# Collision-induced absorptions by pure CO2 in the infrared: New measurements in the 1150–4500 cm-1 spectral range and empirical modeling for applications

H. Tran, J. M. Hartmann, E. Rambinison, M. Turbet

► To cite this version:

H. Tran, J. M. Hartmann, E. Rambinison, M. Turbet. Collision-induced absorptions by pure CO2 in the infrared: New measurements in the 1150–4500 cm-1 spectral range and empirical modeling for applications. Icarus, 2024, 422, 10.1016/j.icarus.2024.116265. insu-04729827

HAL Id: insu-04729827

https://insu.hal.science/insu-04729827v1

Submitted on 16 Sep 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
1
2

Collision-induced absorptions by pure CO₂ in the infrared: New measurements in the 1150-4500 cm⁻¹ spectral range and empirical modeling for applications

3

H. Tran#, J.M. Hartmann, E. Rambinison, M. Turbet

4
5

Laboratoire de Météorologie Dynamique, IPSL, Sorbonne Université, ENS, Université PSL,
École polytechnique, Institut Polytechnique de Paris, CNRS, Paris France

6

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

7

**Abstract**

8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Knowledge of collision-induced absorptions (CIA) by pure CO₂ for wide temperature ranges is necessary for atmospheric and climate studies of planets and exoplanets with CO₂-rich atmospheres. In this work, using spectra measured with a Fourier transform spectrometer for temperatures between 230 K and 295 K at pressures up to 40 bar, several CIA bands in the 1150-4500 cm⁻¹ spectral range have been determined, in some cases for the first time. The results are compared with values reported in the literature, showing good agreements. From data obtained in this work and those in the literature, we propose simple analytical models for the temperature dependent band shape and integrated band intensity (IBI) which enable the calculation of all investigated CIA transitions in a wide temperature range.

17

**1.Introduction**

Precise modeling of infrared absorption by carbon dioxide is of primary importance for radiative transfer calculations in CO₂-thick atmospheres such as those of Venus (Lebonnois et al., 2015) and early Mars (Wordsworth et al., 2010), as well as of an expectedly large range of exoplanet (Forget and Leconte, 2014; Grenfell et al., 2020). Lack of precise knowledge of the opacity of gases can have significant consequences on calculations of the greenhouse effect (Wordsworth et al., 2010; Turbet and Tran 2017) and the thermal structure of planets (Lebonnois et al., 2015), and on the interpretation of spectroscopic observations of exoplanetary atmospheres (Niraula et al., 2022). At high gas pressures, line-mixing effects strongly modify the absorption shapes of the monomers [see (Hartmann et al., 2021) and references therein] and contributions of continuum absorptions (due to monomer lines far wings, collision-induced absorptions and molecular complexes) become significant. For the absorption around the center and in near wings of monomer lines, theoretical approaches, mainly based on the impact and the Energy Corrected Sudden approximations, have been developed [e.g. (Tran et al., 2011; Daneshvar et al., 2014; Predoi-Cross and Buldyreva, 2021; Cole et al., 2023)]. Comparisons between measured and computed spectra in wide pressure, temperature and spectral ranges showed satisfactory agreements for the band center and near wing regions [e.g. (Tran et al., 2011; Cole et al., 2023)]. In the far wings, due to the breakdown of the impact approximation, most of the above-mentioned models cannot be used anymore, and empirical approaches have been proposed in order to represent the absorptions and their temperature dependences [e.g. (Perrin and Hartmann, 1989; Tran et al., 2011)]. These models and associated data have been included in several radiative transfer calculations for various applications such as early-Mars climate (Turbet et al., 2020) and Venus atmosphere (Grassi et al., 2014) studies. Many investigations also require an accurate knowledge of the contribution of collision-induced absorptions (CIAs), or more generally, the binary absorptions. The latter, due to the dipole moment induced by collisions or to CO₂ dimers (the relative contribution of different binary absorption mechanisms to the total
absorption is largely unknown), are generally very weak (Frommhold, 1994; Hartmann et al., 2021). However, being proportional to the square of the gas density, they can be of significant contribution at high pressures.

For pure CO₂, numerous laboratory studies have been devoted to the characterization of various CIA bands, from the far to the near infrared [e.g. (Ho et al., 1971; Gruszka and Borysov, 1997; Vigasin et al., 2002; Baranov et al., 2004, Stefani et al., 2018; Filippov et al., 1997)]. The main outcomes of these investigations (i.e. the measured or computed CIAs together with information about the spectral band, the considered temperature, etc.) are summarized in this paper. However, a large amount of data is still missing for various spectral ranges and thermodynamic conditions of (exo)planetary interest. From the experimental point of view, this is due to the difficulty to measure weak absorptions with the path lengths and pressure conditions available in the laboratories. On the other hand, as far as we know, theoretical investigations were performed for induced absorptions in the far infrared (Gruszka and Borysow, 1997; Gruszka and Borysow, 1998; Hartmann et al., 2011) and in the 2ν₃ bands (Filippov et al., 1997) only.

In this paper, we revisit the measurements of the transmission of pure CO₂ reported in (Tran et al., 2011) in order to deduce CIA data. These experiments were performed with a Fourier transform spectrometer, from 1000 to 6000 cm⁻¹, for temperatures and pressures ranging respectively from 230 to 295 K and from 1 to 40 bar. We here deduce data for several CIA bands for the considered temperatures, in some cases for the first time, and compare our results with values reported in literature. From the latter and data obtained in this work, we propose simple analytical models for the temperature dependent band shape and integrated band intensity (IBI) for all investigated CIA transitions.

This paper is organized as follows: The experimental setup and conditions are recalled in the next section. Results obtained for each measured CIA band are then presented and compared with previous data in Sec. 3. Section 4 is devoted to the simple empirical modeling of CO₂ binary absorptions while conclusions and perspectives of this work are presented in Sec. 5.

## 2. Experiments

Measurements were performed with a Bruker 66V Fourier transform spectrometer for pure CO₂ in the 1000-6000 cm⁻¹ spectral region for temperatures ranging from 230 to 295 K and pressures from 1 up to 40 bar. The apparatus uses a L = 215 cm long single-pass cell that can be cooled through circulation of liquid nitrogen. A spectral resolution of 1 cm⁻¹ was used and each spectrum was obtained by accumulating 512 scans. High purity CO₂ gas was used and pressures were measured by various gauges (0-1.5 atm, 0-25 atm and 0-400 atm) with an accuracy better than 1%. The temperature inside the cell is measured by several type-K thermocouples. Thanks to the high thermal inertia of the cell, the temperature did not vary by more than 1 K during the acquisition of one spectrum (about 10 minutes). Transmissions were obtained by dividing the spectrum obtained with the gas sample by the empty cell one. Note that these spectra were measured in 2011 at the LISA laboratory and presented in (Tran et al., 2011) where detailed information on the experimental setup and conditions can be found. The densities of CO₂ were deduced from the pressure and temperature readings by using the van der Waals equation (tools to compute molecular densities for given temperature and pressure are available at http://webbook.nist.gov/chemistry/form-ser.html). While these measurements were used to study the pressure-broadened absorption spectrum by the monomers of CO₂
(Tran et al., 2011) no analysis of CO₂ absorptions induced by collisions was made. The density and temperature conditions of all the considered measured spectra are listed in Table 1, along with *L*, the absorption cell length.

<table><caption>Table 1: Experimental conditions of the CO₂ measured spectra.</caption><thead><tr><th><i>T</i> (K)</th><th><i>L</i> (cm)</th><th>Spectral range (cm<sup>-1</sup>)</th><th><i>d</i><sub>CO<sub>2</sub></sub>, CO₂ density (amagat)</th><th><i>d</i><sup>2</sup><sub>CO<sub>2</sub></sub><i>L</i> (cm.amagat<sup>2</sup>)</th></tr></thead><tbody><tr><td>230</td><td rowspan="3">215</td><td>1000-6000</td><td>2.11; 4.47; 6.41; 7.52; 7.60</td><td>from 9.57 10<sup>2</sup> to 1.24 10<sup>4</sup></td></tr><tr><td>260</td><td>1000-6000</td><td>10.02; 19.21; 20.10; 22.88; 25.26; 29.05; 33.67</td><td>from 2.16 10<sup>4</sup> to 2.44 10<sup>5</sup></td></tr><tr><td>295</td><td>1800-6000</td><td>6.55; 9.81; 11.84; 17.31; 20.62; 23.31; 29.49; 32.99; 36.67; 44.19; 49.24; 56.75</td><td>from 9.22 10<sup>3</sup> to 6.92 10<sup>5</sup></td></tr></tbody></table>

Since collision-induced absorptions are proportional to the product of the path length and the squared density, it is important to reach sufficiently high values of $d_{CO_2}^2 L$ to be able to measure these relatively weak absorptions. As can be observed in Table 1, this quantity reaches 6.9 10⁵ cm.amagat² in our measurements. In this case, a binary absorption coefficient of 1.5 10⁻⁸ cm⁻¹ amagat⁻² leads to an absorption of 1% which is close to the limit of our experiments.

