mm oxygen band in the atmosphere[END_REF] line profile, the expression for the collisional absorption coefficient is given by:

( ) ∑ ( ) ( ) ( ) (6)
where " l" designates a rovibrational line . In Eq. ( 6) p is the total pressure, is the line position of the spectral line l, , and are the line mixing coefficients, half-width at half maximum and pressure induced shift coefficients per atm, respectively.

There are several semi-empirical scaling laws such as the Energy Corrected Sudden (ECS), Exponential Power Gap (EPG) and Modified Exponential Gap Law (MEGL) that can be used to predict the values of the relaxation matrix elements [START_REF] Hartmann | Collisional Effects on Molecular Spectra[END_REF][START_REF] Levy | Spectroscopy of the Earth's atmosphere and of the interstellar medium[END_REF].

The EPG scaling law makes use of standard collisional transfer rates, ( ), between the rotational levels j i and j i ' belonging to the same vibrational state v i . The expression for the collisional transfer rate from lower to a higher rotational level, exploiting the EPG law is given by the following equation [START_REF] Hartmann | Collisional Effects on Molecular Spectra[END_REF][START_REF] Levy | Spectroscopy of the Earth's atmosphere and of the interstellar medium[END_REF]:

( ) [ | | ] ( | | ) (7)
Here, is the energy difference (in cm -1 ) between each two rotational levels, is the rotational constant (in cm -1 ) corresponding to the ground vibrational state, a, b and c are the adjustable parameters that need to be optimized applying nonlinear least squares technique. The real part of the diagonal element of the relaxation matrix can be approximated as follows (the so called random phase approximation):

( ) {∑ ( ) ∑ ( ) } (8)
In our approach we have ignored the vibrational dependence of the collisional rates.

Theoretical calculations of CO-and H 2 -broadening coefficients

In this section, we present the first results of classical trajectory calculations of CO pressure-broadening coefficients for pure CO-CO and mixtures of CO and H 2 . A classical trajectory approach to compute the impact line broadening, shift and line mixing coefficients was proposed by R.G. Gordon [START_REF] Gordon | Theory of the width and shift of molecular spectral lines in gases[END_REF][START_REF] Gordon | Semiclassical theory of spectra and relaxation in molecular gases[END_REF] in 1966. The classical approach enables an exact threedimensional (3D) self-consistent characterization of translational and rotational motion of molecules without fitting for any parameters. This method is simple, visual, and computationally efficient. This classical approach, with applications to a variety of molecular systems [START_REF] Buldyreva | Collisional line broadening in the atmosphere of light particles: problems and solutions in the framework of semiclassical treatment[END_REF][START_REF] Ivanov | Comparative analysis of purely classical and semiclassical approaches to collision line broadening of polyatomic molecules: I. C 2 H 2 -Ar case[END_REF][START_REF] Nguyen | Comparative analysis of purely classical and semiclassical approaches to collision line broadening of polyatomic molecules: II. C 2 H 2 -He case[END_REF][START_REF] Ivanov | Classical calculation of self-broadening in N 2 Raman spectra[END_REF][START_REF] Ivanov | On the accuracy of classical, semiclassical and quantum methods in collision line broadening calculations: comparative analysis for C 2 H 2 -Ar, He systems[END_REF][START_REF] Thibault | Comparison of classical, semiclassical and quantum methods in hydrogen broadening of acetylene lines[END_REF][START_REF] Gomez | Comparison of quantum, semiclassical and classical methods in hydrogen broadening of nitrogen lines[END_REF][START_REF] Thibault | Comparison of quantum, semiclassical and classical methods in the calculation of nitrogen self-broadened linewidths[END_REF][START_REF] Povey | Low pressure line shape study of nitrogen-perturbed acetylene transitions in the ν 1 + ν 3 band over a range of temperatures[END_REF][START_REF] Ivanov | Precision considerations of classical and semiclassical methods used in collision line broadening calculations: different linear molecules perturbed by argon[END_REF][START_REF] Thibault | An experimental and theoretical study of nitrogen-broadened acetylene lines[END_REF][START_REF] Ivanov | Line mixing effects in isotropic Raman spectra of pure N 2 : a classical trajectory study[END_REF][START_REF] Ivanov | Quasi-bound complexes in collisions of different linear molecules: Classical trajectory study of their manifestations in rotational relaxation and spectral line broadening[END_REF],

has been shown to be efficient and constitutes an accurate tool that provides theoretical results that are in much better agreement with benchmark quantum and/or experimental data, when compared with the results of semi-classical formalisms in cases where an accurate and robust ab initio based potential energy surface (PES) is used.

In the framework of the classical impact theory, the collisional half-width, γ, and pressure shift, δ, of electric dipole vibration-rotational spectral line are given by [START_REF] Gordon | Theory of the width and shift of molecular spectral lines in gases[END_REF][START_REF] Gordon | Semiclassical theory of spectra and relaxation in molecular gases[END_REF]:

̅ ̅ ̅ √ ⁄ (9)
where the cross sections,  are as follows for P-lines

〈 { [ ( )] }〉 ̅ (10)
for R-lines

〈 { [ ( )] }〉 ̅ . ( 11
)
Here, n b is number density of perturbing particles; c is the speed of light; µ is the reduced mass of the colliding pair; T is the temperature and k B is the Boltzmann constant. P el is the probability of a given collision to be elastic (P el is calculated using box-quantization [START_REF] Ivanov | Classical calculation of self-broadening in N 2 Raman spectra[END_REF]). The average … is calculated over the impact parameter b, at relative speed and using the initial orientations (denoted here by O) of the axes 1 r and 2 r of both interacting molecules and the directions of their angular velocities, 1

 and 2  . The variable  characterizes the "rotational dephasing" due to collisions and ?? is the angle between the before and after collision orientations of the active molecule's angular momentum ("rotational reorientation"). The values of P el ,  and ?? are calculated from the dynamics of each particular collision by the modified method described in [START_REF] Buldyreva | Collisional line broadening in the atmosphere of light particles: problems and solutions in the framework of semiclassical treatment[END_REF][START_REF] Ivanov | Precision considerations of classical and semiclassical methods used in collision line broadening calculations: different linear molecules perturbed by argon[END_REF].

The vibrational phase shift,  vib , is defined by [START_REF] Gordon | Theory of the width and shift of molecular spectral lines in gases[END_REF][START_REF] Gordon | Semiclassical theory of spectra and relaxation in molecular gases[END_REF] ∫ ( )

where, V l and V u are the full intermolecular potential energies in the lower and upper vibrational states of the optical transition under consideration and the integral is taken over the collision trajectory. In our present calculations, we neglect this vibrational phase shift since molecules are treated as rigid rotors and we use the simple vibrationally independent PES. Line shift calculations are not performed since line shift is much more sensitive to vibrational dephasing than line width.

