1. Self- and H2-Broadened Line Parameters of Carbon Monoxide in the First Overtone Band
Koorosh Esteki1, Adriana Predoi-Cross1*, Hossein Naseri1,7, Sergey Ivanov2, Aziz Ghoufi3, Franck Thibault3, V. Malathy Devi4, Mary Ann H. Smith5 and Arlan Mantz6
1 Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB, Canada
2Institute on Laser and Information Technologies, Russian Academy of Sciences, Troitsk, Moscow, Russia.
3 Institute de Physique de Rennes, Université de Rennes 1, Rennes, France
4 Department of Physics, College of William and Mary, Williamsburg, VA, USA
5 Science Directorate, NASA Langley Research Center, Hampton, VA, USA
6 Department of Physics, Astronomy and Geophysics, Connecticut College, New London, CT, USA.
7 Present address: Farmers Edge, Lethbridge, AB, Canada *
71st International Symposium on Molecular Spectroscopy, June 20-24, Paper WB03.

2. Research Context
High-resolution molecular line shape studies are often used to obtain precise information on molecular species located in areas that are not directly accessible to us, such as high altitude layers of the Earth’s atmosphere, planetary atmospheres, or interstellar space.
Science Advisory Groups for remote sensing missions have strongly recommended that new laboratory spectroscopic studies using the best experimental techniques and/or sophisticated theoretical models are required, to enable accurate retrievals of concentration profiles for trace planetary atmospheric constituents.
Knowledge of H2-broadened line shapes is especially important for remote sensing of the atmospheres of giant planets in our Solar System and beyond.

3. Analysis Details
The Fourier transform spectra were recorded at the National Solar Observatory on Kitt Peak, AZ; wavenumber scales were calibrated using line positions in the HITRAN2012 database. Previous analyses (Malathy Devi et al., 2002, 2004) were done assuming the Voigt line shape without line mixing.
The interactive multispectrum nonlinear least squares fitting technique (Benner et al. (1995)) was used to analyze all spectra recorded, simultaneously.
Different line shape profiles were applied (Voigt, Rautian). Including speed-dependence in our spectral profiles did improve the fit residuals (observed-calculated). Weak line mixing was necessary to accurately model the absorption.
Initial values for all line parameters were taken from the HITRAN2012 database.
Spectral backgrounds (including some channeling), zero transmission levels, instrument line shapes were appropriately modeled.

4. Expressions for Broadening and Shift Parameters
bL(p,T) is the Lorentz halfwidth (in cm-1) of the spectral line at pressure p and temperature T, and the broadening coefficient bL0(Gas)(p0,T0) is the Lorentz halfwidth of the line at the reference pressure p0 (1 atm) and temperature T0 (296 K), and  is the ratio of the partial pressure of CO to the total sample pressure in the cell. The temperature dependence exponents of the pressure-broadening coefficients are n1 and n2.
Where 0 is the zero-pressure line position (in cm-1),  is the line position corresponding to the pressure p, δ0 is the pressure-induced line shift coefficient at the reference pressure p0(1 atm) and temperature T0(296 K) of the broadening gas (foreign or self broadener), and  is as defined above.

5. The Voigt Line Shape Profile
Fig. Ref: W. Demtroder, Atoms, Molecules and Photons, Springer (2006).
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Text adapted from slides of Ha Tran, Université Paris-Est Créteil and Université Paris Diderot

6. Speed Dependence References:
J.-M. Hartmann, C. Boulet, and D. Robert, Collisional Effects on Molecular Spectra (2008).
References:
Berman, J. Quant. Spectrosc. Radiat. Transf. 12, 1331 (1972)
Rohart, Wlodarczak, Colmont, Cazzoli, Dore, Puzzarini, J. Mol. Spectrosc. 251, 282 (2008)

7. Dicke Narrowing
If the mean free path of the molecules becomes equal to, or less than to the wavelength of the incident radiation λ, the resulting motion of the molecules becomes Brownian in nature and the gas diffusion becomes relevant.
There are two standard line shape functions that can be used to determine the narrowing parameter for a transition:
Galatry profile or often called the soft collision model. This line shape incorporates the Brownian movement model and assumes only small changes in the radiators velocity during collisions.
(2) Nelkin-Ghatak profile or often called the hard collision model. A different implementation of the hard collision model is the Rautian-Sobelman model. For this line shape each collision erases any information about the radiators velocity. This randomizes the velocities of the radiators.

8. Line Mixing Effects
Collisions induce transfers of populations between the levels of the two lines that lead to transfers of intensity between the lines.
Absorption Coefficient
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Ref. Ha Tran, Université Paris-Est Créteil, France, private communication

9. Summary of experimental conditions of the measured spectra of pure CO and CO-H2 mixtures used in this study.
Note: All spectra were recorded using the high resolution 1-m Fourier transform spectrometer at the National Solar Observatory on Kitt Peak, AZ. Previous analyses of some of these spectra, using the Voigt line shape without line mixing, were published by Malathy Devi et al. (2002, 2004).
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10. Multispectrum fit of 10 spectra of CO using the speed-dependent Voigt (SDV) profile in the 4146−4332 cm−1 region covering the P(24) to R(24) transitions in the 2←0 band of CO. Lower panel: Observed spectra. Upper Panel: Observed minus Calculated residuals.
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11. Measured self-broadened half-width coefficients of CO in the 2←0 band.
Measured CO 2←0 self broadening and shift coefficients
Preliminary results for the Voigt line shape compared with other published measurements
Measured self-broadened half-width coefficients of CO in the 2←0 band.
Measured self-pressure-induced line shift coefficients of CO in the 2←0 band.

