# Data for the Ariel space mission and other exoplanet applications 1 Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications

Katy L Chubb, Séverine Robert, Clara Sousa-Silva, Sergei N Yurchenko, Nicole F Allard, Vincent Boudon, Jeanna Buldyreva, Benjamin Bultel, Athena Coustenis, Aleksandra Foltynowicz, et al.

► To cite this version:

Katy L Chubb, Séverine Robert, Clara Sousa-Silva, Sergei N Yurchenko, Nicole F Allard, et al. Data for the Ariel space mission and other exoplanet applications 1 Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications. RAS Techniques and Instruments, In press. insu-04537914

HAL Id: insu-04537914

https://insu.hal.science/insu-04537914

Submitted on 8 Apr 2024

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.
# Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications

Katy L Chubb, Séverine Robert, Clara Sousa-Silva, Sergei N Yurchenko, Nicole F Allard, Vincent Boudon, Jeanna Buldyreva, Benjamin Bultel, Athena Coustenis, Aleksandra Foltynowicz, et al.

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

## To cite this version:

Katy L Chubb, Séverine Robert, Clara Sousa-Silva, Sergei N Yurchenko, Nicole F Allard, et al. Data availability and requirements relevant for the Ariel space mission and other exoplanet atmosphere applications. RAS Techniques and Instruments, 2024, 3 (1), pp.636-690. 10.1093/rasti/rzae039. insu-04537914v3

HAL Id: insu-04537914

https://insu.hal.science/insu-04537914v3

Submitted on 3 Dec 2024

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published 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_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Data availability and requirements relevant for the Ariel space
mission and other exoplanet atmosphere applications

Katy L. Chubb1,2*, Séverine Robert3†, Clara Sousa-Silva4,5‡, Sergei N. Yurchenko6§,
Nicole F. Allard7, Vincent Boudon8, Jeanna Buldyreva9, Benjamin Bultel10, Athena Coustenis11,
Aleksandra Foltynowicz12, Iouli E. Gordon13, Robert J. Hargreaves13, Christiane Helling14,15,
Christian Hill16, Helgi Rafn Hrodmarsson17, Tijs Karman18, Helena Lecoq-Molinos14,15,31,
Alessandra Migliorini19, Michaël Rey20, Cyril Richard8, Ibrahim Sadiek21, Frédéric Schmidt10,
Andrei Sokolov6, Stefania Stefani19, Jonathan Tennyson6, Olivia Venot17, Sam O. M. Wright6,
Rosa Arenales-Lope22, Joanna K. Barstow23, Andrea Bocchieri24, Nathalie Carrasco25,
Dwaipayan Dubey22, Oleg Egorov26, Antonio García Muñoz27, Ehsan (Sam) Gharib-Nezhad28,
Leonardos Gkouvelis22, Fabian Grübel22, Patrick Gerard Joseph Irwin29, Antonín Knížek30,
David A. Lewis14, Matt G. Lodge1, Sushuang Ma6, Zita Martins32, Karan Molaverdikhani22,
Giuseppe Morello33, Andrei Nikitin26, Emilie Panek34, Miriam Rengel35, Giovanna Rinaldi19,
Jack W. Skinner36,40, Giovanna Tinetti6, Tim A. van Kempen37, Jingxuan Yang29,
Tiziano Zingales38,39

<footnote n="1">¹University of Bristol, School of Physics, HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK</footnote>

<footnote n="2">²Centre for Exoplanet Science, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK</footnote>

<footnote n="3">³Royal Belgian Institute for Space Aeronomy (BIRA-IASB), Av. Circulaire 3, 1180 Uccle, Belgium</footnote>

<footnote n="4">⁴Bard College, Institute of Astrophysics and Space Sciences, 30 Campus Rd, Annandale-On-Hudson, NY 12504</footnote>

<footnote n="5">⁵Institute of Astrophysics and Space Sciences, Rua das Estrelas, 4150-762 Porto, Portugal</footnote>

<footnote n="6">⁶Department of Physics and Astronomy, University College London, London WC1E 6BT, UK</footnote>

<footnote n="7">⁷Observatoire de Paris, PSL Research University, 61, Avenue de l'Observatoire, F-75014 Paris, France</footnote>

<footnote n="8">⁸Lab. ICB, UMR 6303 CNRS / Université de Bourgogne, 9 Av. A. Savary, BP 47870, F-21078 Dijon Cedex, France</footnote>

<footnote n="9">⁹Institut UTINAM, UMR CNRS 6213, Université de Franche-Comté, 16 Route de Gray, 25030 Besançon cedex, France</footnote>

<footnote n="10">¹⁰Université Paris-Saclay, CNRS, GEOPS, 91405, Orsay, France</footnote>

<footnote n="11">¹¹LESA, Paris Observatory, CNRS, PSL Univ., 5 place Jules Janssen, 92190 Meudon Cedex, France</footnote>

<footnote n="12">¹²Umeå University, Department of Physics, 901 87 Umeå, Sweden</footnote>

<footnote n="13">¹³Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA</footnote>

<footnote n="14">¹⁴Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria</footnote>

<footnote n="15">¹⁵TU Graz, Fakultät für Mathematik, Physik und Geodäsie, Petersgasse 16, A-8010 Graz, Austria</footnote>

<footnote n="16">¹⁶International Atomic Energy Agency, Wagramer Strasse 5, Vienna A-1400, Austria</footnote>

<footnote n="17">¹⁷Université Paris Cité and Univ Paris Est Creteil, CNRS, LISA, F-75013 Paris, France</footnote>

<footnote n="18">¹⁸Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, Netherlands</footnote>

<footnote n="19">¹⁹IAPS-INAF, Via Fosso del Cavaliere, 100, 00133, Rome, Italy</footnote>

<footnote n="20">²⁰Université de Reims Champagne-Ardenne, UMR CNRS 7331, BP 1039, F-51687, Reims Cedex 2, France</footnote>

<footnote n="21">²¹Leibniz Institute for Plasma Science and Technology (INP), Felix-Hausdorff-Straße 2, 17489 Greifswald, Germany</footnote>

<footnote n="22">²²Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstraße 1, D-81679 München, Germany</footnote>

<footnote n="23">²³School of Physical Sciences, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK</footnote>

<footnote n="24">²⁴Dipartimento di Fisica, La Sapienza Università di Roma, Piazzale Aldo Moro 5, Roma, 00185, Italy</footnote>

<footnote n="25">²⁵University of Paris-Saclay and ENS Paris-Saclay, LATMOS, 11 bourlevard d'Alembert, 78280 Guyancourt, France</footnote>

<footnote n="26">²⁶V.E. Zuev Institute of Atmospheric Optics SB RAS, 1, Akademician Zuev Sq., Tomsk, 634055 Russia</footnote>

<footnote n="27">²⁷Université Paris-Saclay, Université Paris Cit'e, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France</footnote>

<footnote n="28">²⁸Space Science and Astrobiology Division, NASA Ames Research Center, Moffett Field, CA, 94035 USA</footnote>

<footnote n="29">²⁹University of Oxford, Atmospheric, Oceanic and Planetary Physics, Department of Physics, Parks Rd, Oxford OX1 3PU, UK</footnote>

<footnote n="30">³⁰J. Heyrovský Institute of Physical Chemistry, Czech Academy of Sciences, Dolejškova 2155/3, 18223, Prague, Czech Republic</footnote>

<footnote n="31">³¹Institute of Astronomy, KU Leuven, Celestijnenlaan 200D bus 2401, 3001 Leuven</footnote>

<footnote n="32">³²CQE, IMS, Department of Chemical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Portugal</footnote>

<footnote n="33">³³Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, 18008, Granada, Spain</footnote>

<footnote n="34">³⁴Institut d'Astrophysique de Paris (CNRS, Sorbonne Université), 98bis Bd Arago, 75014 Paris, France</footnote>

<footnote n="35">³⁵Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany</footnote>

<footnote n="36">³⁶Division of Geological and Planetary Sciences, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125, USA</footnote>

<footnote n="37">³⁷SRON Netherlands Institute for Space Research, Niels Bohrweg 4, 2333 CA, Leiden, the Netherlands</footnote>

<footnote n="38">³⁸Dipartimento di Fisica e Astronomia, Università degli studi di Padova, Vicolo dell'Osservatorio 3, 35122 Padova, Italy</footnote>

<footnote n="39">³⁹INAF, Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy</footnote>

<footnote n="40">⁴⁰Martin A. Fisher School of Physics, Brandeis University, 415 South St, Waltham, MA, 02453, USA</footnote>
<figure><img src="image_3.png" /></figure>