All calculations of half-widths of 12 C 16 O electric dipole transitions perturbed by H 2 and CO were made for the room temperature (T = 296 K). The classical 3D dynamics (C3D) for collision of two rigid diatomic molecules is characterized by applying 17 first-order Hamilton differential equations within body-fixed frames [START_REF] Ivanov | Classical calculation of self-broadening in N 2 Raman spectra[END_REF]. Broadening coefficients of CO molecule were calculated by considering perturbing molecules located in the ground vibrational state with J 2 values up to 10 for H 2 and up to 57 for CO, weighted by the nuclear spin (1 for collisions with CO and ( ) for collisions with H 2 ) and Boltzmann factors. The initial intermolecular distance was set as R max =15 Å for CO and H 2 mixtures and R max =20 Å for pure CO, to ensure that there will be no interaction between molecules. Other collision parameters (initial relative speed v, impact parameter b, initial orientations of molecular axes and vectors of angular momentum) were selected via a Monte Carlo procedure. The sample relative velocities were set to follow a Maxwell distribution with temperature, T. Uniform sampling was used to select b 2 , the orientations of both molecules in 3D space, and the directions of angular momenta. In order to decrease the computation time in the present Monte Carlo calculations we have implemented an efficient algorithm of b-sampling developed by Chapman and Green [START_REF] Chapman | Rotational excitation of linear molecules by collisions with atoms: Comparison of classical and quantum methods[END_REF]. The parameters impact parameter of collisions were set to: (0-13) Å for CO-H 2 and (0-19) Å for pure carbon monoxide; and the relative velocities were set to (0.01-3)v p, where v p is the most probable relative speed of a given colliding pair.

The bond lengths, r, of the molecules and their rotational constants, B, were fixed to their values in the ground vibrational level (see Table 2, all parameters are taken from Ref. [START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF]). The initial rotation frequency  1 of CO molecule was determined via its rotational quantum number J=J 1 by the rigid rotor formulae based on the so called Langer prescription [START_REF] Gordon | Theory of the width and shift of molecular spectral lines in gases[END_REF][START_REF] Gordon | Semiclassical theory of spectra and relaxation in molecular gases[END_REF][START_REF] Chapman | Rotational excitation of linear molecules by collisions with atoms: Comparison of classical and quantum methods[END_REF][START_REF] Langer | On the connection formulas and the solutions of the wave equation[END_REF]:

for P-lines and ( ) for R-lines.

Hamilton equations of motion were integrated numerically by employing the Gear method [START_REF] Gear | Numerical initial value problems in ordinary differential equations[END_REF] (recommended as a method to solve "stiff" problems) using standard IMSL Math Library routine IVPAG. All numerical calculations were performed within fixed time-grid intervals 1fs using double precision, 10 -8 tolerance parameter and a variable step of integration. The RMS error of Monte Carlo averaging was below 1 % for calculated line widths at different T s and J s .

In our classical calculations for pure carbon monoxide and for mixtures of carbon monoxide and hydrogen, a simple expression of the PES was used for both systems, namely, the sum of the Tipping-Herman (TH) potential, V TH [START_REF] Tipping | Impact theory for the noble gas pressure-induced HCl vibrationrotation and pure rotation line widths -I[END_REF] and electrostatic interactions, V el [START_REF] James | Linewidths in the 2-0 band of carbon monoxide broadened by nitrogen and hydrogen[END_REF] The Tipping-Herman potential is defined by a three-term expansion in Legendre polynomials as follows:

( ) ( ) ( ) ( ) ( ) ( ) (14)
( ) [( ) ( ) ] ( ) [ ( ) ( ) ] ( ) [ ( ) ( ) ].
Here  1 is the angle between the axis of CO molecule and the vector of intermolecular center-ofmass separation, R ; ( ) and (

) are the Legendre polynomials;  and  are the Lennard-Jones (LJ) potential parameters. Electrostatic interactions include dipole-dipole, dipolequadrupole and quadrupole-quadrupole interactions (see, e.g., [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF]):

( ) , (15)
( ) ; ( ); ( ) ; ( ).
Here  1 ,  2 are the dipole moments and Q 1 , Q 2 are the quadrupole moments of the interacting molecules;  1 ,  2 and φ 1 , φ 2 are usual polar and azimuth angles of molecular axes in the bodyfixed coordinate system (note that its z-axis is always directed along the R vector). Note also that for CO-H 2 interaction 12 0 V   since H 2 molecule has no dipole moment. Angular functions for electrostatic interactions are given by [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF]:

) cos( sin sin cos cos ) , , , ( f 2 1 2 1 2 1 2 1 2 1 2 1 2                (16) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ( ) ]
In above equations we set The values of dipole and quadrupole moments of CO and H 2 molecules used in the calculations are given in Table 2. In the present classical calculations we did not fit the parameters of the Tipping-Herman interaction potential to experimental data (as was done in previous papers [START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 2←0 band of CO and CO-N 2 : experimental results and theoretical calculations[END_REF][START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF] using the semi-classical Robert-Bonamy method) but tried to use unadjusted (theoretical or measured) ones. We used three different sources for LJ interaction parameters,  and , (see Table 3). For reduced polarizability anisotropy of CO molecule,

R 1 = 2A 1 = 12d mc /σ , R 2 = A 2 = ,
 ( ) ( ) ⁄
, where α and α are the polarizabilities of CO molecule along the bond and perpendicular to the bond, respectively,, we used two very different data:  = 0.16667 [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF] and  = 0.089 [START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF][START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 20 band of CO and CO-N 2 : Experimental results and theoretical calculations[END_REF][START_REF] Gray | Theory of molecular fluids[END_REF].

For the separation of the CO center-of-mass and center-of-charge, we used fixed value

d mc = 0.21 Å [62]. Then ⁄ , A 1 = R 1 /2,  ( ) ( ) ⁄
. As for LJ interaction parameters,  and  , we took their values from the books [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF] and [START_REF] Poling | The properties of gases and liquids[END_REF] and from the article [START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF] (see Table 3).

5.

Results and data analysis

Narrowing coefficients

In order to account for the narrowing effects for both hard and soft collisional cases we have first determined the dynamical friction parameter ( in cm -1 /atm) which is given by the following equation for the frequency of elastic velocity-changing collisions:

.

Here, k B is the Boltzmann constant, T is the temperature (K), D is the mass diffusion constant (m 2 /s), M is the mass of the absorber (kg) and c is the speed of light (cm/s).