### 3. Measured CIA bands

Since measurements were performed at high densities and because we focus on binary absorptions which vary slowly with wavenumber, the influence of the FTS instrument function can be neglected. The measured absorption $\alpha$ (in cm⁻¹), deduced from the transmittance and the optical path, can thus be written as:

$$ \alpha(\sigma, T, d_{CO_2}) = \alpha^{CO_2}(\sigma, T, d_{CO_2}) + \alpha^{CO_2-CO_2}(\sigma, T, d_{CO_2}). \quad (1) $$

The first contribution is due to the monomers of CO₂. It was computed for each temperature and density condition of the measurements using spectroscopic line parameters provided in the HITRAN database (Gordon et al., 2022) and the spectra modeling of (Tran et al., 2011), which takes into account either line-mixing effects (around the band center and in the near wings) or the non-Lorentzian far line wings by using the empirical $\chi$-factors proposed in (Tran et al., 2011). The computed values of $\alpha^{CO_2}(\sigma, T, d_{CO_2})$ were then subtracted from the measured spectra. The remaining absorptions were attributed to CIA when they are proportional to the squared density [i.e. $\alpha^{CO_2-CO_2}(\sigma, T, d_{CO_2}) = d_{CO_2}^2 A^{CO_2-CO_2}(\sigma, T)$] and located at a possible CIA transition frequency. The resulting density-square-normalized absorption coefficient, $A^{CO_2-CO_2}(\sigma, T)$ was then determined for the considered temperature. For each temperature and CIA band, we finally retained this absorption coefficient versus wavenumber and the integrated band intensity (IBI). The obtained results are presented in the following subsections.

#### 3.1. Absorptions in the 1150-1575 cm⁻¹ spectral region

Binary absorptions in this spectral region are due to the Fermi doublet [10⁰⁰OII-00⁰⁰ and 10⁰⁰OI-00⁰⁰, see (Rothman et al., 1992)], and were investigated in several studies. Note that since all bands considered in this work are fundamental bands, for simplicity, only the upper vibrational level will be given from now on for band notation. The two most complete sets of measurements can be found in (Vigasin et al., 2002) and (Baranov et al., 2004). In (Vigasin et
al., 2002), CO₂-CO₂ binary absorption coefficients were determined for the 206-295 K temperature range from spectra recorded for pressures up to 3 atm with a Fourier transform spectrometer coupled to a multi-pass cell with a 30.05 m path. Later, the Fermi doublet bands were re-measured in (Baranov et al., 2004) for temperatures ranging from 193 K to 346 K using a longer optical path (84.05 m). The integrated band intensity (IBI, integrated over the two Fermi doublet components) was determined for 9 temperatures with a much smaller uncertainty of 1.5%. For both Fermi components, the spectra show sharp P, Q, R structures superimposed on a broad background. While the latter is due to collision-induced absorption, the former structure was attributed to CO₂-CO₂ dimers (Baranov and Vigasin, 1999). These results demonstrated a strong temperature dependence of the measured binary absorptions, the IBI decreasing by a factor of two from 200 K to 300 K. More recently, (Stefani et al., 2013) and (Stefani et al., 2018) experimentally investigated these bands from spectra recorded with an FTS and a 2 cm long cell for pressures up to 40 bars at temperatures from 294 to 473 K. They showed that the temperature dependence in this range is much smaller and that for temperatures above 400 K, the IBI tends to increase with T.

In the present study, binary absorptions in the 1150-1575 cm⁻¹ spectral region were deduced from spectra at 230K and 260K only, since those recorded at room temperature do not cover this spectral region (see Table 1). Firstly, the weak but not negligible contribution of monomer bands (mainly due to absorptions by the minor isotopologues ¹⁸O¹²C¹⁶O and ¹⁷O¹²C¹⁶O) was computed and removed from the measurements. For each spectrum, a linear base line was adjusted assuming that absorptions at 1150 cm⁻¹ and 1575 cm⁻¹ are zero, an assumption consistent with the results of (Baranov et al., 2004) and the fact that the influence of monomer band wings can be neglected in this spectral region. Figure 1 displays the remaining absorptions obtained at 230 K for various gas densities. Note that the sharp dimer Q branch observed in (Baranov et al., 2004) is present here but strongly reduced and broadened by the much higher densities and the poorer spectral resolution used in this work.
The binary absorption coefficient ACO₂-CO₂(σ, T) at each wavenumber was obtained through a linear fit of the absorptions versus the CO₂ squared density. They are plotted for both T = 230 K and T = 260 K in Fig. 2 where the error bars correspond to the statistical uncertainties of the linear fits.

Our results are compared with the data of (Baranov et al., 2004; Karman et al., 2019) in Fig. 2 where a very good agreement is observed, for both the magnitude and the shape, except for T=230 K around 1325 cm⁻¹ in between the two absorption structures where our values are larger. The IBIs of the binary absorptions measured in this spectral region are listed in Table 2 and displayed in Fig. 3. As can be seen, our values are in good agreement with those of (Vigasin et al., 2002), both slightly larger than those of (Baranov et al., 2004). All reported data were then fitted with an exponential decay function in order to empirically model the temperature dependence of the IBI of the Fermi doublet. The obtained function [i.e. IBI(T) = 10⁻³{3.9136 + 4.73636 exp(-T/206)/51.4329}] is also displayed in Fig. 3. Note that in the high temperature range (above 350 K), the data from (Adiks, 1982; Stefani et al., 2013) follow quite well this function while those of (Stefani et al., 2018) indicate an increase of the IBI with temperature. It is clear that more accurate high-temperature measurements are necessary to better determine the temperature dependence of the IBI of the Fermi doublet.
<figure><img src="image_2.png" /><figcaption>Figure 1: Binary absorption coefficients measured at 230K for various CO₂ densities.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Squared density normalized binary absorption coefficients in the 1150-1600 cm⁻¹ spectral region measured in the present study (PS, symbols with error bars) at 230K (top panel) and 260K (bottom panel) and comparison with the data (red lines) provided by the HITRAN database (Karman et al., 2019) which are the measured values obtained in Ref. (Baranov et al., 2004).</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3: Temperature dependences of the IBI of the squared density normalized measured binary absorptions in the 1150-1600 cm⁻¹ spectral region. The black line is the exponential decay function fitted to all measured data reported in this figure: $IBI_{Fermi-doublet}(T) = 10^{-3}[3.9136 + 4.73636 \exp(-\frac{T-206}{51.4329})]$.</figcaption></figure>

## 3.2. Absorptions in the 2500-3400 cm⁻¹ spectral region

Binary absorptions in this spectral region were experimentally determined in (Adiks, 1982; Thomas and Linevski, 1989; Lamouroux et al., 2010; Baranov et al., 2003; Stefani et al., 2013; Stefani et al., 2018; Baranov, 2018) and the data provided in the HITRAN database are values from (Baranov et al., 2003) and (Baranov, 2018). In the latter, the 2500-3500 cm⁻¹ interval was investigated using Fourier transform spectra recorded at room temperature for pressures between 2 to 4.6 atm with a 100 m long optical path. Although there are several CIA structures in the spectral region, the authors focused on the strongest one only: the $01^11_1$ band centered at 3014 cm⁻¹. In (Baranov et al., 2003), absorption spectra in the 2500-2900 cm⁻¹ interval were measured at 211, 235, 264 and 297 K with two Fourier transform spectrometers of 0.5 cm⁻¹ of resolution. Two absorption cells of total path lengths of 30.09 and 84 m were used, with pressures from 1 to 8 atm, providing a maximum value of the product $d_{CO_2}^2L$ of about $4.7 \times 10^5$ cm.amagat² which is comparable to our maximum value at room temperature (i.e. $6.9 \times 10^5$ cm.amagat²).