# Data availability and requirements relevant for the *Ariel* space mission and other exoplanet atmosphere applications

Katy L. Chubb<sup>1,2*</sup> Séverine Robert,<sup>3</sup> Clara Sousa-Silva,<sup>4,5*</sup> Sergei N. Yurchenko<sup>6*</sup>
Nicole F. Allard<sup>7</sup> Vincent Boudon,<sup>8</sup> Jeanna Buldyreva,<sup>9</sup> Benjamin Bultel,<sup>10</sup> Athena Coustenis,<sup>11</sup>
Aleksandra Foltynowicz,<sup>12</sup> Iouli E. Gordon<sup>13</sup>, Robert J. Hargreaves<sup>13</sup>, Christiane Helling,<sup>14,15</sup>
Christian Hill,<sup>16</sup> Helgi Rafn Hrodmarsson,<sup>17</sup> Tijs Karman,<sup>18</sup> Helena Lecoq-Molinos,<sup>14,15,19</sup>
Alessandra Migliorini<sup>10</sup>,<sup>20</sup> Michaël Rey,<sup>21</sup> Cyril Richard,<sup>8</sup> Ibrahim Sadiek,<sup>22</sup> Frédéric Schmidt,<sup>10</sup>
Andrei Sokolov,<sup>6</sup> Stefania Stefani,<sup>20</sup> Jonathan Tennyson<sup>10</sup>,<sup>6</sup> Olivia Venot<sup>10</sup>,<sup>17</sup> Sam O. M. Wright,<sup>6</sup>
Rosa Arenales-Lope,<sup>23</sup> Joanna K. Barstow<sup>10</sup>,<sup>24</sup> Andrea Bocchieri,<sup>25</sup> Nathalie Carrasco,<sup>26</sup>
Dwaipayan Dubey,<sup>23</sup> Oleg Egorov,<sup>27</sup> Antonio García Muñoz,<sup>28</sup> Ehsan (Sam) Gharib-Nezhad,<sup>29</sup>
Leonardos Gkouvelis,<sup>23</sup> Fabian Grübel,<sup>23</sup> Patrick Gerard Joseph Irwin<sup>30</sup>, Antonín Knížek,<sup>31</sup>
David A. Lewis,<sup>14</sup> Matt G. Lodge<sup>1</sup>,<sup>1</sup> Sushuang Ma,<sup>6</sup> Zita Martins,<sup>32</sup> Karan Molaverdikhani<sup>10</sup>,<sup>23</sup>
Giuseppe Morello,<sup>33</sup> Andrei Nikitin,<sup>27</sup> Emilie Panek,<sup>34</sup> Miriam Rengel,<sup>35</sup> Giovanna Rinaldi,<sup>20</sup>
Jack W. Skinner,<sup>36,37</sup> Giovanna Tinetti,<sup>6</sup> Tim A. van Kempen,<sup>38</sup> Jingxuan Yang<sup>30</sup>
and Tiziano Zingales<sup>39,40</sup>

*Affiliations are listed at the end of the paper*

Accepted 2024 September 4. Received 2024 August 7; in original form 2024 March 29

## ABSTRACT

The goal of this white paper is to provide a snapshot of the data availability and data needs primarily for the *Ariel* space mission, but also for related atmospheric studies of exoplanets and cool stars. It covers the following data-related topics: molecular and atomic line lists, line profiles, computed cross-sections and opacities, collision-induced absorption and other continuum data, optical properties of aerosols and surfaces, atmospheric chemistry, UV photodissociation and photoabsorption cross-sections, and standards in the description and format of such data. These data aspects are discussed by addressing the following questions for each topic, based on the experience of the ‘data-provider’ and ‘data-user’ communities: (1) what are the types and sources of currently available data, (2) what work is currently in progress, and (3) what are the current and anticipated data needs. We present a GitHub platform for *Ariel*-related data, with the goal to provide a go-to place for both data-users and data-providers, for the users to make requests for their data needs and for the data-providers to link to their available data. Our aim throughout the paper is to provide practical information on existing sources of data whether in data bases, theoretical, or literature sources.

**Key words:** Data Methods – Numerical methods – Algorithms – Ariel – Data needs.

## 1 INTRODUCTION

### 1.1 The *Ariel* space mission

The *Ariel* space mission is due to launch in 2029. It will measure spectra of exoplanet atmospheres between 0.5 and 7.8 µm (~ 1280–20 000 cm⁻¹), with the highest resolving power (R = 100) between 1.95 and 3.9 µm (~ 2500–5100 cm⁻¹), undertaking a chemical survey of around 1000 of the planets in our galaxy (Tinetti et al. 2018; Venot et al. 2018a; Zingales et al. 2018). *Ariel* will be used to constrain elemental abundances in hot gas giant atmospheres (Wang

et al. 2023b), as well as allowing for detections of rocky Super-Earth atmospheric signatures (Ito et al. 2022) and the observation of temperate exoplanet atmospheres (Encrenaz et al. 2022). *Ariel* has inspired various data challenges, such as in retrievals (Barstow et al. 2022) and machine learning (Changeat & Yip 2023; Nikolaou et al. 2023). As highlighted in Tinetti et al. (2021), there is a synergy between *Ariel* and other exoplanet atmosphere missions; both high-resolution ground-based spectroscopic observations such as the Telescopio Nazionale Galileo (TNG) (Guilluy et al. 2022), and space-based missions such as PLATO (PLAnetary Transits and Oscillations of stars) and TESS (Transiting Exoplanets Survey Satellite) (Kálmán et al. 2023), and JWST (Changeat et al. 2022).

The *Hubble Space Telescope* (HST) has been widely used in exoplanet science; in particular the coverage of optical and UV regions, for example by the Wide Field Camera 3 WFC3/UVIS

<footnote>* E-mails: katy.chubb@bristol.ac.uk (KLC); csousasilva@bard.edu (CSS); s.yurchenko@ucl.ac.uk (SNY)</footnote>
# ABSTRACT

The goal of this white paper is to provide a snapshot of the data availability and data needs primarily for the Ariel space mission, but also for related atmospheric studies of exoplanets and brown dwarfs. It covers the following data-related topics: molecular and atomic line lists, line profiles, computed cross-sections and opacities, collision-induced absorption and other continuum data, optical properties of aerosols and surfaces, atmospheric chemistry, UV photodissociation and photoabsorption cross-sections, and standards in the description and format of such data. These data aspects are discussed by addressing the following questions for each topic, based on the experience of the “data-provider” and “data-user” communities: (1) what are the types and sources of currently available data, (2) what work is currently in progress, and (3) what are the current and anticipated data needs. We present a GitHub platform for Ariel-related data, with the goal to provide a go-to place for both data-users and data-providers, for the users to make requests for their data needs and for the data-providers to link to their available data. Our aim throughout the paper is to provide practical information on existing sources of data whether in databases, theoretical, or literature sources.

# 1 INTRODUCTION

## 1.1 The Ariel space mission

The Ariel space mission is due to launch in 2029. It will measure spectra of exoplanet atmospheres between 0.5 - 7.8 µm (~ 1280 - 20,000 cm⁻<fnref n="1" />), with the highest resolving power (R = 100) between 1.95 - 3.9 µm (~ 2500 - 5100 cm⁻<fnref n="1" />), undertaking a chemical survey of around 1000 of the planets in our galaxy (Zingales et al. 2018; Venot et al. 2018; Tinetti et al. 2018). Ariel will be used to constrain elemental abundances in hot gas giant atmospheres (Wang et al. 2023a), as well as allowing for detections of rocky Super-Earth atmospheric signatures (Ito et al. 2022) and the observation of temperate exoplanet atmospheres (Encrenaz et al. 2022). Ariel has inspired various data challenges, such as in retrievals (Barstow et al. 2022) and machine learning (Changeat & Yip 2023; Nikolaou et al. 2023). There is a synergy between Ariel and other exoplanet atmosphere missions; both high-resolution ground-based spectroscopic observations such as the Telescopio Nazionale Galileo (TNG) (Guilluy et al. 2022), and space-based missions such as PLATO (PLAnetary Transits and Oscillations of stars) and TESS (Transiting Exoplanets Survey Satellite) (Kálmán et al. 2023), and JWST (Changeat et al. 2022).

Overviews of potential exoplanet targets for Ariel can be found in Edwards et al. (2019a); Edwards & Tinetti (2022). The mission’s instrument wavelength coverage is summarised in Table 1. Although the main spectral coverage (besides photometric bands) of Ariel is from 1.1 - 7.8 µm, we consider data which cover the wavelength region from the UV to the far infrared, because of their use in atmospheric models relevant to the Ariel mission and other exoplanet atmosphere applications, such as climate models and analysing observed spectra from complementary exoplanet atmosphere telescopes. To characterise different exoplanet atmospheres, spectra are typically modelled using radiative transfer calculations. These calculations rely on a priori knowledge, often based on assumptions, of a variety of atmospheric processes, such as: molecular absorption and emission, scattering, chemistry, atmospheric dynamics, cloud formation, and atmosphere-surface interaction.