The H 2 molecule was modeled by means of a single united atom force field [START_REF] Frost | Effects of surface area, free volume, and heat of adsorption on hydrogen uptake in metal-organic frameworks[END_REF] while CO was described as a three electrostatic sites model [START_REF] Martín-Calvo | Understanding carbon monoxide capture using metal-organic frameworks[END_REF]. Intermolecular interactions were described by combining electrostatic and van der Waals interactions. For both interactions, a cutoff of 12 Å was used. Electrostatic contribution was computed by using the Ewald sum with a convergence parameter of 0.36 Å -1 while the van der Waals interactions were modeled from Lennard-Jones (LJ) potential. Crossed LJs interactions were evaluated from the Lorentz-Berthelot mixing rule. For CO-H 2 mixtures, eight volume fractions, corresponding to the experimental spectra, were investigated (Table 4). Lengths of box are L z = L y = L x = 344 Å.

Molecular dynamics (MD) simulations were carried out from DLPOLY software [START_REF] Todorov | DL_POLY_3: new dimensions in molecular dynamics simulations via massive parallelism[END_REF]. Time-step of 1 fs was used. The acquisition phase corresponds to 10 ns after an equilibration period of 5 ns.

MD runs were performed in the NVT statistical ensemble where N is the number of particles, T the temperature, V the volume of the simulation box. Temperature and pressure are 300 K and 1 bar respectively. In canonical ensemble temperature was kept constant by means of Nosé-Hoover algorithm [START_REF] Nosé | A unified formulation of the constant temperature molecular dynamics methods[END_REF] such that the relaxation time of the thermostat was 0.5 fs. Integration of the motion equations was performed by using the velocity Verlet algorithm [START_REF] Allen | Computer Simulation of Liquids[END_REF]. Mean Square Displacement (MSD) was computed by using the following correlation expression:

( ) 〈 ∑ (( ⃗ ⃗ ( ) ⃗ ⃗ ( )) 〉 (18)
where () i rt denotes the position of a particle i at time t and N the number of particles. In an isotropic medium, self-diffusion coefficient (D s ) in an isotropic phase was computed from MSD

. ( 19
)
The Maxwell-Stephan diffusion was managed by means of the model of Darken [START_REF] Darken | Diffusion, mobility and their interrelation through free energy in binary metallic systems[END_REF]:

(20)
where x 1 and x 2 are the molar fraction of both 1 and 2 components and D 1 and D 2 are the selfdiffusion constants of 1 and 2. Indeed, it has been shown that the model of Darken is in quantitative agreement with the expression for the binary Maxwell-Stefan diffusion coefficient [START_REF] Fernández | Self diffusion and binary Maxwell-Stefan diffusion in simple fluids with the Green-Kubo method[END_REF][START_REF] Van De Ven-Lucassen | Using molecular dynamics to obtain Maxwell-Stefan diffusion coefficients in liquid systems[END_REF]. Calculated self and binary diffusion coefficients as well as related dynamical friction coefficients are gathered in Table 4. Ultimately, the latter coefficients were directly used in our line shape analysis to account for the Dicke narrowing regime in RP and SDR models.

Fits of the experimental spectra

The pressure broadening, pressure shift and line mixing parameters as well as the line positions and intensities for both pure carbon monoxide and carbon monoxide perturbed by hydrogen were determined applying the nonlinear least square multispectrum nonlinear least squares technique described in Ref. [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF] to fit all the spectra simultaneously to noise level. Four line shape models as defined in Section 3 were employed to retrieve the required sets of line parameters. All initial values for line parameters for the pure gas were taken from the HITRAN2012 database [START_REF] Rothman | The HITRAN2012 molecular spectroscopic database[END_REF]. In the case of CO-H 2 , all values of H 2 broadened widths and line shifts were taken from the GEISA database [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF]. We did not use the values from the study in

Ref. [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF] as initial guesses because we did not want to bias the fit towards those results.

The multispectrum software [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF] allows users to fit all the spectra simultaneously to the noise level. In retrieving the line broadening coefficients, we tried to float all the experimental values reported in this work. A list of all adjustable parameters for the EPG scaling law is given in the Table 5. These coefficients have been computed based upon the retrieved Voigt profile results. Since the line mixing coefficients should not depend of the line shape model used, we calculated them only using the line parameters retrieved with the Voigt profile.

All line parameters retrieved experimentally using the VP, SDV, RP and SDR line shape Panel (A) of Figure 3 shows that our pure carbon monoxide line broadening coefficients retrieved with the SD-Voigt model are in better with the results from Refs. [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF], as compared with the results from Ref. [START_REF] Brault | Selfbroadened 12 C 16 O line shapes in the =2←0 band[END_REF]. For the results obtained using the Voigt profile, we have very good agreement with the results in Ref. [START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 2←0 band of CO and CO-N 2 : experimental results and theoretical calculations[END_REF]. Our measured shifts plotted in Figure 3 (A) determined using the Voigt or SD-Voigt models with inclusion of line mixing agree very well with the results obtained through the same type of fit, i.e. Ref. [START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 2←0 band of CO and CO-N 2 : experimental results and theoretical calculations[END_REF] for Voigt results and both

Refs. [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF][START_REF] Brault | Selfbroadened 12 C 16 O line shapes in the =2←0 band[END_REF] for SD-Voigt results, respectively. Panel (B) of Figure 3 shows that the speeddependent profiles provide slightly higher broadening coefficients than the Voigt or Rautian profiles. The differences between the sets of broadening coefficients obtained with the four profiles are small, but noticeable and are fairly consistent over the range of m values.

The results presented in Fig. 5 for H 2 -broadening show a good agreement for |m|<14 with both sets of previous results. The scatter in our results for values |m|>14 and the departures from the two previous sets [START_REF] Sung | Hydrogen-broadened half-widths and hydrogen-induced line shifts of 12 C 16 O relevant to the Jovian atmospheric spectra[END_REF][START_REF] Devi | Self-and H 2 -broadened width and shift coefficients in the 2 ← 0 band of 12 C 16 O: revisited[END_REF] are attributed to the fact that our set of spectra was not optimal for retrievals of H 2 -broadening coefficients at high |m| values. Also, the fact that unlike done in Ref.

[23], we have not used a constrained analysis method which is known to remove the scatter in broadening coefficients. The H 2 -pressure induced line shifts presented in Figure 6 do not agree very well with previous studies which is not surprising since we have retrieved also H 2 -line mixing parameters and the two sets of parameters are known to be highly correlated.

The line mixing coefficients are difficult to retrieve accurately from experimental spectra.