Figure 4 provides an example of CO₂ absorptions measured (black points) in the present work, at 295 K and 44.19 amagat together with the calculated absorption due to local transitions of CO₂ monomers [red line, computed using the data and model of (Tran et al.,
200 2011) and updated in (Cole et al., 2023]. The difference (blue points) between the measured values and this contribution is due to absorption in the wing of the strong $v_3$ band and to three CIA structures centered at about 2670, 2796 and 3014 cm$^{-1}$ [the latter corresponds to the 01$^1$1$_1$ band while the two first bands belong to the Fermi triad (i.e. the 20$^0$0$_{II}$ and 20$^0$0$_{I}$ bands)]. Note that in our measurements, the CIA band at 2515 cm$^{-1}$ [a component of the Fermi triad, measured in (Baranov et al., 2003)] is not detected since its absorption is completely saturated for our considered densities. It is clear that an accurate representation of the 00$^0$1$_1$ ($v_3$) band wing is of upmost importance for a precise determination of the CIA bands in the 2600-2800 cm$^{-1}$ spectral range. Figure 4 shows this contribution calculated with the $\chi$-factors proposed in (Tran et al., 2011).

<figure><img src="image_5.png" /></figure>

Figure 4: Measured absorption (black points) of pure CO$_2$ at 295 K and 44.19 amagat and the calculated contribution due to local bands of CO$_2$ monomers (red line). The difference (blue points) between the measured values and the calculated monomer absorption plotted in blue clearly shows the presence of three CIA bands: the two Fermi triad bands, 20$^0$0$_{II}$ and 20$^0$0$_{I}$, and the 01$^1$1$_1$ band, centered at 2670 cm$^{-1}$, 2796 cm$^{-1}$ and 3014 cm$^{-1}$, respectively. Finally, the magenta and green lines represent the contribution due to absorption in the $v_3$ band wing calculated using the $\chi$-factors of (Tran et al., 2011), and fitted with an exponential decay (see text), respectively.

As the $\chi$-factors used to compute the 00$^0$1$_1$ band wing were adjusted from data measured up to 2600 cm$^{-1}$ only (Tran et al., 2011), we decided not to use them but the following procedure: i) We first computed the contribution of the monomer bands centered between 2500 and 3400 cm$^{-1}$ and subtracted it from the measured spectra (e.g. red line and blue points of Fig. 4); ii) we then assumed that CIA absorptions at 2597 cm$^{-1}$, 2740 cm$^{-1}$, 2860 cm$^{-1}$ and 3175 cm$^{-1}$ [see Fig. 4 and (Baranov et al., 2003, Baranov, 2018)] are zero. These points were used to adjust the contribution of the 00$^0$1$_1$ band wing using a single exponential decay function (e.g. the green line in Fig. 4) which was then removed from the measured spectra. Note that regarding
the CIA bands centers (at about 2670, 2795 and 3014 cm⁻¹) and the typical shape of a CIA band (Baranov et al., 2003; Baranov, 2018; Tonkov et al., 1996), assuming that CIA absorptions at these four points (2597 cm⁻¹, 2740 cm⁻¹, 2860 cm⁻¹ and 3175 cm⁻¹) are zero may underestimate the true contribution of the CIA, especially for the two Fermi triad bands.

Finally, for each temperature, the squared density normalized absorption coefficients $A^{CO_2-CO_2}(\sigma, T)$ at each wavenumber were then deduced as the slope of the linear fit of the absorption coefficients versus the CO₂ density square. Figure 5 presents some examples of the results of this exercise.

<figure><img src="image_6.png" /><figcaption>Figure 5: Binary absorptions deduced from spectra measured at 295 K versus $d_{CO_2}^2$ and the corresponding linear fits.</figcaption></figure>

The $A^{CO_2-CO_2}(\sigma, T)$ coefficients obtained from spectra recorded at 295 K are shown in Fig. 6, for the two bands of the Fermi triad bands centered at 2670 cm⁻¹ and 2796 cm⁻¹ and the 01¹¹¹₁ band at 3014 cm⁻¹. They are compared with measured values from (Baranov et al., 2003) for the two Fermi triad bands and of (Baranov, 2018) for the 01¹¹¹₁ band. A very good agreement is obtained for the 01¹¹¹₁ band, as well as for the weak Fermi triad band located at 2796 cm⁻¹ while for the strong Fermi triad band at 2670 cm⁻¹ our values are significantly smaller than those of (Baranov et al., 2003). This is probably due to the unperfect determination of the 00⁰¹₁ band wing contribution since the latter mostly affects the 2670 cm⁻¹ transition. The integrated band intensities IBIs were computed from 2597 cm⁻¹ to 2740 cm⁻¹, 2740 cm⁻¹ to 2860 cm⁻¹ and from 2860 cm⁻¹ to 3175 cm⁻¹ for the CIA bands centered at 2670 cm⁻¹, 2796 cm⁻¹ and 3014 cm⁻¹, respectively, giving IBI(2597-2740)=8.15(±0.40)10⁻⁵ cm⁻²amagat⁻², IBI(2740-2860)=1.88(±0.18)10⁻⁵ cm⁻²amagat⁻², and IBI(2860-3175)= 2.27(±0.12)10⁻⁴ cm⁻²amagat⁻².
<figure><img src="image_7.png" /><figcaption>Figure 6: Squared density normalized binary absorption coefficients of the two Fermi triad bands and the 01<sup>1</sup>I<sub>1</sub> band measured in this work at 295 K (symbols with error bars obtained from statistical uncertainties of the linear fits, see Fig. 5) and comparison with measured data of (Baranov, 2018) (red line), and of (Baranov et al., 2003) (pink line).</figcaption></figure>

The same procedure was used to analyse the spectra recorded at 260 K and 230 K. For these temperatures, the stability of the experimental base line was not as good as for the room temperature spectra. In addition, the CO<sub>2</sub> density is smaller, leading to larger uncertainties. The obtained results are plotted in Fig. 7 where a very good agreement between our data and those of (Baranov et al., 2003) is observed at 230 K. Again, no clear dimer structure appears in our measured CIAs contrary to the data of (Baranov et al., 2003). The IBIs obtained for each band and each temperature are displayed in Fig. 8, together with data from the literature. Our values are in good agreement with those of (Baranov et al., 2003) for the two Fermi triad bands and with those of (Baranov, 2018) for the 01<sup>1</sup>I<sub>1</sub> band at room temperature. Good agreements are also observed between our data and those of (Adiks, 1982) for the Fermi triad component centered at 2796 cm<sup>-1</sup> and for the 01<sup>1</sup>I<sub>1</sub> band, while for the band centered at 2670, the values from (Adiks, 1982) are significantly larger. In order to estimate the temperature dependences of the IBIs measured for these three CIA bands, we assumed that the IBIs of all CIA bands (including contributions of dimers) follow the same relative evolution with T. We therefore used the exponential decay function obtained from fits of all the reported IBIs of the Fermi doublet (see Fig. 3) and multiplied this function by a scaling factor in order to match the IBI measured at room temperature for each CIA band considered here. The resulting functions are plotted in Fig. 8 showing that, even if a rough approximation was made, they rather well describe the evolution with temperature of the measured IBIs for temperatures lower than 350 K. Figure 8 also demonstrates that accurate measurements in this spectral region for temperatures higher than 350 K are clearly needed. Note that, for the 01<sup>1</sup>I<sub>1</sub> band, the IBIs of (Stefani et al., 2018) [and (Thomas and Linevski, 1989)] show almost no
temperature dependence, in contrast with our data and those of (Adiks, 1982). Recall that the three studied CIA bands are weak, with a maximum absorption at room temperature (see Fig. 6) of about 3 10⁻⁶ cm⁻¹amagat⁻² (smaller for higher temperatures) and that the maximum value of $d_{CO_2}^2L$ in (Stefani et al., 2018) at room temperature is about 5 10³ cm.agamat² (with $L = 2$ cm and $d_{CO_2}$ about 50 amagat) which corresponds to a maximum absorbance of 1.5% only. This may explain the observed differences of the measured IBIs.

