Prediction of high-order line-shape parameters for air-broadened O2 lines using requantized classical molecular dynamics simulations and comparison with measurements

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Prediction of high-order line-shape parameters for air-broadened O2 lines using requantized classical molecular dynamics simulations and comparison with

measurements

D.D. Tran, V.T. Sironneau, J.T. Hodges, Raymond Armante, J. Cuesta, H.

Tran

To cite this version:

D.D. Tran, V.T. Sironneau, J.T. Hodges, Raymond Armante, J. Cuesta, et al.. Prediction of high-

order line-shape parameters for air-broadened O2 lines using requantized classical molecular dynamics

simulations and comparison with measurements. Journal of Quantitative Spectroscopy and Radiative

Transfer, Elsevier, 2019, 222-223, pp.108-114. �10.1016/j.jqsrt.2018.10.013�. �hal-01976150�

1

Prediction of high-order line-shape parameters for air-broadened O

lines using requantized classical molecular dynamics simulations and comparison with

measurements

D. D. Tran

, V.T. Sironneau

, J. T. Hodges

, R. Armante

, J. Cuesta

, H. Tran

1

Laboratoire de Météorologie Dynamique, IPSL, CNRS, Sorbonne Université, École normale supérieure, PSL Research University, École polytechnique, F-75005 Paris, France

2

National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899, USA

3

Laboratoire Interuniversitaire des Systèmes Atmosphériques (LISA, CNRS UMR 7583), Université Paris Est Créteil, Université Paris Diderot, Institut Pierre-Simon Laplace, 94010 Créteil, France

October 3, 2018 Abstract

Line-shape models such as the Hartmann-Tran (HT) profile have adjustable high-order parameters that are usually determined by fits to experimental spectra. As an alternative approach, we demonstrate that fitting the HT profile to theoretical spectra provides high-order line-shape parameters for O

transitions that are consistent with experimentally determined values. To this end, normalized absorption spectra of air-broadened O

lines were computed without adjustable parameters using requantized classical molecular dynamics simulations (rCMDS). These theoretical calculations were made at a pressure of 203 kPa and for values of the Doppler width that cover near-Doppler-limited to collisional-broadened pressure conditions. Hartmann-Tran (HT) line profiles with adjustable line-shape parameters were then simultaneously fit to the set of rCMDS-calculated spectra in a global multispectrum analysis.

The retrieved high-order line-shape parameters (i.e. the speed dependence of the line broadening and the Dicke narrowing coefficient) were subsequently used as fixed HT parameters in the analysis of seven air-broadened O

lines of the band.

The spectra were measured over a fifteen-fold range of total gas pressure at high spectral resolution and signal-to-noise ratio with a frequency-stabilized cavity ring-down spectroscopy system. We show that these predicted parameters enable all the measured lines to be fit to within 1 %, which is much better than best fits of the Voigt line profile to the measured spectra. This approach opens the route for predicting high-order line-shape parameters from first-principles calculations and for their inclusion in spectroscopic databases. Furthermore, the temperature dependences of the broadening coefficient and its speed dependent component for air-broadened O

lines were also calculated using rCMDS.

1. Introduction

It is now widely known that accurate and precise line-shape modeling is necessary to meet the requirements of laboratory measurements and a wide variety of applications (see [1]

and references therein, for instance). To this aim, it is recommended that the Hartmann-Tran (HT) [2,3] profile be used for high-resolution spectroscopy [4] to replace the usual Voigt

*

Corresponding author: ha.tran@lmd.jussieu.fr

2

model. The HT profile accounts for various collisional effects affecting the measured line shape: the collision-induced line broadening and shifting and their speed dependences; the velocity changes due to collisions and the temporal correlation between changes in velocity and internal state. It was shown that this profile can model measured transitions of various molecular systems to within a few 0.1 % (e.g. [5–13]). The international spectroscopic database HITRAN [14] now provides parameters of this profile when available. These line- shape parameters are usually obtained from fits of laboratory measured spectra. However, correct use of the HT profile for spectra analysis requires two key conditions. First, because of the large number of line-shape parameters involved, a multi-spectrum fitting technique applied to spectra measured over a large pressure range is recommended in order to avoid numerical correlation between various parameters. Second, high signal-to-noise ratio spectra are needed to accurately retrieve all the line-shape parameters. Both conditions are not easily met for many molecular systems, over wide spectral ranges and for various pressure and temperature conditions. Therefore, addressing the precision and accuracy requirements of wide-ranging applications as well as populating spectroscopic databases with HT parameters constitutes a huge amount of experimental and data analysis effort.