Our retrieved values for CO-broadened line mixing coefficients presented in Fig. 7 (A In Fig. 8 we present our measured results for speed dependence parameters obtained for pure CO (panel (A)) and for the CO-H 2 system (panel (B)). One striking observation that has to be verified experimentally using new spectra is the very small size of speed-dependence parameters for the CO-H 2 system. As discussed by Kochanov [START_REF] Kochanov | Manifestations of small-angle molecular scattering in spectral line profiles[END_REF], the speed-dependence coefficients are not expected to have a visible J-dependence. The strong J-dependence observed both in the speed-dependence results of Devi et al. [START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF] and in our retrieved speed dependence coefficients is due to the fact that both Dicke narrowing and the speed-dependence effect introduce a narrowing of the lines [START_REF] Kochanov | Manifestations of small-angle molecular scattering in spectral line profiles[END_REF][START_REF] Kochanov | On parameterization of spectral line profiles including the speed-dependence in the case of gas mixtures[END_REF], hence making the narrowing and speed-dependence coefficients to be highly correlated. Since in our study we have fixed the narrowing parameter, its J-dependence is neglected and it may have resurfaced in the retrieved speed-dependence coefficients. We have calculated the speed-dependence parameters according to the expressions of Kochanov [START_REF] Kochanov | On parameterization of spectral line profiles including the speed-dependence in the case of gas mixtures[END_REF] and we have obtained best agreement with our experimental values for a value of q = 5 in the expression of effective potential V~r -q , a fact that can be attributed to the contributions from the Van der Waals and quadrupole-quadrupole terms in the interaction potentials.

Classical calculations of widths and comparisons with experimental data

The results of classical calculations of CO line broadening coefficients are shown in Figures 9-14. First of all, we have ascertained that the values of b max (maximum impact parameter) which we used are sufficiently large to provide converged results for the line widths.

Fig. 9 and Table 11 represent the broadening convergence with increasing b max . We have checked the validity of the approximation by performing calculations only at the mean thermal velocity (MThV), thus avoiding a thermal average over speeds. This assumption is widely used in line broadening and shift calculations since it greatly reduces CPU time. In this approximation, the initial relative speed, v, in all collisions is fixed to its mean arithmetic speed (see Eq. ( 9)). The results are presented in Fig. 10 and gathered in Table 12. It is seen that for pure CO this assumption works quite well but for mixtures of CO and H 2 there are some small problems (non-physical behavior of J-dependence). So, in all our further calculations we decided (for reliability) to refuse MThV approximation and use Maxwell-Boltzmann speed averaging.

It is known that in molecular collisions sometimes the so called quasi-bound complexes (see, e.g. [START_REF] Ivanov | Quasi-bound complexes in collisions of different linear molecules: Classical trajectory study of their manifestations in rotational relaxation and spectral line broadening[END_REF]) arise which may influence the spectral line shape. Special additional calculations showed, however, that their influence on CO line broadening in our cases is negligible. At least, it is so when the Tipping-Herman + electrostatic PES is used.

The comparison of theoretical results with experimental data for self-perturbed CO and CO perturbed by H 2 is shown respectively in Fig. 11 and Fig. 12. Note that calculated pressure broadening coefficients in P-and R-branches are identical for the same |m| values. For selfperturbed CO, the theoretical broadening coefficients were calculated using three different sets of potential parameters (see curves 1-3 in Fig. 11). Classical results for both systems and different potentials used are gathered in Table 13. As one can see there is practically no difference between theoretical results obtained with these different potential parameters. The theoretical and experimental results for the self-and H 2 -broadened CO systems were in satisfactory agreement. The magnitudes of maximum and mean relative errors are 16% and 8%

for pure CO and 31% and 15% for mixtures of CO and H 2 . Note that these values of errors are derived from the comparison of data for R-lines. In this estimation, we used theoretical data with the set of potential parameters designated in Fig. 9.

In Fig. 13 and Fig. 14 we analyzed the contributions of different parts of the interaction potential into the CO pressure broadening coefficients. It is clear from these figures that in both the self-and the H 2 -perturbed carbon monoxide cases, the main contributions come, firstly, from the Tipping-Herman (TH) part of the potential and, secondly, from the quadrupole-quadrupole interactions. As for dipole-dipole (dd) and dipole-quadrupole (dQ) interactions, they are very weak and may be neglected and this corroborates the results of Ref. [START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 20 band of CO and CO-N 2 : Experimental results and theoretical calculations[END_REF]. Table 14 summarizes these results.

The main problem in present classical trajectory calculations relates to the line shifts, more precisely, with accounting for vibrational dephasing,  vib arising from the variation of the PES with the vibrational quantum numbers relevant to the optical transition. In a previous article [START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF] this variation was taken into account somewhat crudely using fitting parameters for long-range interactions. It was the necessity of that time. Meanwhile, line shift is very sensitive to vibrational dephasing and more delicate methods and PESs should be applied.

There is no such problems with CO line broadening since line-widths only slightly depend on band (they are nearly the same for 10, 20 and 30 bands, see Fig. 2 and 3 of Ref. [START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF]).

So, in this work, both molecules were treated as rigid rotors in calculations of widths (namely, widths are the same for all vibrational bands involving quite low vibrational numbers owing to the CO triple bound).

Conclusion and directions for future work

We have reported experimentally measured and theoretical line parameters for transitions in the first overtone (20) band of 12 C 16 O at the ambient temperature (~298 K) to determine the pressure broadening coefficients for 48 (P(24) to R( 23)) rovibrational transitions. Applying a nonlinear least square technique (Labfit software, [START_REF] Benner | A multispectrum nonlinear least squares fitting technique[END_REF]), all the analyzed spectra were fitted simultaneously to the noise level. Our results agreed well with previous results as mentioned before. Note that there are many experimental studies of carbon monoxide in the first overtone band, and for this reason only a few selected studies have been plotted and compared in the present work. Pressure-broadened half-width coefficients of CO self-perturbed and perturbed by H 2 and collisional line mixing coefficients generated using the EPG scaling law are in good agreement with the experimental values.

Additionally, we present the first results of calculations of self-and H 2 -broadened width coefficients of CO using classical impact theory. For a start, we applied very simple interaction PESs which were used in previous works on these molecular systems using the semi-classical Robert and Bonamy approach. However, in our present calculations we did not adjust potential energy parameters but used theoretical (or measured) ones. In spite of the simplicity of the PESs, we obtained quite good results for half-widths, especially for pure CO. It is important to include vibrational state dependence into intermolecular interaction surfaces. It would be the best of all to have robust and up-to-date PESs decomposed into series of bi-spherical harmonics separately for different vibrational states of the CO molecule. After this a reliable classical calculations of line broadening, shift and kinetic parameters (Dicke narrowing, etc.) are straightforward. This study is a step forward towards obtaining information on the narrowing, speed dependence and line mixing parameters that may be needed in the future if databases implement the Hartmann-Tran model recommended by IUPAC [START_REF] Tennyson | Recommended isolated-line profile for representing high-resolution spectroscopic transitions (IUPAC Technical Report)[END_REF].