<figure><img src="image_8.png" /><figcaption>Figure 7: Squared density normalized binary absorption coefficients deduced from spectra recorded at 260 K and 230 K (symbols with error bars). The pink line represents the measured data from (Baranov et al., 2003; Karman et al., 2019) at 235 K.</figcaption></figure>

<figure><img src="image_9.png" /></figure>
Figure 8: The integrated band intensities of the CIA bands measured in the 2597-3175 cm⁻¹ spectral region. The black line is the exponential decay function obtained from the temperature dependent IBIs of the Fermi doublet (see Fig. 3), multiplied by a constant in order to match the IBI measured, in the present study, at room temperature for each band.

### 3.3. Absorptions in the 4000-4500 cm⁻¹ spectral region

Collision-induced absorptions in this spectral region, close to the strong $10^01_1$ band, were investigated in (Burch et al., 1969; Adiks, 1976; Moskalenko et al., 1979, Thomas and Linevski, 1989; Tonkov et al., 1996) with a quantitative analysis in (Tonkov et al., 1996). The binary absorptions in this spectral region are much smaller than those considered above and we were able to study some CIA bands from measurements at 295 K and 260 K only. The contributions of the wing of the strong $10^01_1$ band and of other monomer local bands were removed from the measured absorptions using the updated model and data (Cole et al., 2023) of (Tran et al., 2011). In addition, a quadratic (versus wavenumber) base line was applied assuming that binary absorptions at 3995 cm⁻¹, 4168 cm⁻¹ and 4500 cm⁻¹ are zero. Figure 9 presents the absorption spectrum measured at 295 K and 56.75 amagat and the corresponding computed monomer contribution. Three remaining structures are observed, centered at about 4060, 4277 and 4380 cm⁻¹, respectively, for which the associated squared density normalized values are presented in Fig. 10.

<figure><img src="image_10.png" /></figure>

Figure 9: Measured absorption (black line) of pure $CO_2$ at 295 K and 56.75 amagat and the computed contribution due to $CO_2$ monomers (red curve). The difference between them plotted in blue, clearly shows the presence of three CIA structures, centered at 4060, 4277 and 4380 cm⁻¹.

These CIA structures were measured in (Tonkov et al., 1996) in which absorption spectra in the 3800-4700 cm⁻¹ spectral region were recorded at room temperature in the 10-50 atm pressure range. In this paper, the authors identified five CIA structures between 4000 and 4500 cm⁻¹ and assigned three of them. The structure located at 4060 cm⁻¹ is due to the $30^00_{II}$ band, that centered at about 4277 cm⁻¹ to the $10^00_{II}+01^11_1$ band and that at 4380 cm⁻¹ to the $10^00_1+01^11_1$ and the $11^11_1$ bands. In order to describe the measured CIA bands, Tonkov et al
(Tonkov et al., 1996) proposed a model for the CIA band shape and assumed that it is independent of the vibrational transition. Its central part, within +/- 40 cm⁻¹ from its maximum, was obtained from the observed shape of the band at 4060 cm⁻¹, while its wings were deduced from measured CIA in the far infrared (Ho et al., 1971; Birnbaum et al., 1971). The absorption coefficient for each CIA band can thus be computed as the product of the normalized band shape and the measured integrated band intensity. From the band position, band intensity and the normalized band shape given in Ref. (Tonkov et al., 1996) we then reconstructed the binary absorption coefficients in the considered spectral region which are compared with our measured data in Fig. 10. As can be observed in the top panel, there is a good agreement except for the band at 4060 cm⁻¹ where the computed values of (Tonkov et al., 1996) overestimate our measured CIA. The intensity and position of some contributing CIA bands were then adjusted in order to match the (total) measured binary absorption coefficients (see Table 2). The results are plotted in the bottom panel of Fig. 10. Similarly, binary absorptions measured at 260 K are plotted in Fig. 11 where only the first CIA band centered at 4060 cm⁻¹ can be determined, the other structures being completely masked by experimental noise. As it was done for the Fermi triad and the $v_2 + v_3$ band, we plot in Fig. 12 the IBIs measured for the CIA band located at 4060 cm⁻¹ together with the modeled temperature dependent IBI (i.e. the exponential decay function obtained from the temperature dependent IBIs of the Fermi doublet, multiplied by a constant in order to match the IBI measured at room temperature). Due to the large uncertainty of the measured IBIs, extrapolation the temperature dependence using these values is probably hazardous. Thus, even if the analytical temperature dependent IBI is in rather good agreement with the measured IBIs, this figure clearly calls for more accurate measurements of CIAs in a broader temperature range in this spectral region.

<figure><img src="image_11.png" /><figcaption>Figure 10: Measured squared density normalized binary absorption coefficient at 295 K in the 4000-4500 cm⁻¹ spectral region. In the top panel, our data are compared with values reconstructed from the measured band positions, intensities and the normalized band shape proposed in Ref. (Tonkov et al.,</figcaption></figure>
349
350
351
352

1996). The computed contribution of each CIA band measured in this spectral region is also displayed using data from (Tonkov et al., 1996). In the lower panel, the measured absorption coefficients are compared with computed values using the band shape of (Tonkov et al., 1996) but with modified band intensities and positions in order to better represent the values measured in the present study.

<figure><img src="image_12.png" /></figure>

353
354
355
356
357

Figure 11: Squared density normalized absorption coefficients measured in the 4000-4170 cm⁻¹ spectral region at 260 K and comparison with absorption modeled using absorption band shapes and positions obtained at room temperature while the IBI was adjusted in order to match the measured values. The calculated absorption at 296 K is also displayed for comparison.

<figure><img src="image_13.png" /></figure>

358
359
360
361

Figure 12: IBIs measured for the CIA band centered at 4060 cm⁻¹ at 260 K and 295 K and comparison with values of (Tonkov et al., 1996) in which measurements were made for temperatures from 290 K to 297 K. The black line is the exponential decay function obtained from the temperature dependent
to determine $\phi_{CIA+dimer}$ from the Fermi doublet. Note that since the two components of this doublet are strongly overlapping, we first determined $\phi_{CIA+dimer}^{\text{Fermi}}(\sigma, T_0)$ for the whole doublet (this is consistent with the fact that the IBI of the Fermi doublet was obtained by integrating over the two components). The quality of the fit is demonstrated in Fig. 13 for both the far infrared band and the Fermi doublet while Fig. 14 presents the obtained $\phi_{CIA}(\sigma - \sigma_0, T_0)$ and $\phi_{CIA+dimer}(\sigma - \sigma_0, T_0)$, the latter being deduced from the left hand side component of the Fermi doublet. That was done using measured values from $\sigma - \sigma_0 = -285 \text{ cm}^{-1}$ to up to $18 \text{ cm}^{-1}$ only. Then, for $\sigma - \sigma_0$ larger than $18 \text{ cm}^{-1}$ we assumed that the band shape is symmetric and we built the right side of the band from the left side. Figure 14 demonstrates that, even if the two shapes are obtained from different bands (the FIR band and the Fermi doublet which includes dimer signatures), they are quite close to each other, thus confirming that assuming that the band shape is independent of the transition is reasonable. This is again confirmed by comparing these band shapes with that proposed by (Tonkov et al., 1996) obtained from the measured Fermi quadruplet component located at $4060 \text{ cm}^{-1}$.