In parallel with precise and accurate laboratory measurements, theoretical calculations can be used to predict high-order line-shape parameters (i.e. parameter characterizing refined effects such as the speed dependence of the collisional width, the collision-induced velocity changes). In [15,16], it was shown that first-principles calculations based on molecular configurations and intermolecular potentials, combined with a limited amount of information obtained from measurements successfully predicts the shapes of CO and H

O ro-vibrational lines. Indeed, these theoretical calculations are based either on classical molecular dynamics simulations (CMDS) [15] or a combination of CMDS and semi-classical methods (see [16]

and references therein). It was shown that the non-Voigt effects observed in the measured spectra are well predicted by these first-principles calculations, for various molecular systems (e.g. [17–22]) although the difference between the computed and measured line widths could be several percent. In [15,16], the calculations were thus empirically improved by introducing a measured value of the line width into the computed auto-correlation function of the transition dipole moment, where the line-shape equals the Fourier-Laplace transform of the latter quantity. With this correction procedure, it was shown that the calculations can predict measured spectra of several lines of CO [15] and H

O [16] over a large pressure range to within 1 %, significantly better than the best fits of the measurements with the usual Voigt profile. In this work, first-principles CMDS calculations of line-shapes were used to provide theoretical spectra from which high-order line-shape parameters could be retrieved.

Specifically, we determined the (quadratic) speed dependence of the line broadening and the Dicke narrowing parameter by global multi-spectrum fitting of HT profiles to CMDS- calculated spectra. This procedure is applied and validated, in this work, for air-broadened absorption spectra of O

. Absorption by O

is very important in atmospheric applications because the molar fraction of O

in dry air is nearly constant and well known. The optical interrogation of O

absorption lines therefore allows accurate determination of the atmospheric airmass (pathlength) traversed by the measured photons. This measurement can reduce errors caused by uncertainties in airmass associated with simultaneous measurements of other gases of scientific interest (e.g. CO

, CH

), for instance. Therefore, precise spectroscopic parameters of O

are required in order to retrieve reliable results from atmospheric observations.

The remainder of this paper is divided into three sections. The theoretical simulations

and measurements are briefly described in Sec. 2. Multi-spectrum fits of the HT profile to

theoretical and experimental spectra as well as theoretical predictions of the temperature

3

dependence of certain line parameters are discussed in Sec. 3. Finally, we give concluding remarks in Sec. 4.

2. Data used and analysis procedure

2.1 Requantized classical molecular dynamics simulations (rCMDS)

Classical molecular dynamics simulations (CMDS) [23] were carried out for the O

(20 %) and N

(80 %) mixture at 203 kPa and three temperatures: 200 K, 250 K and 296 K using the same calculations as those of [18,24] where details on the calculations procedure can be found. The intermolecular potentials used were described by pairwise 6-12 Lennard- Jones atom-atom contributions, complemented by Coulombic forces between fictitious charges that were introduced to reproduce the electric quadrupoles of the molecules. The atom-atom data for O

-O

and N

-N

were taken from Refs. [24] and [25], respectively, and the corresponding parameters for O

-N

were deduced from the standard combination rules [26]. During the CMDS, the force and torques applied to each molecule by its surrounding neighbors are computed classically. This provides the center-of-mass position and velocity, the molecular axis and the rotational momentum for each molecule at each time. The auto- correlation function of the dipole moment (along the molecular axis) can thus be computed, its Fourier-Laplace transform directly yields the corresponding normalized absorption band spectrum. The requantization procedure of Ref. [17] was applied here by matching the classical rotation frequency of the molecules to the quantum position of P branch lines. The electronic spin of O

was neglected, as done in Refs. [17,18]. The rotational quantum number is thus equal to the total rotational quantum number and PP and PQ transitions are identical (as for RR and RQ lines). Note that our rCMDS do not take into account the dephasing of the dipole, which is associated with the fact that the effects of intermolecular interactions for molecules in the upper and lower states of the optical transitions are different.

Consequently, the calculated spectra do not show any pressure shift.