In the future we intend to extend our study using spectra recorded over a large range of pressures and temperatures, to enable us to determine the temperature dependence of line parameters for the CO-CO and CO-H 2 systems. If possible, we would like to test line shape models such as the ones given in Refs. [START_REF] Pine | N 2 and Ar broadening and line mixing in the P and R branches of the 3 band of CH4[END_REF][START_REF] Kochanov | Collision line narrowing and mixing of multiplet spectra[END_REF][START_REF] Ciurylo | Speed-dependent line mixing profiles[END_REF][START_REF] Kochanov | Line profiles for the description of line mixing, narrowing, and dependence of relaxation constants on speed[END_REF][START_REF] Kochanov | Speed-dependent spectral line profile including line narrowing and mixing[END_REF][82] that can be used over a range of pressures and include speed dependent effects and line narrowing or line mixing.

[82] Cherkasov M.R. Theory of relaxation parameters of the spectrum shape in the impact approximation-I: General consideration. J Quant Spectrosc Radiat Transfer. 2014; 141. P.73-88. doi: 10.1016/j.jqsrt.2013.11.013. Interaction PES parameters for pure CO are  =110 K,  =3.59 Å [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF],  =0.089 [START_REF] Predoi-Cross | Broadening, shifting, and line asymmetries in the 20 band of CO and CO-N 2 : Experimental results and theoretical calculations[END_REF][START_REF] Gray | Theory of molecular fluids[END_REF].

List of Figures

Interaction parameters for CO broadened by H 2 are  =48.8787 K,  =3.3872 Å [START_REF] Bouanich | Theoretical calculations for line-broadening and pressureshifting in the fundamental and first two overtone bands of CO-H 2[END_REF],  = 0.16667 [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF]. Line broadening coefficients (cm -1 atm -1 ) for pure CO (Fig. 3, panel (C)) and CO-H 2 (Fig. 5, panel (B)) for transitions in the first overtone band obtained using the Voigt, Speed-Dependent Voigt, Rautian and Speed-Dependent Rautian line shape models. Calculated values obtained using the EPG method are also included. 9. Note that all the values are calculated in cm -1 atm -1 at 296 K.

Table 12. Theoretical line broadening coefficients in cm -1 atm -1 at 296 K obtained applying the Maxwell-Boltzmann speed averaging and Mean Thermal Velocity (MThV) approximation shown in Fig. 10. CO-CO:R max = 20 Å,b max = 19 Å. Parameters of interaction PES are given as follows: 1. =110 K,  =3.59 Å,γ =0.089; 2. =91.7 K,  =3.690 Å, γ =0.089; 3. =91.7 K,  =3.690 Å, γ =0.089.

J

CO-H 2 :R max = 15 Å,b max = 13 Å. Parameters of interaction PES are given as follows: 1. =48.8787 K,  =3.3872 Å, γ = 0.16667; 2. =91.7 K,  =3.690 Å, γ =0.089.

Table 14.

Thermally averaged line broadening coefficients (cm -1 atm -1 ) at 296 K resulting from contribution of different parts of the interaction PES in the case of CO-CO and CO-H 2 shown in Fig. 13 and Fig. 14.

J

  where d mc is the separation of the CO center-of-mass and the center-of-charge and  is the reduced polarizability anisotropy of CO molecule.

functions are listed in Tables 6 - 10 .

 610 Fig. 2(A) shows a nearly the same average difference of 0.000785 cm -1 between the newly retrieved line positions and those stored in the HITRAN or GEISA databases. Fig. 2(B) shows that our retrieved line intensities match better the ones in HITRAN, with average ratios of 1.009 (Voigt) and 1.010 (SD-Voigt). The agreement with the intensities available in the GEISA database is worse with average values of 0.972 (Voigt) and 0.974 (SD-Voigt). The plots for uncertainties in line positions (Fig. 2 (C)) and in line intensities (Fig. 2 (D)) show that the parameters are determined with lower uncertainties when we use the SD-Voigt profile.

  ) agree well at medium |m| values with previous measurements and show more scatter at both low and high |m| values where the transitions are weaker. Dicke narrowing, speed-dependence and line mixing, all lead to an effective line narrowing, so these three parameters are all correlated. It is possible that our method of introducing the narrowing parameter based on calculated diffusion constants leads to a underestimation of this parameter. Hence, the experimental values obtained by us for the line mixing coefficients are a bit overestimated. For both CO-and H 2 -broadened line mixing coefficients, the best agreement is observed with the semi-empirical results calculated with the Exponential Power Gap law.

Fig. 1 .Fig 2

 12 Fig. 1. Multispectrum fits of 10 spectra of CO using the (A) Voigt, (B) Speed-Dependent Voigt, (C) Rautian, (D) Speed-Dependent Rautian profiles, all with weak line mixing, covering the region 4149.5 and 4170.5 cm -1 belonging to the P(20) to R(24) transition in the 20 band of CO.

Fig. 3 .

 3 Fig. 3. (A) Measured Lorentz self-broadened half-width coefficients of CO using the Voigt and speed-dependent Voigt (SD-Voigt) models and comparison with published results. The line shape model used is mentioned in the figure legend. (B) Sample of broadening coefficients obtained using the speed-dependent Voigt, Voigt, Rautian and speed-dependent Rautian line shape models. (C) Measured Lorentz self-broadened half-width coefficients of CO in the present study using Voigt, speed-dependent Voigt (SD-Voigt), Rautian and speed-dependent Rautian models.

Fig. 4 .

 4 Fig. 4. (A) Measured room temperature pressure-induced shift coefficients of pure CO from present study using the Voigt and speed-dependent Voigt (SD-Voigt) models and their comparisons with the literature values. (B) Room temperature self-induced pressure-shift coefficients retrieved with four different line shape models.

Fig. 5 .

 5 Fig. 5. Measured Lorentz half-width coefficient of H 2 -broadened CO from the present study using the Voigt and speed-dependent Voigt models and comparisons with published results obtained using the Voigt model.

Fig. 6 .

 6 Fig. 6. Measured pressure-induced shift coefficients of H 2 -broadened CO from present study using Voigt and speed-dependent Voigt models and their comparisons with published measurements obtained using the Voigt model.