<figure><img src="image_14.png" /><figcaption>Figure 13: Band shapes (black curves) deduced from the binary absorption coefficients computed by (Gruszka and Borysov, 1997; Karman et al., 2019) in the FIR band at 200 K and 651 K (top panel) and from the measured ones by (Baranov et al., 2004; Karman et al., 2019) in the Fermi doublet at 200 K and 350 K (bottom panel) and their fits (red dashed curves). The latter were obtained by fitting the absorption band shapes for each wavenumber with the analytical function of Eq. (3).</figcaption></figure>

From these temperature dependent band shapes we can compute the absorption coefficient of any induced band if we know its IBI. The relative temperature dependence of the latter can be assumed to be the same for all considered bands, which is a rough approximation but can be used in the absence of any more accurate information (see the quality of the approximation in Figs. 3 and 8). Note that removing the emission term or not in the calculation of the IBI of course changes the resulting IBI but only very slightly changes the temperature dependence of the IBI.
429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

We used the obtained temperature dependent band shapes to simulate several binary absorption bands. That was done here for the Fermi triad and CIA bands in the 4000-4500 cm⁻¹ spectral region using the φ<sub>CIA+dimer</sub>(σ − σ<sub>0</sub>, T) function since these bands carry dimer signatures. On the other hand, the φ<sub>CIA</sub>(σ − σ<sub>0</sub>, T) band shape was used to compute the absorption coefficients of the 01<sup>1</sup>1<sub>I</sub> band for which no dimer signature is observed. The obtained absorption coefficients are compared with those measured in this work and in the literature, as exemplified in Figs. 15-17. The results plotted in Fig. 15 show that the measured Fermi triad band shapes are narrower than the modeled ones, especially at room temperature. This is probably due to the fact that, in the experimental studies of this work and of (Baranov et al., 2003), one assumed that binary absorptions at 2597 cm⁻¹, 2740 cm⁻¹, 2860 cm⁻¹ and 3175 cm⁻¹ are zero while they may be greater. Since, at room temperature, the band shapes are broader than at lower temperatures, assuming that absorptions at these points are zero would have a larger consequences at room temperature. This is consistent with the fact that at room temperature, the agreement between the measured and modeled CIAs is not as good as at 230 K (Fig. 15). It is clear that new and more accurate measurements and calculations for these CIA bands, as well as for the ν<sub>3</sub> band wing which contributes to CO₂ absorption in the same spectral region, are needed in order to refine these data.

<figure><img src="image_15.png" /></figure>

446

447

448

449

450

451

Figure 14: Normalized spectral band shape at 296 K, deduced from fits of the calculated CIAs in the FIR (Gruszka and Borysov, 1997; Karman et al., 2019) (black line) and from the binary absorption coefficients measured in the Fermi doublet (Baranov et al., 2004; Karman et al., 2019) (blue line) using Eqs. (2) and (3). The empirical band shape of (Tonkov et al., 1996), deduced from the measured shape of the 30⁰⁰₀<sub>II</sub> band, is also displayed for comparison.
The agreements between the modeled and measured CIAs observed in Figs. 15-17 demonstrate that the proposed model, although simple, is capable to satisfactorily represent the temperature dependence of the band shapes. From these data and the model, we can compute the binary absorption coefficients for all considered bands in the 200-350 K range. This range may be extended up to 500 K, but its accuracy is limited by the insufficient available data above 350 K (see Figs. 3 and 8). Since the models for the temperature dependences of the band shape (and of the IBI, see Sec. 3.1) are fully empirical, we do not suggest extrapolations of these data and model for other temperature conditions. Finally, note that the coefficients needed [Eq. (3)] to compute the band shapes $\phi_{CIA}$, $\phi_{CIA+dimer}^{\text{Fermi}}$ and $\phi_{CIA+dimer}$ for a given temperature condition are published as complementary data of this paper.

<figure><img src="image_16.png" /><figcaption>Figure 15: Comparison between the binary absorption coefficients in the CO₂ Fermi triad measured in the PS (black points) and by (Baranov et al., 2003) (pink curve) with those computed (blue curve) using the $\phi_{CIA+dimer}$ band shape and the measured IBIs of (Baranov et al., 2003) for various temperature conditions.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure 16: The same as for Fig. 15 but for the 01¹¹I₁ band at various temperatures. The modeled absorption coefficient was obtained using the $\phi_{CIA}$ band shape and IBIs measured in the present study.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 17: The same as Fig. 15 but for the 4000-4500 cm⁻¹ spectral region. The band shape $\phi_{CIA+dimer}$ was used along with the IBIs obtained in the present work and in (Tonkov et al., 1996) for the modeled absorption coefficients.</figcaption></figure>