## 1.2 Atmospheric modelling and retrieval codes

A comprehensive list of exoplanetary retrieval codes (as of March 2023) can be found in MacDonald & Batalha (2023), with updates online<fnref n="1" />. Another detailed overview of radiative transfer and retrieval codes (as of May 2023) can be found in Rengel & Adamczewski (2023). In the Ariel science team, several radiative transfer retrieval packages are available, including ARCiS (Ormel & Min 2019; Min et al. 2020), NEMESIS (Irwin et al. 2008), Pyrat Bay (Cubillos & Blecic 2021), POSEIDON (MacDonald 2023) and TauREx3 (Al-Refaie et al. 2021). They have been compared in the frame of a retrieval challenge for the Ariel mission (Barstow et al. 2022). Table 2 lists a non-exhaustive selection of atmospheric modelling and retrieval codes and their respective repositories.

## 1.3 Paper structure

The intention of this community white paper is to ensure the data necessary to interpret observations from exoplanet atmosphere characterisation missions such as Ariel are up to a standard required for successful analyses, and to allow comparability between analyses (for example, line lists which are complete and accurate at the relevant atmospheric temperatures for all expected species, refractive indices for all aerosol types expected in exoplanet atmospheres, etc). We provide a summary of the types of data typically used by atmospheric retrieval and modelling codes, and we identify potential weaknesses in the data and therefore motivate further research. For different data types, as described below, we will provide an overview of what data is currently: 1) available, 2) typically used, 3) being worked on, and 4) needed. Although the focus is on data required for characterising exoplanet atmospheres related to the Ariel space mission, we also include some discussion on more general data used in the field of astronomical spectroscopy, for example broader wavelength regions. We focus on a number of different data types: molecular and atomic line lists (Section 2), molecular and atomic line shapes (Section 3), computed absorption cross-sections and opacities (Section 4), collision induced absorption (CIA) and other continuum data (Section 5), data for aerosols (Section 6), data for atmospheric chemistry models (Section 7), and data required for UV photodissociation

<footnote>‡ katy.chubb@bristol.ac.uk</footnote>

<footnote>‡ severine.robert@aeronomie.be</footnote>

<footnote>‡ csousasilva@bard.edu</footnote>

<footnote>‡ s.yurchenko@ucl.ac.uk</footnote>

<footnote n="1">¹ https://doi.org/10.5281/zenodo.7675743</footnote>
<table><caption>**Table 1.** Summary of *Ariel* instruments and their wavelength coverage and resolving power $R = \frac{\lambda}{\Delta\lambda}$, from Edwards et al. (2019b). AIRS is the *Ariel* InfraRed Spectrometer and NIRSpec the Near-InfraRed Spectrometer. VISPhot, FGS1, and FGS2 are photometers (Szabó et al. 2022).</caption><thead><tr><th>Instrument</th><th>Wavelength range (µm)</th><th>Wavenumber range (cm<sup>-1</sup>)</th><th>R = λ/Δλ</th></tr></thead><tbody><tr><td>VISPhot</td><td>0.5–0.6</td><td>16 667–200 000</td><td>Photometric bands</td></tr><tr><td>FGS 1</td><td>0.6–0.81</td><td>12 346–16 667</td><td>Photometric bands</td></tr><tr><td>FGS 2</td><td>0.81–1.1</td><td>9091–12 346</td><td>Photometric bands</td></tr><tr><td>NIRSpec</td><td>1.1–1.95</td><td>5128–9091</td><td>20</td></tr><tr><td>AIRS Ch0</td><td>1.95–3.9</td><td>2564–5128</td><td>100</td></tr><tr><td>AIRS Ch1</td><td>3.9–7.8</td><td>1282–2564</td><td>30</td></tr></tbody></table>

and Space Telescope Imaging Spectrograph (STIS) instruments, are important for understanding aerosol properties in exoplanet atmospheres (Wakeford et al. 2020; Fairman, Wakeford & MacDonald 2024). The WFC3 infrared (IR) instrument has been extensively used for IR observations of hot exoplanet atmospheres, particularly for characterizing H$_2$O spectral features which have been detected in abundance in such atmospheres (see for example, Iyer et al. 2016). The wider spectral coverage and improvement in spectral resolution of both *Ariel* and *JWST* compared to HST/WFC3 allows for the improved detection and characterization of several molecular species in the optical and IR regions (Guilluy et al. 2022). While *JWST* has a larger telescope than *Ariel*, allowing for observations of smaller cooler exoplanets using less transits (Changeat et al. 2022), *JWST* was designed to make observations for many more astronomy fields than only exoplanets. *Ariel*, on the other hand, will observe simultaneously over a wide wavelength range; it is the first space mission fully dedicated to the study of exoplanet atmospheres and has the unique ability to probe the atmosphere of warm and hot exoplanets with a statistical approach, aiming to observe ~1000 exoplanet atmospheres during its first tier (Tinetti et al. 2021). *Ariel* is optimized to observe transiting exoplanets, and can be equally or more efficient than *JWST* for characterizing exoplanets orbiting bright stars (see fig. 8-2 of Tinetti et al. 2021). Meanwhile, some of the exoplanets observed by *JWST* will be used by *Ariel* for calibration purposes in the first months of observation, and will likely be used to refine the *Ariel* target list (Edwards et al. 2019b), highlighting the strong synergy between these two missions.

High-resolution spectroscopy utilizes cross-correlation techniques to allow for the detection of individual species present at lower abundances than can be observed using the lower resolution observations of spectroscopic missions such as *Ariel* (Guilluy et al. 2022). The two types of observation together allow for a more complete understanding of an atmosphere (see for example, Brogi & Line 2019).

Overviews of potential exoplanet targets for *Ariel* can be found in Edwards et al. (2019b) and Edwards & Tinetti (2022). The mission's instrument wavelength coverage is summarized in Table 1. Although the main spectral coverage (besides photometric bands) of *Ariel* is from 1.1 to 7.8 µm, we consider data which cover the wavelength region from the UV to the far infrared, because of their use in atmospheric models relevant to the *Ariel* mission and other exoplanet atmosphere applications, such as climate models and analysing observed spectra from complementary exoplanet atmosphere telescopes. To characterize different exoplanet atmospheres, spectra are typically modelled using radiative transfer calculations. These calculations rely on a priori knowledge, often based on assumptions, of a variety of atmospheric processes, such as: molecular absorption and emission, scattering, chemistry, atmospheric dynamics, cloud formation, and atmosphere-surface interaction.

## 1.2 Atmospheric modelling and retrieval codes

A comprehensive list of exoplanetary retrieval codes (as of 2023 March) can be found in MacDonald & Batalha (2023), with updates online.<fnref n="1" /> Another detailed overview of radiative transfer and retrieval codes (as of 2023 May) can be found in Rengel & Adamczewski (2023). In the *Ariel* science team, several radiative transfer retrieval packages are available, including ARCIS (Ormel & Min 2019; Min et al. 2020), NEMESIS (Irwin et al. 2008), Pyrat Bay (Cubillos & Blicic 2021), POSEIDON (MacDonald 2023), and TauReX3 (Al-Refaie et al. 2021). They have been compared in the frame of a retrieval challenge for the *Ariel* mission (Barstow et al. 2022). Table 2 lists a non-exhaustive selection of atmospheric modelling and retrieval codes and their respective repositories used in exoplanetary studies. Whilst these multiple retrieval codes all perform the same basic function – comparing a range of typically 1D, parametric radiative transfer simulations to observed data via a sampling algorithm such as MCMC or nested sampling – they each have slightly different methods for parametrizing often complex atmospheric processes. Previous retrieval comparison efforts by Barstow et al. (2020, 2022) showcase the agreement between them for simple cases where all codes are able to implement the same parametrizations. However, Barstow et al. (2020) compared a range of cloud parametrizations and showed that whilst the overall conclusions using each method were not in disagreement with each other, the different ways of representing cloud in each model meant that the sensitivity to different aspects of the cloud varied between approaches. Therefore, a multiplicity of retrieval codes is considered to be an asset for the *Ariel* mission, since each has been written with different priorities in mind. Some codes include more complex chemistry than others (see e.g. Al-Refaie et al. 2022) and others have focused particularly on representation of cloud physics (see e.g. Ormel & Min 2019). Applying multiple retrieval codes to a single data set is rapidly becoming accepted as field best-practice as it allows these different strengths to be captured and also provides a useful cross-check for cases where solutions may be model dependent (see e.g. Kilpatrick et al. 2018; Lewis et al. 2020; Welbanks et al., in preparation). Regardless of any differences in parametrizations in these codes used to model exoplanet atmospheres and interpret observations, they all rely on various data inputs crucial for successful analyses of atmospheres, as will be discussed in this paper.