12. Measured CO 2←0 H2 broadening and shift coefficients
Preliminary results for the Voigt line shape compared with other published measurements
Measured H2-broadened Lorentz half-width coefficients of CO in the 2←0 band.
Measured H2 pressure-induced shift coefficients of CO in the 2←0 band.

13. Speed Dependence Parameters for CO-CO
Present Study ◊
CO-CO, Devi et al. 2012
CO-air, Devi et al. 2012

14. Scaling Laws Exponential Power Gap Model - EPG
To find the relaxation matrix we use a nonlinear Marquardt algorithm to optimally fit the parameters a, b and c in the state to state transfer equation.
The best fit is found by optimizing the diagonal elements of the relaxation matrix to be equal to the experimentally determined broadening coefficients.
Measured Lorentz half-widths of CO-CO retrieved using the Voigt line shape model compared with EPG results.
Measured line mixing coefficients of CO-CO retrieved using the Voigt line shape model, compared with other published results and results obtained with EPG law.

15. Measured CO-H2 Lorentz half-width coefficients, obtained using the Voigt line shape model, compared with results obtained using the EPG scaling law.
Measured CO-H2 line mixing coefficients, retrieved using the Voigt line shape model, compared with results obtained with the EPG scaling law.
EPG
 Constants
CO-CO
CO-H2
P and R a
4.55510-2
2.03110-2 b
4.19810-1
2.30410-1 c
1.1063
1.1903
Optimized adjustable parameters for the EPG scaling law.

16. Theoretical calculations of broadening coefficients
A full classical approach was applied to calculate the half-width coefficients of CO absorption lines in CO-H2 and CO-CO collisions. The calculations utilize simple vibrationally independent intermolecular interaction potential (Tipping-Herman + electrostatic). Both molecules are treated as rigid rotors. The dependences of CO half-width coefficients on rotational quantum number J, for J ≤ 24 are computed and compared with measured data at room temperature.
Molecular parameters for CO and H2 used in the calculations of CO line broadening coefficients.
Molecule
r(Å)
B(cm-1)
(D)
Q (DÅ)
12C16O
1.1309
1.9225
0.11
-2.0 H2
0.7508
0.6522
CO-CO, H2-H2 and CO-H2 Lennard-Jones interaction parameters,  ,  used in calculations.
Interaction
 (K)
 (Å)
CO-CO
110
91.7
3.59
3.69
H2-H2
59.7
2.827
CO-H2
3.3872
3.2585

18. Theoretical calculations of diffusion constants for the CO-CO and CO-H2 systems
To estimate the mass diffusion of CO and H2, H2 was modeled by means a single united atom force field [H. Frost et al., J. Phys. Chem. B 110 (2006)] while CO was described from a three electrostatic sites model [A. Martín- Calvo et al., J. Phys. Chem. C 116 (2012)].
Intermolecular interactions were described by combining electrostatic and van der Waals interactions.
Molecular dynamics (MD) simulations were carried out from DLPOLY software.
In the canonical ensemble, the temperature was kept constant by means of Nose-Hoover algorithm such that the relaxation time of the thermostat was fs.
The integration of motion equations was performed by using the velocity Verlet algorithm [M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford University Press, United States (1987)].

19. D (Diffusion constant) m2/s
Theoretical calculations of diffusion constants for the CO-CO and CO-H2 systems
The Maxwell-Stephan diffusion was managed by means of the model of Darken [L.S. Darken, Trans. AIME, 175 (1948)]:
𝑫 𝟏𝟐 = 𝒙 𝟏 𝑫 𝟏 + 𝒙 𝟐 𝑫 𝟐 where x1 and x2 are the molar fraction of both 1 and 2 components and, D1 and D2 are the self-diffusion constants of 1 and 2.
Calculated diffusion constants for pure CO and H2 as well as for
some different molar fractions.
D (Diffusion constant) m2/s
Pure CO
Pure H2
Mixture of CO and H2
D12
D1(H2)
D2(CO)
10-5
10-4
CO-H2(0.0126)
10-4
10-4
10-5
CO-H2 (0.050)
10-4
10-4
10-5
CO-H2 (0.183)
10-5
10-4
10-5
CO-H2 (0.203)
10-5
10-5
10-5
CO-H2 (0.240)
10-5
10-5
10-5
CO-H2 (0.500)
10-5
10-5
10-5

20. Theoretical narrowing parameters calculated using the diffusion constants presented here are currently used in our line parameter retrievals using the Rautian and speed-dependent Rautian models.
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21. Conclusions
We have reported preliminary experimental and theoretical line parameters for 48 (P(24) to R(23)) rotational transitions of the first overtone (2←0) band of 12C16O at room temperature (~298 K). Both self-broadened and H2-broadened CO spectra were analyzed in this study.
We present the first results of calculations of self- and H2-broadened width coefficients of CO using classical impact theory. We have used a simple interaction PES, with good results for half-widths of the molecular systems, especially for CO-CO.
The EPG scaling law was used to compute line mixing coefficients and broadening coefficients.
The diffusion constants for CO-CO and CO-H2 mixtures, necessary for the narrowing parameters in the Rautian line profiles, were determined using molecular dynamics calculations.

22. “We are a way for the cosmos to know itself. “
Acknowledgements
The research carried out at the University of Lethbridge is funded by the Natural Sciences and Engineering Research Council of Canada through the Discovery and CREATE grant programs. Dr. D. Chris Benner at the College of William and Mary is thanked for allowing us to use his multispectrum fitting software in analysing the data.
Thank you!
“We are a way for the cosmos to know itself. “
(Carl Sagan)
February 2009
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