<table><thead><tr><th>Band, range or band center (cm<sup>-1</sup>)</th><th>Temperature (K)</th><th>Integrated intensity (cm<sup>-2</sup>/amagat<sup>-2</sup>)</th><th>Method</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="3">00°0I, 7-250</td><td>233</td><td>8.2 510<sup>-3</sup></td><td rowspan="3">Measurement</td><td rowspan="3">Ho et al., 1971</td></tr><tr><td>273</td><td>6.3 10<sup>-3</sup></td></tr><tr><td>296</td><td>5.5 10<sup>-3</sup></td></tr></tbody></table>
<table><tbody><tr><td rowspan="6">00°0i, 0-250</td><td>303</td><td>4.4 10<sup>-3</sup></td><td rowspan="6">Theoretical prediction</td><td rowspan="6">Gruszka and Borysow, 1997</td></tr><tr><td>200</td><td>10.4 10<sup>-3</sup></td></tr><tr><td>233</td><td>8.34 10<sup>-3</sup></td></tr><tr><td>300</td><td>6.04 10<sup>-3</sup></td></tr><tr><td>400</td><td>4.50 10<sup>-3</sup></td></tr><tr><td>500</td><td>3.95 10<sup>-3</sup></td></tr><tr><td rowspan="6">00°0i, 0-250</td><td>800</td><td>3.91 10<sup>-3</sup></td><td rowspan="6">Theoretical prediction</td><td rowspan="6">Gruszka and Borysow, 1998</td></tr><tr><td>233</td><td>8.28 10<sup>-3</sup></td></tr><tr><td>273</td><td>5.84 10<sup>-3</sup></td></tr><tr><td>300</td><td>5.47 10<sup>-3</sup></td></tr><tr><td>400</td><td>4.61 10<sup>-3</sup></td></tr><tr><td>296</td><td>4.33 10<sup>-3</sup></td></tr><tr><td rowspan="3">00°0i, 0-250</td><td>233</td><td>7.97 10<sup>-3</sup></td><td rowspan="3">Measurement</td><td rowspan="3">Hartmann et al., 2011</td></tr><tr><td>296</td><td>6.06 10<sup>-3</sup></td></tr><tr><td>333</td><td>5.38 10<sup>-3</sup></td></tr><tr><td>00°0i, 40-640</td><td>296</td><td>0.74 (0.32) 10<sup>-3</sup><br>(from 60 to 250 cm<sup>-1</sup>)</td><td>Measurement</td><td>Turbet et al., 2019</td></tr><tr><td rowspan="2">10°0ii, 10°0i, 1200-1500</td><td>293</td><td>5.45 10<sup>-3</sup></td><td>Measurement</td><td>Moskalenko et al., 1979</td></tr><tr><td>273</td><td>5.36 (0.57) 10<sup>-3</sup></td><td>Measurement</td><td>Manzanares et al., 1984</td></tr><tr><td rowspan="12">10°0ii, 10°0i, 1130-1600</td><td>298</td><td>5.38 (0.38) 10<sup>-3</sup></td><td rowspan="12">Measurement</td><td rowspan="12">Vigasin et al., 2002</td></tr><tr><td>323</td><td>5.19 (0.64) 10<sup>-3</sup></td></tr><tr><td>206</td><td>8.65 (0.52) 10<sup>-3</sup></td></tr><tr><td>211</td><td>8.44 (0.51) 10<sup>-3</sup></td></tr><tr><td>212</td><td>7.93 (0.48) 10<sup>-3</sup></td></tr><tr><td>218</td><td>8.00 (0.48) 10<sup>-3</sup></td></tr><tr><td>219</td><td>7.62 (0.46) 10<sup>-3</sup></td></tr><tr><td>233</td><td>7.33 (0.44) 10<sup>-3</sup></td></tr><tr><td>235</td><td>6.96 (0.42) 10<sup>-3</sup></td></tr><tr><td>250</td><td>6.76 (0.41) 10<sup>-3</sup></td></tr><tr><td>264</td><td>6.13 (0.37) 10<sup>-3</sup></td></tr><tr><td>292</td><td>5.20 (0.31) 10<sup>-3</sup></td></tr><tr><td>295</td><td>5.03 (0.30) 10<sup>-3</sup></td></tr><tr><td rowspan="10">10°0ii, 10°0i, 1200-1550</td><td>192.8</td><td>9.34 (0.14) 10<sup>-3</sup></td><td rowspan="10">Measurement</td><td rowspan="10">Baranov et al., 2004</td></tr><tr><td>206.7</td><td>8.10 (0.12) 10<sup>-3</sup></td></tr><tr><td>220.7</td><td>7.13 (0.11) 10<sup>-3</sup></td></tr><tr><td>229.3</td><td>6.66 (0.10) 10<sup>-3</sup></td></tr><tr><td>239.3</td><td>6.21 (0.09) 10<sup>-3</sup></td></tr><tr><td>249.2</td><td>5.84 (0.09) 10<sup>-3</sup></td></tr><tr><td>270.3</td><td>5.23 (0.08) 10<sup>-3</sup></td></tr><tr><td>297.1</td><td>4.84 (0.07) 10<sup>-3</sup></td></tr><tr><td>330.5</td><td>4.56 (0.07) 10<sup>-3</sup></td></tr><tr><td>345.6</td><td>4.49 (0.07) 10<sup>-3</sup></td></tr><tr><td rowspan="3">10°0ii, 10°0i, 1200-1500</td><td>294</td><td>4.62 (0.2) 10<sup>-3</sup></td><td rowspan="3">Measurement</td><td rowspan="3">Stefani et al., 2013</td></tr><tr><td>373</td><td>4.06 (0.2) 10<sup>-3</sup></td></tr><tr><td>473</td><td>3.94 (0.2) 10<sup>-3</sup></td></tr><tr><td rowspan="5">10°0ii, 10°0i, 1150-1550</td><td>302.3</td><td>5.01 (0.25) 10<sup>-3</sup></td><td rowspan="5">Measurement</td><td rowspan="5">Stefani et al., 2018</td></tr><tr><td>322.8</td><td>4.46 (0.23) 10<sup>-3</sup></td></tr><tr><td>373.8</td><td>4.43 (0.22) 10<sup>-3</sup></td></tr><tr><td>424.0</td><td>4.58 (0.23) 10<sup>-3</sup></td></tr><tr><td>475.2</td><td>4.83 (0.24) 10<sup>-3</sup></td></tr><tr><td rowspan="2">10°0ii, 10°0i, 1150-1575</td><td>230</td><td>7.85 (0.33) 10<sup>-3</sup></td><td rowspan="2">Measurement</td><td rowspan="2">This work</td></tr><tr><td>260</td><td>6.32 (0.45) 10<sup>-3</sup></td></tr><tr><td rowspan="3">20°0iii, 2515-2600</td><td>211</td><td>6.3 (0.2) 10<sup>-5</sup></td><td rowspan="3">Measurement</td><td rowspan="3">Baranov et al., 2003</td></tr><tr><td>235</td><td>4.3 (0.1) 10<sup>-5</sup></td></tr><tr><td>297</td><td>3.0 (0.3) 10<sup>-5</sup></td></tr><tr><td rowspan="2">20°0ii, 2600-2740</td><td>273</td><td>17.5 10<sup>-5</sup></td><td rowspan="2">Measurement</td><td rowspan="2">Adiks, 1982</td></tr><tr><td>296</td><td>16.2 10<sup>-5</sup></td></tr></tbody></table>
<table><tbody><tr><td></td><td>336</td><td>14.1 10<sup>-5</sup></td><td></td><td></td></tr><tr><td></td><td>359</td><td>13.3 10<sup>-5</sup></td><td></td><td></td></tr><tr><td rowspan="4">20<sup>0</sup>O<sub>II</sub>,<br>2600-2740</td><td>211</td><td>20.1 (0.5) 10<sup>-5</sup></td><td rowspan="4">Measurement</td><td rowspan="4">Baranov et al., 2003</td></tr><tr><td>235</td><td>15.7 (0.5) 10<sup>-5</sup></td></tr><tr><td>264</td><td>12.0 (0.5) 10<sup>-5</sup></td></tr><tr><td>297</td><td>10.0 (0.5) 10<sup>-5</sup></td></tr><tr><td rowspan="4">20<sup>0</sup>O<sub>II</sub>,<br>2590-2730</td><td>302.3</td><td>9.8 (0.9) 10<sup>-5</sup></td><td rowspan="4">Measurement</td><td rowspan="4">Stefani et al., 2018</td></tr><tr><td>322.8</td><td>8.1 (0.7) 10<sup>-5</sup></td></tr><tr><td>373.8</td><td>5.9 (0.5) 10<sup>-5</sup></td></tr><tr><td>424.0</td><td>2.7 (0.3) 10<sup>-5</sup></td></tr><tr><td rowspan="3">20<sup>0</sup>O<sub>II</sub>,<br>2590-2740</td><td>475.2</td><td>3.5 (0.3) 10<sup>-5</sup></td><td rowspan="3">Measurement</td><td rowspan="3">This work</td></tr><tr><td>230</td><td>14.83 (2.75) 10<sup>-5</sup></td></tr><tr><td>260</td><td>11.87 (1.03) 10<sup>-5</sup></td></tr><tr><td rowspan="4">20<sup>0</sup>O<sub>I</sub>,<br>2740-2850</td><td>295</td><td>8.15 (0.4) 10<sup>-5</sup></td><td rowspan="4">Measurement</td><td rowspan="4">Adiks, 1982</td></tr><tr><td>273</td><td>3.0 10<sup>-5</sup></td></tr><tr><td>296</td><td>2.7 10<sup>-5</sup></td></tr><tr><td>336</td><td>2.2 10<sup>-5</sup></td></tr><tr><td>359</td><td>2.0 10<sup>-5</sup></td><td></td><td></td></tr><tr><td>20<sup>0</sup>O<sub>I</sub>,<br>2750-2870</td><td>295-470</td><td>1.74 10<sup>-5</sup></td><td>Measurement</td><td>Thomas and<br>Linevski, 1989</td></tr><tr><td rowspan="3">20<sup>0</sup>O<sub>I</sub>,<br>2740-2850</td><td>211</td><td>3.4 (0.5) 10<sup>-5</sup></td><td rowspan="3">Measurement</td><td rowspan="3">Baranov et al., 2003</td></tr><tr><td>235</td><td>2.6 (0.3) 10<sup>-5</sup></td></tr><tr><td>297</td><td>1.5 (0.3) 10<sup>-5</sup></td></tr><tr><td rowspan="2">20<sup>0</sup>O<sub>I</sub>,<br>2730-2870</td><td>302.3</td><td>11.3 (1) 10<sup>-6</sup></td><td rowspan="2">Measurement</td><td rowspan="2">Stefani et al., 2018</td></tr><tr><td>322.8</td><td>8.9 (0.8) 10<sup>-6</sup></td></tr><tr><td rowspan="3">20<sup>0</sup>O<sub>I</sub>,<br>2740-2850</td><td>230</td><td>4.59 (2.41) 10<sup>-5</sup></td><td rowspan="3">Measurement</td><td rowspan="3">This work</td></tr><tr><td>260</td><td>2.60 (0.22) 10<sup>-5</sup></td></tr><tr><td>295</td><td>1.88 (0.18) 10<sup>-5</sup></td></tr><tr><td>01<sup>1</sup>I<sub>1</sub>, 3014</td><td>296</td><td>2.5 (0.5) 10<sup>-6</sup></td><td>Measurement</td><td>Adiks, 1982</td></tr><tr><td>01<sup>1</sup>I<sub>1</sub>, 2870-3120</td><td>295-470</td><td>3.17 10<sup>-4</sup></td><td>Measurement</td><td>Thomas and<br>Linevski, 1989</td></tr><tr><td>01<sup>1</sup>I<sub>1</sub>, 2850-3150</td><td>295.15</td><td>2.8 10<sup>-4</sup></td><td>Measurement</td><td>Lamouroux et al.,<br>2010</td></tr><tr><td rowspan="4">01<sup>1</sup>I<sub>1</sub>, 2900-3100</td><td>294</td><td>3.38 (0.2) 10<sup>-4</sup></td><td rowspan="4">Measurement</td><td rowspan="4">Stefani et al., 2013</td></tr><tr><td>373</td><td>3.50 (0.4) 10<sup>-4</sup></td></tr><tr><td>473</td><td>3.54 (0.6) 10<sup>-4</sup></td></tr><tr><td>302.3</td><td>3.5 (0.35) 10<sup>-4</sup></td></tr><tr><td rowspan="4">01<sup>1</sup>I<sub>1</sub>, 2870-3180</td><td>322.8</td><td>3.3 (0.33) 10<sup>-4</sup></td><td rowspan="4">Measurement</td><td rowspan="4">Stefani et al., 2018</td></tr><tr><td>373.8</td><td>2.9 (0.29) 10<sup>-4</sup></td></tr><tr><td>424</td><td>3.5 (0.35) 10<sup>-4</sup></td></tr><tr><td>475.2</td><td>3.5 (0.35) 10<sup>-4</sup></td></tr><tr><td>01<sup>1</sup>I<sub>1</sub>, 2870-3175</td><td>294.8</td><td>2.39 (0.04) 10<sup>-4</sup><br>2.62 (0.05) 10<sup>-4</sup></td><td>Measurement</td><td>Baranov, 2018</td></tr><tr><td rowspan="3">01<sup>1</sup>I<sub>1</sub>, 2870-3175</td><td>230</td><td>4.48 (1.70) 10<sup>-4</sup></td><td rowspan="3">Measurement</td><td rowspan="3">This work</td></tr><tr><td>260</td><td>3.21 (0.59) 10<sup>-4</sup></td></tr><tr><td>295</td><td>2.27 (0.12) 10<sup>-4</sup></td></tr><tr><td>30<sup>0</sup>O<sub>III</sub>, 3942</td><td>290-301</td><td>7 (2) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td>30<sup>0</sup>O<sub>II</sub>, 4060</td><td>290-301</td><td>5 (1) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td rowspan="2">30<sup>0</sup>O<sub>II</sub>, 4060</td><td>260</td><td>5.03 (3.08) 10<sup>-6</sup></td><td rowspan="2">Measurement</td><td rowspan="2">This work</td></tr><tr><td>295</td><td>4.10 (0.65) 10<sup>-6</sup></td></tr><tr><td>30<sup>0</sup>O<sub>I</sub>, 4220</td><td>290-301</td><td>0.6 (0.3) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td>11<sup>1</sup>I<sub>II</sub>, 4250</td><td>290-301</td><td>0.2 (0.1) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td>10<sup>0</sup>O<sub>II</sub>+01<sup>1</sup>I<sub>1</sub>, 4278</td><td></td><td>1.3 (0.5) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td>10<sup>0</sup>O<sub>I</sub>+01<sup>1</sup>I<sub>1</sub>,<br>4383</td><td>290-301</td><td>2.5 (0.5) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td>00<sup>0</sup>2<sub>I</sub>, 4680</td><td>290-301</td><td>14 (5) 10<sup>-6</sup></td><td>Measurement</td><td>Tonkov et al., 1996</td></tr><tr><td>00<sup>0</sup>1<sub>I</sub>+00<sup>0</sup>2<sub>I</sub>,<br>6980-7060</td><td>293</td><td>1 (0.6) 10<sup>-5</sup></td><td>Measurement</td><td>Filippov et al., 1997</td></tr></tbody></table>
476
477
478