## 1.3 Paper structure

The intention of this community white paper is to ensure the data necessary to interpret observations from exoplanet atmosphere

<footnote n="1">¹https://doi.org/10.5281/zenodo.7675743</footnote>
<table><caption>**Table 1.** Summary of Ariel instruments and their wavelength coverage and resolving power $R=\frac{d}{\Delta\lambda}$, from Edwards et al. (2019a). AIRS is the Ariel InfraRed Spectrometer, NIRSpec the Near-InfraRed Spectrometer, and VISPhot, FGS1 and FGS2 are photometers (Szabó et al. 2022).</caption><thead><tr><th>Instrument</th><th>Wavelength range (μm)</th><th>Wavenumber range (cm<sup>-1</sup>)</th><th>R= d / Δλ</th></tr></thead><tbody><tr><td>VISPhot</td><td>0.5 - 0.6</td><td>16,667 - 20,000</td><td></td></tr><tr><td>FGS 1</td><td>0.6 - 0.81</td><td>12,346 - 16,667</td><td>Photometric bands</td></tr><tr><td>FGS 2</td><td>0.81 - 1.1</td><td>9091 - 12,346</td><td></td></tr><tr><td>NIRSpec</td><td>1.1 - 1.95</td><td>5128 - 9091</td><td>20</td></tr><tr><td>AIRS Ch0</td><td>1.95 - 3.9</td><td>2564 - 5128</td><td>100</td></tr><tr><td>AIRS Ch1</td><td>3.9 - 7.8</td><td>1282 - 2564</td><td>30</td></tr></tbody></table>

<table><caption>**Table 2.** Examples of typical atmospheric retrieval and modelling codes used by the exoplanetary atmosphere community.</caption><thead><tr><th>Code</th><th>Reference</th><th>Link</th></tr></thead><tbody><tr><td>ARCIS</td><td>Min et al. (2020)</td><td>https://www.exoclouds.com</td></tr><tr><td>ATMO</td><td>Tremblin et al. (2015)</td><td>https://www.erc-atmo.eu</td></tr><tr><td>Helios-r2</td><td>Kitzmann et al. (2020)</td><td>https://github.com/exoclime/Helios-r2</td></tr><tr><td>NASA Planetary Spectrum Generator (PSG)</td><td>Villanueva et al. (2018)</td><td>https://psg.gsfc.nasa.gov/</td></tr><tr><td>NEMESIS</td><td>Irwin et al. (2008)</td><td>https://nemesiscode.github.io/nemesis.html</td></tr><tr><td>NemesisPy</td><td>Yang et al. (2023)</td><td>https://github.com/Jingxuan97/nemesispy/</td></tr><tr><td>petitRADTRANS</td><td>Mollière et al. (2019)</td><td>https://petitradtrans.readthedocs.io/en/latest/</td></tr><tr><td>PICASO</td><td>Batalha et al. (2021)</td><td>https://natashabatalha.github.io/picaso/</td></tr><tr><td>PLATON</td><td>Zhang et al. (2020)</td><td>https://github.com/ideasrule/platon</td></tr><tr><td>POSEIDON</td><td>MacDonald (2023)</td><td>https://github.com/MartianColonist/POSEIDON</td></tr><tr><td>Pyrat Bay</td><td>Cubillos & Blecic (2021)</td><td>https://pyratbay.readthedocs.io/en/latest/</td></tr><tr><td>TauREx3</td><td>Al-Refaie et al. (2021)</td><td>http://github.com/ucl-exoplanets/TauREx3_public</td></tr></tbody></table>

or photoabsorption (Section 8). Needs for data standards, meta data, existing rules and associated tools are discussed in Section 9. Current databases providing such data for characterising exoplanet atmospheres are reviewed across the paper in the relevant sections. Our conclusions can be found in Section 10.

The information associated with this paper is made available via the GitHub project<fnref n="2" />. The goal of this platform is to provide a go-to place both for the data-users and data-providers, for the users to inform others about their data needs and make requests, and for the data providers to link to the available or inform about their soon-to-be-available data (see Section 10.1).

## 2 MOLECULAR/ATOMIC LINE LISTS

Molecular and atomic line lists contain information about the frequency and strength of spectroscopic transitions, sometimes referred to as “lines”, often accompanied by information on the associated initial and final energy states. When it comes to atomic and molecular line lists, the following factors are important: accuracy, which refers to the frequency

or wavelength location of transition lines, and completeness, which refers to both spectral and temperature coverage; i.e. the number of transitions in the latter case. High-resolution spectra ($\frac{d}{\Delta\lambda} \ge 25,000$) of exoplanets, typically measured from ground-based instruments, require very accurate line positions to be known, usually over a shorter wavelength range than required for observations from low- to mid-resolution space-based telescopes such as Ariel and JWST. To interpret these lower-resolution ($\frac{d}{\Delta\lambda} \le 3000$) observations, it is particularly important for overall opacity to be provided by a line list, which requires the line list to be considered complete up to the temperature of the atmosphere being modelled. This metric of completeness is related to the number of spectral line transitions between energy levels which are provided by a line list. There will be transitions between so-called hot bands, for example, which would not be present for a line list computed or based on laboratory measurements at room-temperature, but would be important for characterising the atmospheres of exoplanets at high temperatures of around 1000 K - 2000 K. It is well known that the choice of line list can have a huge impact in interpreting high-resolution spectroscopic observations (see, for example, Serindag et al. 2021; de Regt et al. 2022). There is also an impact on lower-resolution JWST observations, particularly at elevated temperatures > 1000 K (see, for example, Niraula et al. 2022).

<footnote n="2">² https://github.com/Ariel-data</footnote>
<table><caption>**Table 2.** Examples of typical atmospheric retrieval and modelling codes used by the exoplanetary atmosphere community.</caption><thead><tr><td>Code</td><td>Reference</td><td>Link</td></tr></thead><tbody><tr><td>ARCIS</td><td>Min et al. (2020)</td><td>https://www.exoclouds.com</td></tr><tr><td>ATMO</td><td>Tremblin et al. (2015)</td><td>https://www.erc-atmo.eu</td></tr><tr><td>Helios-r2</td><td>Kitzmann et al. (2020)</td><td>https://github.com/exoclime/Helios-r2</td></tr><tr><td>NASA Planetary Spectrum Generator (PSG)</td><td>Villanueva et al. (2018)</td><td>https://psg.gsfc.nasa.gov/</td></tr><tr><td>NEMESIS</td><td>Irwin et al. (2008)</td><td>https://nemesiscode.github.io/nemesis.html</td></tr><tr><td>NemesisPy</td><td>Yang, Irwin & Barstow (2023)</td><td>https://github.com/Jingxuan97/nemesispy/</td></tr><tr><td>petitRADTRANS</td><td>Mollière et al. (2019)</td><td>https://petitradtrans.readthedocs.io/en/latest/</td></tr><tr><td>PICASO</td><td>Batalha, Rooney & MacDonald (2021)</td><td>https://natashabatalha.github.io/picaso/</td></tr><tr><td>PLATON</td><td>Zhang et al. (2020)</td><td>https://github.com/ideasrule/platon</td></tr><tr><td>POSEIDON</td><td>MacDonald (2023)</td><td>https://github.com/MartianColonist/POSEIDON</td></tr><tr><td>Pyrat Bay</td><td>Cubillos & Blecic (2021)</td><td>https://pyratbay.readthedocs.io/en/latest/</td></tr><tr><td>TauREx3</td><td>Al-Refaie et al. (2021)</td><td>http://github.com/ucl-exoplanets/TauREx3_public</td></tr></tbody></table>

characterization missions such as *Ariel* are up to a standard required for successful analyses, and to allow comparability between analyses (for example, line lists which are complete and accurate at the relevant atmospheric temperatures for all expected species, refractive indices for all aerosol types expected in exoplanet atmospheres, etc). We provide a summary of the types of data typically used by atmospheric retrieval and modelling codes, and we identify potential weaknesses in the data and therefore motivate further research. For different data types, as described below, we will provide an overview of what data is currently: (1) available, (2) typically used, (3) being worked on, and (4) needed. Although the focus is on data required for characterizing exoplanet atmospheres related to the *Ariel* space mission, we also include some discussion on more general data usage in the field of astronomical spectroscopy, for example for broader wavelength regions. We focus on a number of different data types: molecular and atomic line lists (Section 2), molecular and atomic line shapes (Section 3), computed absorption cross-sections and opacities (Section 4), collision induced absorption (CIA) and other continuum data (Section 5), data for aerosols (Section 6), data for atmospheric chemistry models (Section 7), and data required for UV photodissociation or photoabsorption (Section 8). Needs for data standards, meta data, existing rules, and associated tools are discussed in Section 9. Current data bases providing such data for characterizing exoplanet atmospheres are reviewed across the paper in the relevant sections. Our conclusions can be found in Section 10.

The information associated with this paper is made available via the GitHub project.<fnref n="2" /> The goal of this platform is to provide a go-to place both for the data-users and for the data-providers, for the users to inform others about their data needs and make requests, and for the data providers to link to the available or inform about their soon-to-be-available data (see Section 10.1).