The calculations were performed with the IBM Blue Gene/P computer

of the Institut du Dévéloppement et des Ressources en Informatique Scientifique. For each temperature condition, calculations were made for 122.88×10

molecules. The molecules were initially randomly distributed in 4096 cubic volumes with periodic conditions, with each volume containing 30,000 molecules. For each temperature condition, twelve values of the Doppler width, ranging from 0.012 cm

to 0.53 cm

, were used in the calculations. This set of parameters provided a large range for the ratio (i.e. from about 0.075 to 4.606) covering the near-Doppler broadened to collisional-broadened regimes.

2.2 Experimental data

The measured spectra of Ref. [18] of air-broadened

O

lines in the singlet  band [ ] were retained here for validation of the procedure that we have proposed. Measurements were made at room temperature and for various pressures ranging from 6.7 kPa to 100 kPa (Table 1). These experiments were done at the National Institute of Standards and Technology (NIST) and were based on the frequency-stabilized cavity ring- down spectroscopy (FS-CRDS) technique described in [27,28]. The ring-down cavity was actively length-stabilized and had a mirror-to-mirror distance of 74 cm, with an effective mirror intensity reflectivity equal to 0.99995 and a minimum detectable absorption coefficient

†

Manufacturers and commercial product names are given solely for completeness. These citations do not imply

recommendation or endorsement by NIST

4

based on a 1 s averaging time of 2×10

cm

. The same mixture of synthetic dry air (79.28 % N

, 20.72 % O

by volume) was used for all measured spectra. The maximum single-pass absorbance levels were all less than 10

cm

. The relative combined standard uncertainties in O

molar fraction, absolute temperature and sample pressure were less than 0.01 %, 0.02 % and 0.05 %, respectively. We measured seven lines for which the temperature of the measurement was almost constant (i.e. variation within 0.5 K) for all considered pressures.

The value of the rotational quantum number of these absorption lines spanned from 1 to 13 (Table 1), thus providing a meaningful test of the calculations. More details of the particular FS-CRDS setup and the measurement procedure can be found in [18] and [8].

Line Line center (cm

)

Temperature (

C)

Pressure

(kPa) Maximum

absorbance (10

/cm) R1Q2 7889.933104 24.8 6.68; 13.4; 20.0; 26.7; 33.3;

46.7; 60.0; 73.2; 86.6; 99.9

3.6

R3Q4 7895.477670 25.3 6.70; 13.4; 20.0; 26.7; 33.4 8.1 R5Q6 7900.826802 25.3 6.70; 10.0; 13.4; 16.7 9.3 P5P5 7867.653563 25.6 6.70; 13.4; 20.1; 26.7 4.2 P9P9 7855.130970 25.0 6.71; 10.0; 13.3; 20.0; 60.0;

73.2; 86.7; 99.8 8.8

P11P11 7848.636972 22.3 6.67; 10.0; 13.3; 26.6; 33.3;

40.3

8.3

P13P13 7841.986547 24.9 6.65; 13.3; 20.0; 33.3; 46.7;

60.0; 73.2; 86.6; 99.9

8.1

Table 1: Experimental conditions for the measured [ ]

O

transitions considered in this work.

2.3 Analysis procedure

We first fit the HT profile to the rCMDS-calculated (or measured) spectra. Because of

the large number of involved parameters, a constrained global fitting procedure was used. For

each line, the line broadening coefficient , the speed dependent component , and the

Dicke narrowing parameter , were constrained to be the same for all considered Doppler

widths (or pressure conditions), where all three parameters have dimensions of wave number

per unit pressure. For each spectrum, the line position and line intensity were fitted

individually, together with a linear base line. For the measured spectra, the speed dependent

component of the pressure shift was also fitted while this quantity was fixed to zero for those

spectra calculated by CMDS, because the pressure shift was totally neglected in the

theoretical calculations. The Doppler widths were fixed to values computed at the temperature

of the rCMDS or to those of the measurements. For the latter, the measured temperatures at

each pressure condition were used for the determination of the Doppler widths and not the

average temperature over all pressures. Both the calculated and measured spectra were

normalized by their peak absorption in the fitting procedure. Because of the limited signal-to-

noise ratio of both the calculated and measured (i.e. about 500 and 2000, respectively)

spectra, it was impossible to retrieve all the parameters of the HT profile. Therefore, we chose

5

to fix the correlation parameter to zero, with the resulting reduced form of the HT profile being equivalent to the quadratic speed dependent hard-collision profile. Note that the assumption of no correlation between velocity- and internal-state-changing collisions, is justified for systems for which the kinetic collision frequency, deduced from the mass diffusion coefficient is much smaller than the broadening frequency (i.e. broadening coefficient), as the case here for the O

lines considered here [i.e. 6 kHz Pa

(0.02 cm

/atm) [29] compared to 15 kHz Pa

(0.05 cm

/atm) (see Table 2)].