Table 2: Measured and/or computed CIA data obtained in this work and reported in the literature, from the far to the near infrared. Note that the results of some very old studies are not reported here because of the large associated uncertainties.

479

5. Conclusion

480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495

Several collision-induced absorption bands in the 1150-4500 cm⁻¹ spectral region were determined in this paper for temperatures from 230 to 295 K, from spectra measured with a Fourier transform spectrometer at pressure up to 40 bars. The obtained binary absorption coefficients and the integrated band intensities are in overall good agreement with data available in literature. Using the latter and those obtained in this work, we propose empirical models for the temperature dependent band shape and integrated band intensity. These models enable to compute the absorption coefficients for all collision-induced absorption bands in the 200-350 K range and may be extended up to 500 K with limited accuracy. They can thus be used for applications when accurate experimental and theoretical data are absent. Our work thus represents a significant advance in the modeling of collision-induced absorptions for hot, CO₂-rich planetary atmospheres. These includes primitive atmospheres of terrestrial planets [e.g. (Massol et al. 2016; Pluriel et al., 2019)] and a wide range of exoplanetary atmospheres [e.g. (Forget and Leconte, 2014)], as well as Venus for which the simulated temperature structure in the deep, hot CO₂-dominated atmosphere has been shown to be particularly dependent on our knowledge of the continuum absorption in the 1400-2000cm⁻¹ and 2500-3300cm⁻¹ spectral regions (Lebonnois et al., 2015).

496

References

497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524

Adiks, TG, 1976. Absorption spectrum of CO₂ in the 2.15–4 µm region under conditions of high pressure and CO₂ content. Opt. Spectrosc. 40, 375-8.

Adiks, TG, 1982. Experimental Study of the CO₂ IR Absorption Spectra as Applied to the Windows of Transparency of Venusian Atmosphere. Ph. D. Thesis, Institute of Atmospheric Physics, USSR Academy of Sciences, Moscow (in Russian).

Baranov, YI, Vigasin, AA, 1999. Collision-Induced Absorption by CO₂ in the Region of v₁, 2v₂. J. Mol. Spectrosc. 193, 319-25.

Baranov, YI, Fraser, GT, Lafferty, WJ, Vigasin AA, 2003. Collision-Induced absorption in the CO₂ Fermi triad for temperatures from 211K to 296K. Weakly Interacting Molecular Pairs: Unconventional absorbers of Radiation in the Atmosphere. Kluwer Academic Publishers, 149-58.

Baranov, YI, Lafferty, WJ, Fraser, GT, 2004. Infrared spectrum of the continuum and dimer absorption in the vicinity of the O₂ vibrational fundamental in O₂/CO₂ mixtures. J. Mol. Spectrosc. 228, 432-40.

Baranov, YI, 2018. Collision-induced absorption in the region of the v₂ + v₃ band of carbon dioxide. J. Mol. Spectrosc. 345, 11-6.

Birnbaum, G, Ho, W, Rosenberg, A, 1971. Far-infrared collision induced absorption in CO₂. II. Pressure dependence in the gas phase and absorption in the liquid. J. Chem. Phys. 55, 1039-45.

Burch, DE, Gryvnak, DA, Patty, RR, Bartky, CE, 1969. Shapes of collision-broadened CO₂ lines. J. Opt. Soc. Am. 59, 267-80.

Cole, RK, Tran, H, Hoghooghi, N, Rieker, GB, 2023. Temperature-dependent CO₂ line mixing models using dual frequency comb absorption and phase spectroscopy up to 25 bar and 1000 K. J. Quant. Spectrosc. Radiat. Transf. 297, 108488.

Daneshvar, L, Földes, T, Buldyreva, J, Vander Auwera, J, 2014. Infrared absorption by pure CO₂ near 3340 cm⁻¹: Measurements and analysis of collisional coefficients and line-mixing effects at subatmospheric pressures. J. Quant. Spectrosc. Radiat. Transf. 149, 258-74.

Filippov, NN, Bouanich, JP, Boulet, C, Tonkov, MV, Le Doucen, R, Thibault, F, 1997. Collision-induced double transition effects in the 3v₃ CO₂ band wing region. J. Chem. Phys. 106, 2067.
525 Forget, F, Leconte, J, 2014. Possible climates on terrestrial exoplanets. Phil. Trans. R. Soc.
526 A.3722013008420130084 http://doi.org/10.1098/rsta.2013.0084

527 Frommhold, L, 1994. Collision-induced Absorption in Gases. Cambridge University Press.

528 Gordon, IE, Rothman, LS, Hargreaves, RJ, Hashemi, R, Karlovets, EV, Skinner, FM, Conway, EK,
529 Hill, C, Kochanov, RV, Tan, Y, Wcisło, P, Finenko, AA, Nelson, K, Bernath, PF, Birk, M,
530 Boudon, V, Campargue, A, Chance, KV, ..., Yurchenko, SN, 2022. The HITRAN2020
531 molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 277, 107949.
532 https://doi.org/10.1016/j.jqsrt.2021.107949

533 Grassi, D, Politi, R, Ignatiev, NI, Plainaki, C, Lebonnois, S, Wolkenberg, P, Montabone, L, Migliorini,
534 A, Piccioni, G, Drossart, P, 2014. The Venus nighttime atmospheres as observed by the
535 VIRTIS-M instrument. Average fields from the complete infrared data set. J. Geophys. Res.
536 119, 837.

537 Grenfell, JL, Leconte, J, Forget, F, Godolt, M, Carrión-González, O, Noack, L, Tian, F, Rauer, H,
538 Gaillard, F, Bolmont, E, Charnay, B, Turbet, M, 2020. Possible Atmospheric Diversity of Low
539 Mass Exoplanets – Some Central Aspects. Space. Sci. Rev. 216, 98.
540 https://doi.org/10.1007/s11214-020-00716-4.