## 2 MOLECULAR/ATOMIC LINE LISTS

Molecular and atomic line lists contain information about the frequency and strength of spectroscopic transitions, sometimes referred to as ‘lines,’ often accompanied by information on the associated initial and final energy states. When it comes to atomic and molecular line lists, the following factors are important: accuracy, which refers to the frequency or wavelength location of transition lines, and completeness, which refers to both spectral and temperature coverage; i.e. the number of transitions in the latter case. High-resolution spectra ($\frac{\lambda}{\Delta\lambda} \gtrsim 25\,000$) of exoplanets, typically measured

from ground-based instruments, require very accurate line positions to be known, usually over a shorter wavelength range than required for observations from low- to mid-resolution space-based telescopes such as *Ariel* and *JWST*. The cross-correlation technique used to analyse observed high-resolution spectra is an efficient tool to characterize exoplanet atmospheres, complementary to observations from space telescopes. It has resulted in numerous detections in exoplanetary atmospheres of hot-Jupiters of molecules and atoms, including CO, H$_2$O, TiO, HCN, CH$_4$, NH$_3$, C$_2$H$_2$, OH, VO, and CrH, as well Ca, V, Cr, Fe, Ti, Mg, He, K, Na, and Li (Guillot et al. 2022; Gandhi et al. 2023).

To interpret the lower resolution ($\frac{\lambda}{\Delta\lambda} \lesssim 3000$) observations, it is particularly important for overall opacity to be provided by a line list, which requires the line list to be considered complete up to the temperature of the atmosphere being modelled. This metric of completeness is related to the number of spectral line transitions between energy levels which are provided by a line list. There will be transitions between the so-called hot bands, for example, which would not be present for a line list computed or based on laboratory measurements at room-temperature, but would be important for characterizing the atmospheres of exoplanets at high temperatures of around 1000–2000 K. It is well known that the choice of line list can have a huge impact in interpreting high-resolution spectroscopic observations (see, for example Serindag et al. 2021; de Regt et al. 2022). Perhaps less intuitive, but the accuracy of line list, especially of the line positions, can be also critical for interpretation of lower resolution space-based observations, particularly at elevated temperatures >1000 K (see for example, Niraula et al. 2022). Therefore it is important that molecular opacities used in the main stream atmospheric retrieval packages are initially built at the highest resolution ($\frac{\lambda}{\Delta\lambda} \sim 100\,000$) before binning them down to the practical resolution ($\frac{\lambda}{\Delta\lambda} \sim 3000–15\,000$) (Chubb et al. 2020b). The aspects of completeness and accuracy for existing molecular line lists will be reviewed below.

### 2.1 State of the art – data availability

The main data bases which host molecular and atomic line lists are given in Table 3, with more details for a number of the molecular data bases found in the subsections below. Of these molecular data bases, HITRAN and GEISA provide highly accurate data with the main focus on terrestrial conditions, while the other listed data bases typically have more extended coverage, for example covering up to higher temperatures, usually >1000 K. Table 4 summarizes the wavelength and temperature coverage of molecular line lists from some of the main spectral data bases. An approximate temperature

<footnote n="2">²https://github.com/Ariel-data</footnote>
The aspects of completeness and accuracy for existing molecular line lists will be reviewed below.

## 2.1 State of the art - Data availability

The main databases which host molecular and atomic line lists are given in Table 3, with more details for a number of the molecular databases found in the subsections below. Of these molecular databases, HITRAN and GEISA provide highly accurate data with the main focus on terrestrial conditions, while the other listed databases typically have more extended coverage, for example covering up to higher temperatures, usually > 1000 K. Table 4 summarises the wavelength and temperature coverage of molecular line lists from some of the main spectral databases. An approximate temperature up to which the line list is considered complete, in terms of completeness of transition data at a given temperature, is given; either hot (≥ 1000 K) or else assumed to be roughly Earth-temperature (≤ 500 K). The latter usually applies to species in the HITRAN database, which was originally designed for terrestrial atmosphere applications. We note that most molecules in the ExoMol database are complete up to at least 3000 K, and hotter for some diatomic species. Some stable diatomic species such as H₂ and HD⁺ are even considered complete up to 10,000 K. C₂H₄ is considered complete up to 700 K in both the TheoReTs (Rey et al. 2016a) and ExoMol (Mant et al. 2018) databases; the same applies to HNO₃ (Pavlyuchko et al. 2015) in the ExoMol database, which is also complete up to 700 K. An overview of some molecular and atomic databases (as of September 2022) can also be found in Rengel (2024); additional databases not detailed here include that of JPL Molecular Spectroscopy<fnref n="3" /> and the Cologne database for molecular spectroscopy (CDMS)<fnref n="4" />.

Atomic line list data can be obtained from various sources such as the NIST<fnref n="5" /> (Kramida et al. 2013) and Kurucz<fnref n="6" /> (Kurucz 2017) databases, and the Vienna atomic line database (VALD3)<fnref n="7" /> (Ryabchikova et al. 2015). The appendix of Grimm et al. (2021) compares the opacities available from these three databases. Atomic partition functions are included in the Kurucz and VALD3 databases, and can also be computed by using various sources such as Irwin (1981). We note that while the Kurucz database is well-used and considered accurate for atomic line lists, the majority of the Kurucz molecular line lists are more approximate than the other line list databases described here.

### 2.1.1 Descriptions of molecular databases

#### 2.1.1.1 CaSDa
The CaSDa (Calculated Spectroscopic Databases) databases<fnref n="8" /> (see Richard et al. 2020, 2024) contain synthetic line lists resulting from fits of the effective Hamiltonian and dipole moment parameters using assigned experimental laboratory spectra. The models used for the

calculations are based on the tensorial formalism developed in the Dijon group, as explained in Boudon et al. (2011). Currently, there are 10 CaSDa databases for 10 different molecules, which amounts to 39 isotopologues in total. A new database, SiCaSDa, has been released very recently for the 3 isotopologues of SiH₄ (a molecule already observed in the interstellar medium). All these databases are listed in Table 5. For the present topic of exoplanetary spectroscopy, the most relevant ones are, of course, CH₄, C₂H₄ and GeH₄, which are present in the atmospheres of the giant planets of the Solar System. CF₄ and SiF₄ are naturally present in Earth's atmosphere due to volcanic emissions; SiF₄ has been suggested as a possible species on Io by Schaefer & Fegley Jr. (2005) and thus may be relevant in the case of potential volcanic exoplanets; CH₃Cl is present in comets (Hardy et al. 2023) and thus could be of interest for exo-comets (Janson et al. 2023). It was also suggested and explored as a biomarker in exoplanetary atmospheres (Seager et al. 2013). In the near future, the intent is for new data (new bands and new isotopologues, like for instance CH₃D in MeCaSDa) to be added to these databases (Richard et al. 2024), and for further ones to be developed, especially for some molecules of astrophysical interest, like C₃H₆O₃ (trioxane that may be relevant for comets, see Richard et al. (2022)).

These databases contain calculated line lists for all spectral regions of these molecules that could be assigned in experimental laboratory spectra and fitted line-by-line using effective Hamiltonians and dipole moments. The databases contain extra information, such as energy levels with all quantum numbers and eigenvectors. When available, different isotopologues data are included in each database. The given accuracy of line positions and intensities is equal to the standard deviation of the fit; extrapolation is limited to only a few rotational quantum number values outside the existing assignment range. The data output is in the 160-character HITRAN2004 format (Rothman et al. 2005). CaSDa use some specific notations for line assignments in the case of CH₃Cl and C₂H₄ since they are based on use of a tensorial formalism similar to that of CH₄. It is also possible to compute absorption cross-sections.

Figure 1 shows a comparison for methane cross-sections computed at 296 K between MeCaSDa (Ba et al. 2013), TheoReTs (Rey et al. 2016b), the latest ExoMol MM line list (Yurchenko et al. 2024a), HITRAN2020 (Gordon et al. 2022) and HITEMP (Hargreaves et al. 2020). It can be seen that all databases are very similar at this temperature: the differences are mostly in the “windows” between the bands and are related to very weak lines. HITRAN lacks those lines, but they are present in HITEMP.

#### 2.1.1.2 ExoMol
ExoMol<fnref n="9" /> is a provider of the molecular<fnref n="10" /> data necessary for modelling spectroscopy of exoplanets (Tennyson et al. 2020). The main data products are line lists, with the emphasis on the molecules important for exoplanetary and stellar atmospheres, but also for spectroscopy of planets, comets as well as industrial applications (see Tennyson & Yurchenko 2021). As of today, the ExoMol database contains line lists for about 100 molecules and over 250 isotopologues, see Table 3 for the current snapshot of the molecular line lists available in ExoMol. Up to the ExoMol

<footnote n="3">³ https://spec.jpl.nasa.gov/</footnote>

<footnote n="4">⁴ https://cdms.astro.uni-koeln.de/</footnote>

<footnote n="5">⁵ https://physics.nist.gov/PhysRefData/ASD/lines_form.html</footnote>

<footnote n="6">⁶ https://lweb.cfa.harvard.edu/amp/ampdata/kurucz23/sekur.html; http://kurucz.harvard.edu/atoms.html</footnote>