Fig. 7 .

 7 Fig. 7. (A) Measured collisional line mixing parameter of pure CO using the Voigt and speeddependent Voigt models compared with other published and calculated results obtained using the exponential power gap (EPG) law. (B) Measured collisional line mixing of CO-H 2 obtained using the Voigt and speed-dependent Voigt models.

Fig. 8 .

 8 Fig. 8. Speed dependence parameters for pure CO (a), and CO and H 2 mixtures (b) obtained using the speed-dependent Voigt profile.

Fig. 9 .

 9 Fig. 9. Test of convergence of thermally averaged theoretical line broadening coefficients for pure CO (panel (A)) and CO broadened by H 2 (panel (B)) with b max (in Å) increasing. Jdependences of CO half-widths calculated using a different parameter b max in the calculation.

Fig. 10 . 9 .Fig. 11 .

 10911 Fig. 10. Test of the MThV approximation. Parameters of interaction PESs are the same as in Fig. 9.

Fig. 12 .

 12 Fig. 12. Comparison of theoretical and experimental results for CO and H 2 mixtures. The theoretical H 2 -broadening coefficients were calculated using two different sets of parameters for PESs (curves 1 and 2). The parameters of the interaction PES are as follows: (1)  =48.8787 K,  =3.3872 Å [53],  = 0.16667 [57]; (2)  =91.7 K,  =3.690 Å ([61] + Berthelot rules),  =0.089 [59]. R max = 15 Å, b max = 13 Å.

Fig. 13 .Fig. 14 .

 1314 Fig. 13. Contributions of different parts of the interaction PES into CO pressure broadening coefficients for pure CO. The parameters of interaction PES correspond to Fig. 9.

Table 1 .

 1 Summary of experimental conditions of the measured spectra of pure CO and CO-H 2 mixtures used in this study.

	Gas	Temperature	Total Pressure	Volume Gas	Path Length
	Sample	(K)	(Torr)	Mixture Ratio	(m)
	Pure CO	298.05	97.26	1.0	0.0205
	Pure CO	298.05	148.30	1.0	0.0205
	Pure CO	298.05	329.50	1.0	0.0205
	Pure CO	298.30	3.15	1.0	0.1
	Pure CO	297.90	4.47	1.0	0.1
	Pure CO	298.20	9.40	1.0	0.1
	Pure CO	298.15	123.85	1.0	0.1
	Pure CO	279.90	279.90	1.0	0.1
	Pure CO	298.20	507.00	1.0	0.1
	Pure CO	298.15	1.36	1.0	1.5
	CO-H 2	298.20	155.15	0.1696	0.1
	CO-H 2	298.05	315.65	0.1899	0.1
	CO-H 2	297.85	474.65	0.2297	0.1
	CO-H 2	275.95	94.33	0.0487	1.5
	CO-H 2	275.65	174.12	0.0509	1.5
	CO-H 2	275.75	332.34	0.0496	1.5
	CO-H 2	296.20	574.70	0.0120	1.5
	CO-H 2	296.35	643.11	0.0474	1.5

Table 2 .

 2 Molecular parameters for CO and H 2 used in the theoretical calculations of CO line broadening coefficients.

	Molecule	r (Å)	B (cm -1 )	(D)	Q (DÅ)
	12 C 16 O	1.1309	1.9225	0.11	-2.0
	H 2	0.7508	59.3345	0	0.6522

Table 3 .

 3 CO-CO, H 2 -H 2 and CO-H 2 Lennard-Jones interaction parameters, , , used in present calculations.

	Type of Interaction	 (K)	 (Å)	Reference
	CO-CO	110 91.7	3.59 3.69	[58] [62]
	H 2 -H 2	59.7	2.827	[62]
	CO-H 2	48.8787 73.9898	3.3872 3.2585	[54] [62] a

a Calculated from data of Ref.

[START_REF] Friedmann | The quantum mechanical distribution function of molecular systems: translational and rotational motions[END_REF]

using Lorentz-Berthelot combination rules.

Table 4 .

 4 Calculated diffusion constants (cm 2 /s) and friction parameter (cm -1 atm -1 ) for pure CO and H 2 as well as for CO-H 2 mixtures with different molar fractions calculated at T=298 K and pressure of 1 atm.

	Diffusion	Diffusion	Volume Mixing	Diffusion	Friction Parameter
	Constant for	Constant for	Ratio of CO-H 2	Constant for gas	(	)×10 4
	Pure CO	Pure H 2	Spectra	mixture (D 12 )
	0.194	1.420	1 (pure CO)	0.19		242.299
			0.0120	1.41		33.424
			0.0474	1.36		34.479
			0.0487	1.36		34.530
			0.0496	1.36		34.555
			0.0509	1.36		34.581
			0.1696	1.21		38.747
			0.1899	1.19		39.563

Table 5 .

 5 Optimized adjustable parameters for semi-empirical calculations using the Exponential Power Gap (EPG) method.

*See text for details.

Table 6 .

 6 Line positions, intensities and Einstein A coefficients obtained using the Speed-Dependent Voigt line shape model.

	m	Line Positions (

cm -1 ) Line Intensity ×10 22 (cm -1 /(molecule⋅cm -2 )) at 296K Einstein A coefficient (s -1 )