541 Gruszka, M, Borysow, A, 1997. Roto-Translational Collision-Induced Absorption of CO₂ for the
542 Atmosphere of Venus at Frequencies from 0 to 250 cm⁻¹, at temperatures from 200 to 800 K.
543 Icarus. 129, 172-7.

544 Gruszka, M, Borysow, A, 1998. Computer simulation of the far infrared collision induced absorption
545 spectra of gaseous CO₂. Mol. Phys. 93, 1007-16.

546 Hartmann, JM, Boulet, C, Jacquemart, D, 2011. Molecular dynamics simulations for CO₂ spectra. II.
547 The far infrared collision-induced absorption band. J. Chel. Phys. 134, 094316.
548 https://doi.org/10.1063/1.3557681

549 Hartmann, JM, Boulet, C, Robert, D, 2021. Collisional effects on molecular spectra: laboratory
550 experiments and models, consequences for applications (2nd edition). Elsevier, Amsterdam.

551 Ho, W, Birnbaum, G, Rosenberg, A, 1971. Far-Infrared Collision-Induced Absorption in CO₂. I.
552 Temperature dependence. J. Chem. Phys. 55, 1028-38.

553 Karman, T, Gordon, IE, van der Avoird, A, Baranov, YI, Boulet, C, Drouin, BJ, Groenenboom, GC,
554 Gustafsson, M, Hartmann, JM, Kurucz, RL, Rothman, LS, Sun, K, Sung, K, Thalmani, R, Tran,
555 H, Wishnow, EH, Wordsworth, R, Vigasin, AA, Volkamer, R, van der Zan, WJ, 2019. Icarus.
556 328, 160-75.

557 Lafferty, WJ, Solodov, AM, Weber, A, Olson, WB, Hartmann, JM, 1996. Infrared collision-induced
558 absorption by N₂ near 4.3 µm for atmospheric applications: measurements and empirical
559 modeling. Appl. Opt. 35, 5911-7.

560 Lamouroux, J, Tran, H, Laraia, AL, Gamache, RR, Rothman, LS, Gordon, IE, Hartmann, JM, 2010.
561 Updated database plus software for line-mixing in CO₂ infrared spectra and their test using
562 laboratory spectra in the 1.5–2.3 µm region. J. Quant. Spectrosc. Radiat. Transf. 111, 232131.

563 Lebonnois, S, Eymet V, Lee C, Vatant d'Ollone J, 2015. Analysis of the radiative budget of the
564 Venusian atmosphere based on infrared Net Exchange Rate formalism. J. Geophys. Res.
565 Planets. 120,1186–200, doi:10.1002/2015JE004794.

566 Mannik, L, Stryland, JC, Wels, HL, 1971. An Infrared Spectrum of CO, Dimers in the "Locked"
567 Configuration. Can. J. Phys. 49, 3056-7.

568 Manzanares, C, Munoz, A, Hidalgo, D, 1984. Collision-Induced absorption of infrared radiation by
569 N₂, O₂ and CO₂. Chem. Phys. 84, 363-71.

570 Massol, H, Hamano, K, Tian, F, Ikoma, M, Abe, Y, Chassefière, E, Davaille, A, Genda, H, Gudel, M,
571 Hori, Y, Leblanc, F, Marcq, E, Sarda, P, Shematovich, VI, Stokl, A, Lammer, H, 2016.
572 Formation and evolution of protoatmospheres. Space Science Reviews. 205, 153-211.

573 Moskalenko, NI, Il'in, YA, Parzhin, SN, Rodionov, LV, 1979. Pressure-induced IR radiation
574 absorption in atmospheres. Atmos. Ocean Phys. 15, 632-7.

575 Niraula, P, de Wit, J, Gordon, IE, Hargreaves, RJ, Sousa-Silva, C, Kochanov, RV, 2022. The
576 Impending Opacity Challenge in Exoplanet Atmospheric Characterization. Nat. Astron. 6, 1287-
577 95. https://doi.org/10.1038/s41550-022-01773-1.
578

Perrin, MY, Hartmann, JM, 1989. Temperature-dependent measurments and modeling of absorption

579

by CO₂-N₂ mixtures in the far line-wings of the 4.3 µm CO₂ band. J. Quant. Spectrosc. Radiat.

580

Transf. 42, 311-17.

581

Pluriel, W, Marcq, E, Turbet, M, 2019. Modeling the albedo of Earth-like magma ocean planets with

582

H₂O-CO₂ atmospheres. Icarus. 317, 583-90.

583

Predoi-Cross, A, Buldyreva, J, 2021. Characterization of line mixing effects in the 11101←00001 band of carbon dioxide for pressures up to 19 atm. J. Quant. Spectrosc. Radiat. Transf. 272,

584

107793.

585

Stefani, S, Piccioni, G, Snels, M, Grassi, D, Adriani, A, 2013. Experimental CO₂ Absorption coefficients at high pressure and high temperature. J. Quant. Spectrosc. Radiat. Transf. 117, 21-8.

586

588

Stefani, S, Snels, M, Piccioni, G, Grassi, D, Adriani, A, 2018. Temperature dependence of collisional induced absorption (CIA) bands of CO₂ with implications for Venus' atmosphere. J. Quant.

590

Spectrosc. Radiat. Transf. 204, 242-9.

591

Rothman, LS, Hawkins, RL, Wattson; RB, Gamache, RR, 1992. Energy levels, intensities, and

593

linewidths of atmospheric carbon dioxide bands. J. Quant. Spectrosc. Radiat. Transf. 48, 537-66.

594

Thibault, F, Menoux, V, Le Doucen, R, Rosenmann, L, Hartmann, JM, Boulet, C, 1997. Infrared collision-induced absorption by O₂ near 6.4 µm for atmospheric applications: measurements and empirical modeling. Appl. Opt. 36, 563-7.

595

596

598

599

Thomas, ME, Linevski, MJ, 1989. Integrated intensities of N₂, CO₂ and SF₆ vibrational bands from 1800 to 5000 cm⁻¹ as a function of density and temperature. J. Quant. Spectrosc. Radiat. Transf.

600

42, 465-76.

601

Tonkov, MV, Filippov, NN, Bertsev, VV, Bouanich, JP, Nguyen, VT, Brodbeck, C, Hartmann, JM, Boulet, C, Thibault, F, Le Doucen, R, 1996. Measurements and empirical modeling of pure CO₂ absorption in the 2.3µm region at room temperature: far wings, allowed and collision induces bands. Appl. Opt. 35, 4863-70.

602

603

604

605

606

607

Tran, H, Boulet, C, Stefani, S, Snels, M, Piccioni, G, 2011. Measurements and modelling of high-pressure pure CO₂ spectra from 750 to 8500 cm⁻¹. I-central and wing regions of the allowed vibrational bands. J. Quant. Spectrosc. Radiat. Transf. 112, 925-36.

608

609

610

Turbet, M, Tran, H, 2017. Comment on "Radiative Transfer in CO₂-Rich Atmospheres: 1. Collisional Line Mixing Implies a Colder Early Mars". J. Geophys. Res. Planets. 122, 2362-5. https://doi.org/10.1002/2017JE005373

611

612

613

Turbet, M, Tran, H, Pirali, O, Forget, F, Boulet, C, Hartmann, JM, 2019. Far infrared measurements of absorption by CH₄ + CO₂ and H₂ + CO₂ mixtures and implications for greenhouse warming on early Mars. Icarus. 321, 189-99.

614

615

616

Turbet, M, Gillmann, C, Forget, F, Baudin, B, Palumbo, A, Head, J, Karatekin, O, 2020. The environmental effects of very large bolide impacts on Early Mars explored with a hierarchy of numerical models. Icarus. 335, 113419.

617

618

619

Vigasin, AA, Baranov, YI, Chlenova, GV, 2002. Temperature variations of the Interaction Induced Absorption of CO₂ in the v₁, 2v₂ region: FTIR Measurements and Dimer Contribution. J. Mol. Spectrosc. 213, 51-6.

620

621

Wordsworth, RD, Forget, F, Eymet, V, 2010. Infrared collision-induced and far-line absorption in dense CO₂ atmospheres. Icarus. 210, 992-7.