As demonstrated previously for O

[18,24] and for other molecular systems [15,17,19,20,30], the non-Voigt effects observed on the rCMDS-calculated spectra are in very good agreement with those of measured spectra (through comparison of their Voigt fits residuals and parameters). However, line broadening coefficients predicted by rCMDS can be significantly different from measured values. For O

, it was shown that [24] broadening coefficients obtained from fits of rCMDS spectra with Voigt profiles are about 8 % lower than those obtained from measurements using this same profile. In this work, we observed that by using the HT profile the values of obtained from rCMDS are on average 2 % smaller than the measured values. Hence, we use rCMDS here to predict only the high-order line-shape parameters and not the line broadening coefficient. In the second step, we therefore refit the measured spectra while constraining the speed dependence of the line width,  and the Dicke narrowing parameter, , to those obtained from fits of the rCMDS spectra. We then compared the quality of the fits as well as the obtained parameters to the previous case when we fit all the parameters. Finally, note that we also used a Voigt profile to fit the measured spectra for comparison.

3. Results and discussion

In the following, we denote by VP all results obtained from fits of the measurements with the Voigt profile, by HT those obtained from fits of measurements with the HT profile when all line parameters were adjusted, and by HT_fix all results obtained from fit of measurements with the HT profile but with 

and 

fixed to those obtained from rCMDS.

3.1 Fit residuals and retrieved line-shape parameters

Fig. 1 shows the measured absorption spectra of the R1Q2 and P5P5 transitions (first row) at various values of the total pressure and the fit residuals obtained with VP, HT and HT_fix cases, respectively. As can be observed on this figure, the VP leads to relatively large residuals with magnitudes reaching as much as 3 % of the peak absorption. As expected, the residuals obtained with the HT profile are relatively small, almost within the experimental noise, regardless of the considered pressure. When fixing the values of 

and 

to those obtained from rCMDS (i.e. the HT_fix fitting procedure), the corresponding fit residuals are close to the previous case in which all parameters are adjusted. As an example, the standard deviations of the fits obtained for the R1Q2 (left side of Fig. 1) using VP, HT and HT_fix are 3.816 10

, 0.451 10

and 0.473 10

, respectively. These results show that one can determine the high-order HTP parameters by fitting the HTP to the rCMDS-calculated line-shape.

The maximum-to-minimum amplitudes of residuals (relative to the peak absorption of

unity) obtained from fits of the seven measured lines with VP, HT and HT_fix as a function

of pressure are plotted in Fig. 2. As shown, employing a Voigt profile leads to residuals

significantly higher than the other two cases. Moreover, the use of parameters obtained from

rCMDS provides a precise description of the measured spectra for all considered lines and

6

pressure conditions. Indeed, results obtained with HT_fix are almost as good as those obtained when all parameters of the HT profile are fitted, with maximum relative fit residuals well below 1%.

Table 2 lists the line-shape parameters obtained from fits of the measurements using the HT and HT_fix models. First, comparisons between the values of and obtained from measured spectra and those deduced from rCMDS show that they are rather close. For most of the considered lines, values of obtained from rCMDS are slightly larger than those of the measurements while the opposite trend is observed for . This result indicates that there are some correlations between these two parameters, and their values do not totally reflect the corresponding physical phenomenon. Note also that larger differences are observed for for weak lines (i.e. R1Q2, P11P11 and P13P13 lines, see Table 2). This is probably due to the smaller signal-to-noise ratio of the corresponding spectra and the weak influence of on the line shape. Nevertheless, as can be observed in Fig. 2, the two sets of line-shape parameters lead to very good agreements with measured spectra for a wide pressure range.

Concerning the line broadening coefficient, 

, the values obtained with the HT and HT_fix fitting procedures are very close to each other. Similarly, the obtained (small) values of the speed dependence component of the line shift are quite independent of the fitting procedure used.