<footnote n="7">⁷ http://vald.astro.uu.se</footnote>

<footnote n="8">⁸ https://vamdc.icb.cnrs.fr</footnote>

<footnote n="9">⁹ www.exomol.com</footnote>

<footnote n="10">¹⁰ Also atomic from 2023</footnote>
<table><caption>**Table 3.** An overview of some line list data bases used by the (exo)planetary atmosphere community.</caption><thead><tr><th>Database</th><th>Type of data</th><th>Reference</th><th>Link</th></tr></thead><tbody><tr><td>CaSDa</td><td>Theoretical line lists up to high temperatures</td><td>Richard, Boudon & Rotger (2020), Richard et al. (2024)</td><td>https://vamdc.icb.cnrs.fr</td></tr><tr><td>ExoMol</td><td>Theoretical line lists up to high temperatures</td><td>Tennyson et al. (2020)</td><td>https://exomol.com</td></tr><tr><td>GEISA</td><td>Accurate line lists for terrestrial conditions</td><td>Jacquinet-Husson et al. (2016), Delahaye et al. (2021)</td><td>https://geisa.aeris-data.fr</td></tr><tr><td>HITEMP</td><td>Line lists up to high temperatures</td><td>Rothman et al. (2010)</td><td>https://hitran.org/hitemp</td></tr><tr><td>HITRAN</td><td>Accurate line lists for terrestrial conditions</td><td>Gordon et al. (2022)</td><td>https://hitran.org</td></tr><tr><td>Kurucz</td><td>Semi-empirical line lists up to high temperatures</td><td>Kurucz (1995)</td><td>http://kurucz.harvard.edu/molecules.html</td></tr><tr><td>MoLLIST</td><td>Laboratory line lists up to high temperatures</td><td>Bernath (2020)</td><td>https://bernath.uwaterloo.ca/molecularlists.php</td></tr><tr><td>NASA Ames</td><td>Semi-empirical line lists up to high temperatures</td><td>e.g. Huang et al. (2023b)</td><td>http://huang.seti.org</td></tr><tr><td>NIST</td><td>Atomic line lists up to high temperatures</td><td>Kramida, Ralchenko & Reader (2023)</td><td>https://physics.nist.gov/PhysRefData/ASD/lines_form.html</td></tr><tr><td>S&amp;MPO</td><td>Spectroscopy and Molecular Properties of Ozone</td><td>Tyuterev et al. (2021)</td><td>http://smpo.iao.ru</td></tr><tr><td>TheoReTs</td><td>Theoretical line lists up to high temperatures</td><td>Rey et al. (2016a)</td><td>https://theorets.tsu.ru</td></tr><tr><td>VALD3</td><td>Atomic line lists up to high temperatures</td><td>Ryabchikova et al. (2015)</td><td>http://vald.astro.uu.se</td></tr></tbody></table>

up to which the line list is considered complete, in terms of completeness of transition data at a given temperature, is given; either hot (≥1000 K) or else assumed to be roughly Earth-temperature (≤500 K). The latter usually applies to species in the HITRAN data base, which was originally designed for terrestrial atmosphere applications. We note that most molecules in the ExoMol data base are complete up to at least 3000 K, and hotter for some diatomic species. Some stable diatomic species such as H₂ and HD⁺ are even considered complete up to 10 000 K. C₂H₄ is considered complete up to 700 K in both the TheoReTs (Rey et al. 2016b) and ExoMol (Mant et al. 2018) data bases; the same applies to HNO₃ (Pavlyuchko, Yurchenko & Tennyson 2015) in the ExoMol data base, which is also complete up to 700 K. An overview of some molecular and atomic data bases (as of 2022 September) can also be found in Rengel (2024); additional data bases not detailed here include that of JPL Molecular Spectroscopy<fnref n="3" /> and the Cologne data base for molecular spectroscopy (CDMS).<fnref n="4" />

Atomic line list data can be obtained from various sources such as the NIST<fnref n="5" /> (Kramida et al. 2021) and Kurucz<fnref n="6" /> (Kurucz 2017) data bases, and the Vienna atomic line data base (VALD3)<fnref n="7" /> (Ryabchikova et al. 2015). The appendix of Grimm et al. (2021) compares the opacities available from these three data bases. Atomic partition functions are included in the Kurucz and VALD3 data bases, and can also be computed by using various sources such as Irwin (1981). We note that while the Kurucz data base is well-used and considered accurate for atomic line lists, the majority of the Kurucz molecular line lists are more approximate than the other line list data bases described here.

Fig. 1 (left panel) shows a comparison for methane cross-sections computed at 296 K between MeCaSDa (Ba et al. 2013), TheoReTs (Rey et al. 2016a), the latest ExoMol MM line list (Yurchenko et al. 2024d), HITRAN2020 (Gordon et al. 2022), and HITEMP (Hargreaves et al. 2020). These data bases are detailed in the subsections below. It can be seen that all data bases are very similar at this temperature: the differences are mostly in the ‘transparency windows’ between the strongly absorbing polyads. Transitions in these regions are extremely weak and can be purely extrapolated or

even absent; thus, those regions should be considered with care. For example, HITRAN2020 lacks many weak lines, but they are present in HITEMP.

The situation is however very different at high temperatures. This is when the line list completeness or lack of it becomes especially evident and the choice of the line list to be used in retrievals can make a huge difference. In the right display of Fig. 1 we now compare cross-sections of methane generated for T = 1500 K. The low temperature line lists HITRAN2020 and MeCaSDa lack the essential absorption practically everywhere, with MeCaSDa being more complete at lower wavenumbers. The so-called ‘hot line’ lists of TheoReTs, ExoMol MM, and HITEMP all demonstrate a high level of completeness and generally agree with each across the entire IR region, but also show discrepancies in the near infrared (NIR). The latter are caused by the differences in the theoretical models and essentially reflect the lack of the underlying laboratory data used to constrain these models. Work on the analysis of the experimental spectra of methane in NIR is currently in progress.

### 2.1.1 Descriptions of molecular data bases

**CaSDa:** The CaSDa (Calculated Spectroscopic Data bases) data bases<fnref n="8" /> (see Richard et al. 2020, 2024) contain synthetic line lists resulting from fits of the effective Hamiltonian and dipole moment parameters using assigned experimental laboratory spectra. The models used for the calculations are based on the tensorial formalism developed in the Dijon group, as explained in Boudon et al. (2011). Currently, there are 10 CaSDa data bases for 10 different molecules, which amount to 39 isotopologues in total. A new data base, SiCaSDa, has been released very recently for three isotopologues of SiH₄ (a molecule already observed in the interstellar medium). All these data bases are listed in Table 5. For the present topic of exoplanetary spectroscopy, the most relevant ones are, of course, CH₄, C₂H₄, and GeH₄, which are present in the atmospheres of the giant planets of the Solar System. CF₄ and SiF₄ are naturally present in Earth’s atmosphere due to volcanic emissions; SiF₄ has been suggested as a possible species on Io by Schaefer & Fegley Jr. (2005) and thus may be relevant in the case of potential volcanic exoplanets; CH₃Cl is present in comets (Hardy et al. 2023) and thus could be of interest for exo-comets (Janson et al. 2023). It was also suggested and explored as a biomarker in exoplanetary atmospheres

<footnote n="3">³https://spec.jpl.nasa.gov/</footnote>

<footnote n="4">⁴https://cdms.astro.uni-koeln.de/</footnote>

<footnote n="5">⁵https://physics.nist.gov/PhysRefData/ASD/lines_form.html</footnote>

<footnote n="6">⁶https://lweb.cfa.harvard.edu/amp/ampdata/kurucz23/sekur.html; http://kurucz.harvard.edu/atoms.html</footnote>

<footnote n="7">⁷http://vald.astro.uu.se</footnote>

<footnote n="8">⁸https://vamdc.icb.cnrs.fr</footnote>
<table><caption>**Table 3.** An overview of some line list databases used by the (exo)planetary atmosphere community.</caption><thead><tr><th>Database</th><th>Type of data</th><th>Reference</th><th>Link</th></tr></thead><tbody><tr><td>CaSDa</td><td>Theoretical line lists up to high temperatures</td><td>Richard et al. (2020, 2024)</td><td>https://vamdc.icb.cnrs.fr</td></tr><tr><td>ExoMol</td><td>Theoretical line lists up to high temperatures</td><td>Tennyson et al. (2020)</td><td>https://exomol.com</td></tr><tr><td>GEISA</td><td>Accurate line lists for terrestrial conditions</td><td>Jacquinet-Husson et al. (2016); Delahaye et al. (2021)</td><td>https://geisa.aeris-data.fr</td></tr><tr><td>HITEMP</td><td>Line lists up to high temperatures</td><td>Rothman et al. (2010)</td><td>https://hitran.org/hitemp</td></tr><tr><td>HITRAN</td><td>Accurate line lists for terrestrial conditions</td><td>Gordon et al. (2022)</td><td>https://hitran.org</td></tr><tr><td>Kurucz</td><td>Semi-empirical line lists up to high temperatures</td><td>Kurucz (1995)</td><td>http://kurucz.harvard.edu/molecules.html</td></tr><tr><td>MoLLIST</td><td>Laboratory line lists up to high temperatures</td><td>Bernath (2020)</td><td>https://bernath.uwaterloo.ca/molecularlists.php</td></tr><tr><td>NASA Ames</td><td>Semi-empirical line lists up to high temperatures</td><td>e.g. Huang et al. (2023a)</td><td>http://huang.seti.org</td></tr><tr><td>NIST</td><td>Atomic line lists up to high temperatures</td><td>Kramida et al. (2013)</td><td>https://physics.nist.gov/PhysRefData/ASD/lines_form.html</td></tr><tr><td>S&amp;MPO</td><td>Spectroscopy and Molecular Properties of Ozone</td><td>Tyuterev et al. (2021)</td><td>http://smpo.iao.ru</td></tr><tr><td>TheoReTs</td><td>Theoretical line lists up to high temperatures</td><td>Rey et al. (2016b)</td><td>https://theorets.tsu.ru</td></tr><tr><td>VALD3</td><td>Atomic line lists up to high temperatures</td><td>Ryabchikova et al. (2015)</td><td>http://vald.astro.uu.se</td></tr></tbody></table>