	-9	4222.954945(6)		25.852(12)		0.5063
	-8	4227.354766(5)		27.329(12)		0.5148
	-7	4231.685733(5)		27.873(12)		0.5248
	-6	4235.947753(5)		27.350(12)		0.5362
	-5	4240.140651(6)		25.635(12)		0.5506
	-4	4244.264227(6)		22.662(12)		0.5699
	-3	4248.318396(7)		18.433(11)		0.6038
	-2	4252.303025(8)		13.111(10)		0.6718
	-1	4256.217943(14)		6.848(9)		1.0184
	1	4263.837930(14)		7.038(9)		0.3458
	2	4267.542864(8)		13.901(10)		0.4193
	3 4 5 6	4271.177403(6) Constants * 4274.741533(6) a (cm -1 atm -1 ) 4278.235058(5) 4281.657825(5)	CO-CO P and R 0.04555	CO-H 2 20.192(11) P 25.585(12) 0.0152 29.853(13) 32.875(13)	CO-H 2 R 0.0181	0.4528 0.4734 0.4866 0.4978
	7 8 9	4285.009711(5) b c 4288.290573(5) 4291.500221(5)	0.41980 1.10630	0.1280 34.537(14) 1.2000 34.895(14) 34.018(13)	0.1910 1.1000	0.5064 0.5137 0.5222
	10	4294.638584(5)		32.210(13)		0.5274
	11	4297.705411(5)		29.600(13)		0.5336
	12	4300.700661(5)		26.496(12)		0.5393
	13	4303.624136(6)		23.135(11)		0.5435
	14	4306.475699(6)		19.687(11)		0.5496
	15	4309.255182(7)		16.334(10)		0.5558
	16	4311.962464(8)		13.275(9)		0.5581
	17	4314.597391(9)		10.552(9)		0.5632
	18	4317.159814(11)		8.208(8)		0.5667
	19	4319.649574(14)		6.244(8)		0.5711
	-24 20 -23 21 -22 22 -21 23	4148.797708(99) 4322.066549(18) 4154.212260(93) 4324.410613(24) 4159.560420(64) 4326.681506(33) 4164.841602(45) 4328.879349(46)		0.559(5) 4.616(7) 0.840(5) 3.374(7) 2.401(6) 1.231(5) 1.770(5) 1.691(6)		0.5797 0.4246 0.5824 0.4291 0.5869 0.4371 0.4434 0.5874
	-20	4170.055891(33)		2.504(6)		0.4464
	-19	4175.203163(24)		3.487(7)		0.4495
	-18	4180.283295(18)		4.747(7)		0.4518
	-17	4185.296052(15)		6.272(7)		0.4588
	-16	4190.241224(12)		8.123(8)		0.4647
	-15	4195.118736(10)		10.310(8)		0.4697
	-14	4199.928509(8)		12.694(9)		0.4800
	-13	4204.670277(7)		15.588(10)		0.4790
	-12	4209.343958(7)		18.369(10)		0.4858
	-11	4213.949410(6)		21.171(11)		0.4921
	-10	4218.486447(6)		23.804(11)		0.4961

Table 7 .

 7

Table 8 .

 8 Pressure-induced line shift coefficients (cm -1 atm -1 ) for CO-CO and CO-H 2 for transitions in the first overtone band obtained using the Voigt, Speed-Dependent Voigt, Rautian and Speed-Dependent Rautian line shape models.

	)	0.06276 0.0690(2) 0.0712(1)	0.06899( 10)	0.06887( 10)	0.06804

Table 9 .

 9 Line mixing coefficients (atm -1 ) for CO-CO and CO-H 2 for transitions in the first overtone band obtained using the Voigt, Speed-Dependent Voigt line shape models. Calculated values obtained using the EPG method are also included.

		0.00509(2	0.00529(2	0.00529(2	0.00529(2	0.0037(8) 0.0039(8) 0.0041(5) 0.0041(5)
		6)	0)	0)	0)
	23	-0.00497(3 6)	-0.00500(2 8)	-0.00500(2 8)	-0.00500(2 8)	-0.0056(1 1)	-0.006(11)	-0.0054(8)	-0.0054(8)
						-	-	-	-
	24					0.0091(1	0.0095(1	0.0093(1	0.0092(1
						5)	6)	1)	1)

Table 10 .

 10 Speed dependence parameter for pure CO (present study and Ref.[START_REF] Devi | Spectral line parameters including temperature dependences of self-and air-broadening in the 2←0 band of CO at 2.3 μm[END_REF]), and for CO-H 2 for transitions in the first overtone band obtained using the Speed-Dependent Voigt line shape model.

	2	0.0045(12)	0.00476(6)	0.0128	0.0110(1)	0.0119(1)	0.0121
	3	0.0033(8)	0.00280(6)	0.0076	0.0059(1)	0.0062(1)	0.0068
	4	0.0034(7)	0.00325(5)	0.0053	0.0041(1)	0.0038(0)	0.0044
	5	0.0023(6)	0.00208(5)	0.0037	0.0025(1)	0.0023(0)	0.0027
	6	0.0012(5)	0.00085(5)	0.0026	0.0007(1)	0.0011(0)	0.0014
	7	0.0011(5)	0.00085(5)	0.0018	0.0002(1)	-0.0002(0)	0.0002
	8	0.0003(5)	0.00048(5)	0.0011	-0.001(1)	-0.0011(0)	-0.0008
	9	-0.0013(5)	-0.00123(5)	0.0006	-0.0019(1)	-0.0018(0)	-0.0017
	10	-0.0009(6)	-0.00110(6)	0.0001	-0.0026(1)	-0.0028(0)	-0.0026
	11	-0.0012(6)	-0.00089(5)	-0.0003	-0.0035(1)	-0.0032(0)	-0.0033
	12	-0.0026(7)	-0.00288(6)	-0.0007	-0.0033(1)	-0.0038(0)	-0.0040
	13	-0.0016(7)	-0.00127(9)	-0.0010	-0.0048(1)	-0.0041(0)	-0.0047
	14	-0.0019(9)	-0.00287(7)	-0.0013	-0.0043(1)	-0.0046(1)	-0.0053
	15	-0.0043(10)	-0.00423(8)	-0.0016	-0.0055(1)	-0.0052(1)	-0.0059
	16	-0.0034(12)	-0.00450(7)	-0.0019	0.0005(15)	0.0004(9)	-0.0065
	17	-0.0073(15)	-0.00804(11)	-0.0021	-0.0060(1)	-0.0061(1)	-0.0070
	18	-0.0023(18)	-0.00256(11)	-0.0024	-0.0066(1)	-0.0067(1)	-0.0076
	19	-0.0055(23)	-0.00629(15)	-0.0026	-0.0068(1)	-0.0066(1)	-0.0081
	20	-0.0012(31)	-0.00054(15)	-0.0029	-0.0069(1)	-0.0074(1)	-0.0087
	21	-0.0051(41)	-0.00612(19)	-0.0032	-0.0084(2)	-0.0073(1)	-0.0093
	22			-0.0036			-0.0101
	23			-0.0045			-0.0112
	24			-0.0074			-0.0132
		m	CO-