Parameter /Line

R1Q2 17.720(18)

17.652(18)

1.110(53) 0.722(36)*

0.284(53) 0.281(53)

1.02(20) 1.80(7)*

R3Q4 16.513(18)

16.569(18)

1.092(53) 1.231(18)*

-0.003(41) -0.009(18)

0.98(11) 0.78(5)*

P5P5 16.445(18)

16.524(18)

1.181(41) 1.308(18)*

-0.115(41) -0.118(53)

0.66(12) 0.75(4)*

R5Q6 15.646(18)

15.737(18)

1.175(24) 1.308(18)*

-0.092(24) -0.092(36)

0.74(7) 0.75(4)*

P9P9 14.942(18)

15.060(18)

0.885(30) 1.269(12)*

-0.112(30) -0.104(36)

1.01(9) 0.68(4)*

P11P11 14.711(24) 14.723(30)

1.444(65) 1.278(18)*

-0.098(59) -0.098(71)

-0.27(21) 0.58(4)*

P13P13 14.048(18) 14.007(18)

1.068(36) 0.864(18)*

-0.101(36) -0.107(53)

0.76(14) 1.67(4)*

Table 2. Line-shape parameters for the seven considered transitions obtained from multi-spectrum fitting the HT (non-italicized) and the HT_fix (italicized) models to the measured spectra, respectively.

All parameters have units of kHz Pa

, which can be converted to commonly used cm

atm

units using the conversion factor: 0.003379838 (cm

atm

)/(kHz Pa

). The parenthetical values are multiples of the last significant digit and correspond to three times the standard deviation obtained from the fits. “*” indicates that the parameter was obtained from fits of the rCMDS-calculated spectra and subsequently fixed in the fit to the measurements.

Figure 3 shows the ratio of the line intensities obtained with the HT_fix and VP to

those deduced from the HT. As widely known, the line intensity retrieved with the Voigt

profile strongly depends on the considered pressure. Here the difference between the fitted VP

and that determined by using the HT profile can reach 1.5 % relative to the peak absorption.

7

Using the HT_fix fitting procedure leads to very similar results as for HT with a maximum relative difference of about 0.3 %. These results show that the HT_fix satisfactorily models the measured spectra of all air-broadened O

lines considered here for atmospheric pressure conditions. Therefore, rCMDS can be used to predict high-order line-shape parameters.

We also analyzed measured spectra where we constrained the values of and to those predicted by rCMDS and where we fit the individual spectra corresponding to a single pressure. Our analysis shows that the retrieved value of for each pressure condition is very close (within 0.5%) to that obtained previously by global fits to all the measured spectra.

These differences in the value of lead to a derivation on the calculated line shapes of typically a few 0.1 %. The best overall agreement is obtained when is deduced from spectra measured in the near collision regime (i.e. ). For comparison, the pressure dependence of the O

broadening coefficient obtained from a simple-fitting procedure using the Voigt profile can differ from that obtained using the HTP by as much as 10 % [18]! These results demonstrate that with the rCMDS-predicted and parameters, a single spectrum, measured in the collision regime, can be sufficient to determine the line-broadening coefficient with a relative precision much better than 1 %.

3.2 Temperature dependences of line-shape parameters

From the results obtained previously at room temperature, we extended our rCMDS to various temperatures (see Sec. 2.1) to predict variation of the line-shape parameters with temperature, which are crucial for atmospheric applications. Firstly, the room temperature line-shape parameters were constrained to those obtained previously from fits of the HT profile to room-temperature rCMDS spectra. Only their relative temperature dependences were adjusted in the fit of rCMDS spectra at 200 and 250 K. The usual power law for the temperature dependence of the line broadening was adopted here for , and . Starting from T

= 296K, we can thus compute values at a temperature T as: _, in which is either , or and n the temperature dependence. Note that again we used a global multi-spectrum fitting procedure in which the temperature dependences of , and were constrained to be the same for each corresponding value of the Doppler width (see Sec. 2.1). Based on several analyses, we found that we cannot simultaneously fit the temperature dependences of 

and of . This problem may be caused by the limited signal- to-noise ratio of our calculated spectra and by numerical correlation between these parameters. Therefore, as explained in Ref. [2], we assumed here that is proportional to , thereby constraining the temperature exponent of to be unity. The obtained results for the temperature dependences of and as well as the values of the latter at room temperature are reported in Table 3. Although we do not have any non-room-temperature spectra to directly compare with the predicted results, the latter can be compared to literature data. The predicted temperature exponent parameter for the line broadening was compared with experimental results of [31] in which the temperature exponents of self- and N

- broadening coefficients for the O

A band lines were reported to be about 0.8. Our calculated

values are in good agreement with these measurements. For the temperature dependence

of , no comparison can be made because, to the best of our knowledge, no measured data

are available. Large line-to-line variation of is observed for P1 and for high J lines (Table

8

3). This variation cannot be physically meaningful and probably due to the small signal-to- noise ratio of the calculated spectra for these lines. Higher signal-to-noise ratio spectra, computed using much larger number of molecules in rCMDS, are thus needed to better predict this parameter.