<figure><img src="image_1.png" /><figcaption>**Figure 1.** Comparison of <sup>12</sup>CH<sub>4</sub> cross-sections at 296 K in the far and mid-infrared regions for different databases: MeCaSDa (Ba et al. 2013), TheoReTs (Rey et al. 2016b), the ExoMol MM line list (Yurchenko et al. 2024a), HITRAN2020 (Gordon et al. 2022) and HITEMP (Hargreaves et al. 2020).</figcaption></figure>

2020 release (Tennyson et al. 2020), the emphasis had been on the completeness of the data in terms of the temperature and wavelength coverage especially aimed at lower to medium resolution exoplanetary studies, usually involving transit spectroscopy. Most ExoMol line lists are accurate for resolving power $R \le 1000$ (Bowesman et al. 2024), i.e. appropriate for the Ariel and JWST missions. Higher temperatures applications with the atmospheres of hot Jupiters studied by HST instruments being a typical application meant that the line lists had an emphasis on completeness (Yurchenko et al. 2014). Since 2020, the focus of the ExoMol database has shifted to high resolution (HR) applications (ground-based HR cross-correlation applications). The ExoMol line lists are currently being upgraded to the quality of the HITRAN line lists, where the underlying high-resolution data is available. Other conceptual shifts in the ExoMol data structure are the introduction of uncertainties for the line positions to enable the data users to select the lines according with their

application needs; provision of UV photoabsorption and photodissociation cross-sections (Pezzella et al. 2022; Tennyson et al. 2023) (see Section 8); broadening due to predissociation (Tennyson et al. 2023; Yurchenko et al. 2024b).

The ExoMol line lists are written as simple ascii files using the two file structure: a States file (.states) and a Transition file (.trans). The States file provides a full description of the (rovibronic) states, including the energy (cm<sup>-1</sup>), total degeneracy, the total angular momentum, energy uncertainty (cm<sup>-1</sup>), lifetimes, g-lambda factors as well as the corresponding quantum numbers, with each entry identified by an integer number (State ID). The Transition files provide the Einstein coefficients in the following compact form: *i j A*<sub>ij</sub>, where *i* and *j* are the upper and lower state IDs, respectively. The quantum numbers in the States file, when available, correspond to the standard spectroscopic convention for a given system, but can also include alternative conventions. This is strongly dependent on how the line lists have been produced.
<table><caption>**Table 4.** An overview of the molecules, wavelength coverage, and temperature coverage for some of the major line lists available from listed data bases for the (exo)planetary atmosphere community. See the footnotes to the table for a key of data base and wavelength range. Line lists which are considered complete up to ≥1000 K are labelled with (H), and all others are generally assumed to be complete up to ~500 K. A few exceptions are noted in the text.</caption><thead><tr><th>Molecule</th><th>λ range</th><th>Data base</th></tr></thead><tbody><tr><td>AlCl</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>AlF</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>AlH</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>AlO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>AsH<sub>3</sub></td><td>IR</td><td>Ex</td></tr><tr><td>BeH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>C<sub>2</sub></td><td>IR, Vis, UV</td><td>Ex(H),Ku(H)</td></tr><tr><td>C<sub>2</sub>H<sub>2</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>C<sub>2</sub>H<sub>4</sub></td><td>IR</td><td>Ex,HI,Th,SDa</td></tr><tr><td>C<sub>2</sub>H<sub>6</sub></td><td>IR</td><td>HI</td></tr><tr><td>C<sub>2</sub>N<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>C<sub>4</sub>H<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>C<sub>3</sub></td><td>IR</td><td>Ex(H)</td></tr><tr><td>CaF</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>CaH</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>CaO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>CaOH</td><td>IR,Vis</td><td>Ex(H)</td></tr><tr><td>CF<sub>4</sub></td><td>IR</td><td>HI,SDa,Th</td></tr><tr><td>CH</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>CH<sup>+</sup></td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>CH<sub>2</sub></td><td>IR</td><td>Th(H)</td></tr><tr><td>CH<sub>3</sub></td><td>IR</td><td>Ex(H),Th(H)</td></tr><tr><td>CH<sub>3</sub>Br</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>3</sub>Cl</td><td>IR</td><td>Ex(H),HI,SDa,Th</td></tr><tr><td>CH<sub>3</sub>CN</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>3</sub>F</td><td>IR</td><td>Ex,HI,Th</td></tr><tr><td>CH<sub>3</sub>I</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>3</sub>OH</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>4</sub></td><td>IR, NIR</td><td>Ex(H),HI,HT(H),Th(H),SDa(H)</td></tr><tr><td>ClO</td><td>IR</td><td>HI</td></tr><tr><td>ClONO<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>CN</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>CO</td><td>IR</td><td>Ex(H),HI,HT(H)</td></tr><tr><td>CO<sub>2</sub></td><td>IR</td><td>Am,Ex(H),HI,HT(H)</td></tr><tr><td>COCl<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>COF<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>CP</td><td>IR</td><td>Ex(H)</td></tr><tr><td>CrH</td><td>NIR</td><td>Ex(H),Mo(H)</td></tr><tr><td>CS</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>CS<sub>2</sub></td><td>IR</td><td>Am,HI</td></tr><tr><td>FeH</td><td>NIR</td><td>Ex(H),Mo(H)</td></tr><tr><td>GeH<sub>4</sub></td><td>IR</td><td>HI,SDa,Th</td></tr><tr><td>H<sub>2</sub></td><td>IR, Vis, UV</td><td>Ex(H),HI(H)</td></tr><tr><td>H<sub>2</sub>CO</td><td>IR</td><td>Ex(H),HI,Th</td></tr><tr><td>H<sub>2</sub>CS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>H<sub>2</sub>O</td><td>IR</td><td>Ex(H),HI,HT(H)</td></tr><tr><td>H<sub>2</sub>O<sub>2</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>H<sub>2</sub>S</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>H<sub>3</sub><sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>H<sub>3</sub>O<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>HBO</td><td>IR</td><td>Ex(H)</td></tr><tr><td>HBr</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HCl</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HCN</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>HC<sub>3</sub>N</td><td>IR</td><td>HI</td></tr><tr><td>HCOOH</td><td>IR</td><td>HI</td></tr></tbody></table>