CO Present study CO-CO Devi et al., 2012 CO-H 2 Present study

	-11	0.110	0.077	0.00481
	-10	0.125	0.078	0.00487
	-9	0.106	0.085	0.00531
	-8	0.104	0.087	0.00544
	-7	0.118	0.096	0.00600
	-6	0.104	0.103	0.00644
	-5	0.119	0.107	0.00669
	-4	0.108	0.109	0.00681
	-3	0.114	0.107	0.00669
	-2	0.132	0.104	0.00650
	-1	0.088	0.107	0.00669
	1	0.113	0.106	0.00662
	2	0.110	0.105	0.00656
	3	0.109	0.111	0.00694
	4	0.122	0.117	0.00731
	5	0.123	0.116	0.00725
	6	0.118	0.112	0.00700
	7	0.106	0.106	0.00073
	8	0.114	0.098	0.00613
	9	0.108	0.093	0.00644
	10	0.107	0.088	0.00550
	11	0.100	0.084	0.00525
	12	0.096	0.080	0.00500
	13	0.099	0.077	0.00481
	14	0.092	0.076	0.00475
	15	0.088	0.077	0.00481
	16	0.074	0.077	0.00000
	17	0.084	0.075	0.00469
	18	0.097	0.076	0.00476
	19	0.098	0.073	0.00457
	20		0.074	0.00463
	21		0.072	0.00451
	22		0.069	0.00432
	-24 23 -23 24		0.083 0.069 0.071 0.065	0.00432 0.00625 0.00444 0.01877
	-22		0.066	0.00413
	-21		0.070	0.00439
	-20		0.064	0.00401
	-19	0.086	0.070	0.00438
	-18	0.140	0.070	0.00000
	-17	0.044	0.071	0.00444
	-16	0.056	0.068	0.00426
	-15	0.046	0.074	0.00463
	-14	0.077	0.070	0.00438
	-13	0.111	0.073	0.00456
	-12	0.103	0.074	0.00462

Table 11 .

 11 Thermally averaged theoretical line broadening coefficients convergence for different b max values, as shown in Fig.

CO-CO CO-H 2 Maxwell-Boltzmann Average MThV Maxwell-Boltzmann Average MThV

			CO-CO			CO-H 2
	J	b max =14	b max =19	b max =25 b max =12 b max =13 b max =15
	0	0.09974	0.10075		0.10202 0.07854	0.07792	0.07857
	2	0.08928	0.08974		0.08875 0.07572	0.07551	0.07578
	4	0.08136	0.08108		0.08088 0.07392	0.07453	0.07422
	6	0.07726	0.07667		0.07603 0.07331	0.07316	0.07311
	8	0.07320	0.07265		0.07338 0.07169	0.07159	0.07224
	10	0.06981	0.06899		0.06855 0.07018	0.06993	0.07008
	12	0.06463	0.06466		0.06492 0.06934	0.06916	0.06944
	14	0.06045	0.06091		0.06039 0.06810	0.06837	0.06853
	16	0.05616	0.05661		0.05568 0.06725	0.06742	0.06708
	18	0.05231	0.05255		0.05137 0.06713	0.06664	0.06635
	20	0.04867	0.04847		0.04743 0.06705	0.06662	0.06664
	22	0.04517	0.04522		0.04404 0.06584	0.06609	0.06643
	24	0.04222	0.04227		0.04130 0.06602	0.06603	0.06640
		0	0.10075	0.10109	0.07792	0.07346
		2	0.08974	0.09041	0.07551	0.07191
		4	0.08108	0.08076	0.07453	0.07229
		6	0.07667	0.07543	0.07316	0.07258
		8	0.07265	0.07183	0.07159	0.07190
		10	0.06899	0.06762	0.06993	0.07065
		12	0.06466	0.06403	0.06916	0.06889
		14	0.06091	0.05945	0.06837	0.06689
		16	0.05661	0.05537	0.06742	0.06566
		18	0.05255	0.05042	0.06664	0.06513
		20	0.04847	0.04662	0.06662	0.06443
		22	0.04522	0.04345	0.06609	0.06449
		24	0.04227	0.04075	0.06603	0.06462

Table 13 .

 13 Thermally averaged theoretical line broadening coefficients (cm -1 atm -1 ) at 296 K shown in Figs.10 and 11.

			CO-CO		CO-H 2
	J	1	2	3	1	2
	0	0.10075	0.10012	0.10079	0.07792	0.07947
	2	0.08974	0.08847	0.08901	0.07551	0.07724
	4	0.08108	0.08020	0.08023	0.07453	0.07641
	6	0.07667	0.07547	0.07579	0.07316	0.07563
	8	0.07265	0.07154	0.07142	0.07159	0.07450
	10	0.06899	0.06796	0.06800	0.06993	0.07321
	12	0.06466	0.06363	0.06356	0.06916	0.07282
	14	0.06091	0.05998	0.05968	0.06837	0.07180
	16	0.05661	0.05523	0.05504	0.06742	0.07075
	18	0.05255	0.05106	0.05086	0.06664	0.07037
	20	0.04847	0.04685	0.04658	0.06662	0.06997
	22	0.04522	0.04335	0.04314	0.06609	0.06986
	24	0.04227	0.04029	0.04020	0.06603	0.06960



  Self-and H 2 -broadened line parameters for transitions in the 20 band of CO at 298 K are reported  Line intensities, pressure shifts, line mixing and speed dependence parameters are presented.  Calculations of self-and H 2 -broadening coefficients of CO using classical impact theory are included.

	4	0.05205 0.05211	0.07924	0.08108	0.05846 0.07497	0.07453
	6	0.04886 0.04873	0.07491	0.07667	0.05727	0.0735	0.07316
	8	0.04745 0.04754	0.07162	0.07265	0.05724 0.07196	0.07159
	10 0.04719 0.04730	0.06795	0.06899	0.05764 0.07033	0.06993
	12 0.04677 0.04678	0.06407	0.06466	0.05803 0.06910	0.06916
	14 0.04599 0.04602	0.06017	0.06091	0.05900 0.06837	0.06837
	16 0.04534 0.04527	0.05610	0.05661	0.05926 0.06762	0.06742
	18 0.04357 0.04352	0.05196	0.05255	0.05938 0.06689	0.06664
	20 0.04232 0.04228	0.04787	0.04847	0.05957 0.06666	0.06662
	22 0.04087 0.04088	0.04457	0.04522	0.05989 0.06622	0.06609
	24 0.03925 0.03922	0.04166	0.04227	0.05985 0.06643	0.06603
	Highlights
				CO-CO			CO-H 2
		TH	TH+dd	TH+dd+QQ TH+dd+dQ+QQ	TH	TH+QQ TH+dQ+QQ
	0	0.06548 0.06559	0.09969	0.10075	0.06236 0.07845	0.07792
	2	0.05720 0.05741	0.08811	0.08974	0.05954 0.07593	0.07551
					43

Acknowledgments

This work was carried out at the University of Lethbridge funded through the Natural Sciences and Engineering Research Council of Canada and supported by the Discovery and CREATE grant programs. The research performed at the College of William and Mary, Connecticut College and NASA Langley Research Center was supported under contracts and cooperative agreements with the National Aeronautics and Space Administration. We are thankful to Dr. D.

Chris Benner at the College of William and Mary for his permission of using multispectrum fitting software, LABFIT, to carry out the data analysis. We thank Mr. Hossein Naseri for his contributions to the early stage of the analysis.