Parameter/

Line

P1 17.681(18) 0.80(2) 0.722(36) 1.68(4) 1.799(71)

P3 16.486(18) 0.79(2) 1.231(18) 0.82(4) 0.781(47)

P5 15.675(18) 0.79(2) 1.308(18) 0.75(4) 0.752(36)

P7 15.084(18) 0.79(2) 1.228(12) 0.78(2) 0.760(24)

P9 14.631(18) 0.80(2) 1.269(12) 0.78(4) 0.681(41)

P11 14.276(18) 0.79(2) 1.278(18) 0.62(4) 0.577(36)

P13 13.868(18) 0.80(2) 0.864(18) 1.25(4) 1.672(36)

P15 13.607(18) 0.79(2) 1.166(18) 0.88(6) 0.997(36)

P17 13.305(18) 0.77(2) 1.328(12) 0.37(16) 0.796(41)

P19 12.959(18) 0.78(2) 1.296(18) 0.66(12) 0.956(53)

P21 12.539(18) 0.77(2) 1.027(24) 1.35(6) 1.408(71)

P25 11.782(18) 0.74(2) 0.905(36) 2.20(6) 1.778(101)

Table 3: Room temperature values of , and and the temperature dependences of and retrieved from rCMDS-calculated spectra. The parenthetical values are multiples of the last significant digit and correspond to three times the standard deviation obtained from the fits. The parameters , and have units of kHz Pa

, which can be converted to commonly used cm

atm

units using the conversion factor: 0.003379838 (cm

atm

)/(kHz Pa

).

4. Conclusion

High-order line-shape parameters are required when using refined line-shape models

such as the recently recommended Hartmann-Tran profile. However, a huge amount of

experimental and analytical effort is required to determine these parameters from

rovibrational and rovibronic molecular spectra of relevant species. In this work, we have

shown that these line-shape parameters can be accurately predicted by using requantized

classical molecular dynamics simulations. Specifically, these rCMDS were used to compute

normalized absorption spectra of several air-broadened O

lines, and the simulated spectra

were subsequently fit using the Hartmann-Tran profile, with the high-order line-shape terms

treated as adjustable parameters. Using a FS-CRDS apparatus over a large pressure range, the

resulting line-shape parameters were then used to constrain the HT profile analysis of

measured spectra. We found this approach to be significantly better than fitting the Voigt

profile to the measured spectra and almost as good as when all the parameters of the HT

profile were fitted to the measured spectra. We also show that, providing that the high-order

line-shape parameters are correctly predicted, only one spectrum, measured in the collision

regime is needed to deduce the entire set of line-shape parameters. This opens the route for

the prediction of high-order line-shape parameters for various molecular systems and their

9

inclusion in spectroscopic databases using rCMDS, provided that reliable potentials are available. Finally, rCMDS calculations were also used to deduce the temperature dependences of the line broadening coefficients and the associated speed dependent components. The quality of the prediction could be probably improved by improving the signal-to-noise ratio of the calculated spectra through using larger number of molecules in the rCMDS. These results motivate new measurements for various temperature conditions required to validate these predictions.

Acknowledgments: We thank J.-M. Hartmann for providing the original computational code of CMDS for oxygen and the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS) for giving access to the IBM Blue Gene/Q parallel computer. Authors from LMD were supported by the French Space Agency, Centre National d’Etudes Spatiales.

J.T. Hodges and V.T. Sironneau acknowledge support from the NIST Greenhouse Gas and Climate Science Program.

Figure captions

Fig. 1: Measured absorption spectra of two air-broadened O

lines in the band measured by FS-CRDS at three total pressures (first row) and the corresponding residuals obtained from fitting the VP (second row), the HT and HT_fix (third and fourth rows), respectively.

Fig. 2: Maximum-to-minimum amplitudes of residuals obtained from fits of all the seven considered lines with the VP, HT and HT_fix vs total pressure.

Fig. 3: Ratio of the line intensities obtained with the VP (left) and the HT_fix fitting procedure (right) to those deduced from the use of the HT model, versus pressure.

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