<table><caption>**Table 4 – continued**</caption><thead><tr><th>Molecule</th><th>λ range</th><th>Data base</th></tr></thead><tbody><tr><td>HDO</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>HD<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>HeH<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>HF</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HI</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HNO<sub>3</sub></td><td>IR</td><td>Ex,HI</td></tr><tr><td>HO<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>HOBr</td><td>IR</td><td>HI</td></tr><tr><td>HOCl</td><td>IR</td><td>HI</td></tr><tr><td>KCl</td><td>IR</td><td>Ex(H)</td></tr><tr><td>KF</td><td></td><td>Ex(H),Mo(H)</td></tr><tr><td>KOH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>LaO</td><td>Vis,UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>LiCl</td><td>IR</td><td>Ex(H),Mo(H)</td></tr><tr><td>LiF</td><td>IR</td><td>Ex(H),Mo(H)</td></tr><tr><td>LiH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>LiH<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>LiOH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>MgF</td><td>IR, Vis, U</td><td>Ex(H),Mo(H)</td></tr><tr><td>MgH</td><td>IR, Vis, U</td><td>Ex(H),Mo(H)</td></tr><tr><td>MgO</td><td>IR, Vis, U</td><td>Ex(H)</td></tr><tr><td>N<sub>2</sub></td><td>IR,UV</td><td>Ex(H),HI</td></tr><tr><td>N<sub>2</sub>O</td><td>IR</td><td>Am,Ex(H),HI,HT(H)</td></tr><tr><td>NaF</td><td></td><td>Ex(H),Mo(H)</td></tr><tr><td>NaH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>NaCl</td><td>IR</td><td>Ex(H)</td></tr><tr><td>NaO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>NaOH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>NF<sub>3</sub></td><td>IR</td><td>HI,Th</td></tr><tr><td>NH</td><td>IR, Vis, U</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>NH<sub>3</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>NO</td><td>IR, Vis, U</td><td>Ex(H),HI,HT(H)</td></tr><tr><td>NO<sup>+</sup></td><td>IR</td><td>HI</td></tr><tr><td>NO<sub>2</sub></td><td>IR</td><td>HI,HT(H)</td></tr><tr><td>NS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>O<sub>2</sub></td><td>IR, Vis, UV</td><td>HI</td></tr><tr><td>O<sub>3</sub></td><td>IR</td><td>HI,SM</td></tr><tr><td>OCS</td><td>IR</td><td>Am,Ex(H),HI</td></tr><tr><td>OH</td><td>IR, Vis, UV</td><td>Ex(H),HI,HT(H),Mo(H)</td></tr><tr><td>OH<sup>+</sup></td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>PH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>PH<sub>3</sub></td><td>IR</td><td>Ex(H),HI,Th(H)</td></tr><tr><td>PN</td><td>IR</td><td>Ex(H)</td></tr><tr><td>PO</td><td>IR</td><td>Ex(H)</td></tr><tr><td>PS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>S<sub>2</sub></td><td>UV</td><td>HI</td></tr><tr><td>ScH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>SF<sub>6</sub></td><td>IR</td><td>HI,SDa,Th</td></tr><tr><td>SH</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>SiF<sub>4</sub></td><td>IR</td><td>SDa</td></tr><tr><td>SiH</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H)</td></tr><tr><td>SiH<sub>2</sub></td><td>IR</td><td>Ex(H)</td></tr><tr><td>SiH<sub>4</sub></td><td>IR</td><td>Ex(H),Th,SDa</td></tr><tr><td>SiO</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H)</td></tr><tr><td>SiO<sub>2</sub></td><td>IR</td><td>Ex(H)</td></tr><tr><td>SiH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>SiS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>SO</td><td>IR, Vis, UV</td><td>Ex(H),HI</td></tr><tr><td>SO<sub>2</sub></td><td>IR</td><td>Am,Ex(H),HI</td></tr><tr><td>SO<sub>3</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>TiH</td><td>Vis</td><td>Ex(H),Mo(H)</td></tr><tr><td>TiO</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H),Ku(H)</td></tr></tbody></table>
<table><caption>**Table 4.** An overview of the molecules, wavelength coverage, and temperature coverage for some of the major line lists available from listed databases for the (exo)planetary atmosphere community. See the footnotes to the table for a key of database and wavelength range. Line lists which are considered complete up to ≥ 1000 K are labelled with (H), and all others are generally assumed to be complete up to ~ 500 K. A few exceptions are noted in the text.</caption><thead><tr><th>Molecule</th><th>λ range</th><th>Database</th></tr></thead><tbody><tr><td>AlCl</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>AlF</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>AlH</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>AlO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>AsH<sub>3</sub></td><td>IR</td><td>Ex</td></tr><tr><td>BeH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>C<sub>2</sub></td><td>IR, Vis, UV</td><td>Ex(H),Ku(H)</td></tr><tr><td>C<sub>2</sub>H<sub>2</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>C<sub>2</sub>H<sub>4</sub></td><td>IR</td><td>Ex,HI,Th, SDa</td></tr><tr><td>C<sub>2</sub>H<sub>6</sub></td><td>IR</td><td>HI</td></tr><tr><td>C<sub>2</sub>N<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>C<sub>4</sub>H<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>C<sub>3</sub></td><td>IR</td><td>Ex(H)</td></tr><tr><td>CaF</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>CaH</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>CaO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>CaOH</td><td>IR,Vis</td><td>Ex(H)</td></tr><tr><td>CF<sub>4</sub></td><td>IR</td><td>HI,SDa,Th</td></tr><tr><td>CH</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>CH<sup>+</sup></td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>CH<sub>2</sub></td><td>IR</td><td>Th(H)</td></tr><tr><td>CH<sub>3</sub></td><td>IR</td><td>Ex(H),Th(H)</td></tr><tr><td>CH<sub>3</sub>Br</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>3</sub>Cl</td><td>IR</td><td>Ex(H),HI,SDa,Th</td></tr><tr><td>CH<sub>3</sub>CN</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>3</sub>F</td><td>IR</td><td>Ex,HI,Th</td></tr><tr><td>CH<sub>3</sub>I</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>3</sub>OH</td><td>IR</td><td>HI</td></tr><tr><td>CH<sub>4</sub></td><td>IR, NIR</td><td>Ex(H),HI,HT(H),Th(H),SDa(H)</td></tr><tr><td>ClO</td><td>IR</td><td>HI</td></tr><tr><td>ClONO<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>CN</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>CO</td><td>IR</td><td>Ex(H),HI,HT(H)</td></tr><tr><td>CO<sub>2</sub></td><td>IR</td><td>Am,Ex(H),HI,HT(H)</td></tr><tr><td>COCl<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>COF<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>CP</td><td>IR</td><td>Ex(H)</td></tr><tr><td>CrH</td><td>NIR</td><td>Ex(H),Mo(H)</td></tr><tr><td>CS</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>CS<sub>2</sub></td><td>IR</td><td>Am,HI</td></tr><tr><td>FeH</td><td>NIR</td><td>Ex(H),Mo(H)</td></tr><tr><td>GeH<sub>4</sub></td><td>IR</td><td>HI,SDa,Th</td></tr><tr><td>H<sub>2</sub></td><td>IR, Vis, UV</td><td>Ex(H),HI(H)</td></tr><tr><td>H<sub>2</sub>CO</td><td>IR</td><td>Ex(H),HI,Th</td></tr><tr><td>H<sub>2</sub>CS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>H<sub>2</sub>O</td><td>IR</td><td>Ex(H),HI,HT(H)</td></tr><tr><td>H<sub>2</sub>O<sub>2</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>H<sub>2</sub>S</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>H<sub>3</sub><sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>H<sub>3</sub>O<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>HBr</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HCl</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HCN</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>HC<sub>3</sub>N</td><td>IR</td><td>HI</td></tr><tr><td>HCOOH</td><td>IR</td><td>HI</td></tr><tr><td>HDO</td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>HD<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>HeH<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>HF</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HI</td><td>IR</td><td>Ex(H),HI(H)</td></tr><tr><td>HNO<sub>3</sub></td><td>IR</td><td>Ex,HI</td></tr></tbody></table>

<table><thead><tr><th>Molecule</th><th>λ range</th><th>Database</th></tr></thead><tbody><tr><td>HO<sub>2</sub></td><td>IR</td><td>HI</td></tr><tr><td>HOBr</td><td>IR</td><td>HI</td></tr><tr><td>HOCl</td><td>IR</td><td>HI</td></tr><tr><td>KCl</td><td>IR</td><td>Ex(H)</td></tr><tr><td>KF</td><td>IR</td><td>Ex(H),Mo(H)</td></tr><tr><td>KOH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>LaO</td><td>Vis,UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>LiCl</td><td>IR</td><td>Ex(H),Mo(H)</td></tr><tr><td>LiF</td><td>IR</td><td>Ex(H),Mo(H)</td></tr><tr><td>LiH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>LiH<sup>+</sup></td><td>IR</td><td>Ex(H)</td></tr><tr><td>LiOH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>MgF</td><td>IR, Vis, U</td><td>Ex(H),Mo(H)</td></tr><tr><td>MgH</td><td>IR, Vis, U</td><td>Ex(H),Mo(H)</td></tr><tr><td>MgO</td><td>IR, Vis, U</td><td>Ex(H)</td></tr><tr><td>N<sub>2</sub></td><td>IR,UV</td><td>Ex(H),HI</td></tr><tr><td>N<sub>2</sub>O</td><td>IR</td><td>Am,Ex(H),HI,HT(H)</td></tr><tr><td>NaF</td><td>IR</td><td>Ex(H),Mo(H)</td></tr><tr><td>NaH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>NaCl</td><td>IR</td><td>Ex(H)</td></tr><tr><td>NaO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>NaOH</td><td>IR</td><td>Ex(H)</td></tr><tr><td>NF<sub>3</sub></td><td>IR</td><td>HI,Th</td></tr><tr><td>NH</td><td>IR, Vis, U</td><td>Ex(H),Ku(H),Mo(H)</td></tr><tr><td>NH<sub>3</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>NO</td><td>IR, Vis, U</td><td>Ex(H),HI,HT(H)</td></tr><tr><td>NO<sup>+</sup></td><td>IR</td><td>HI</td></tr><tr><td>NO<sub>2</sub></td><td>IR</td><td>HI,HT(H)</td></tr><tr><td>NS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>O<sub>2</sub></td><td>IR, Vis, UV</td><td>HI</td></tr><tr><td>O<sub>3</sub></td><td>IR</td><td>HI,SM</td></tr><tr><td>OCS</td><td>IR</td><td>Am,Ex(H),HI</td></tr><tr><td>OH</td><td>IR, Vis, UV</td><td>Ex(H),HI,HT(H),Mo(H)</td></tr><tr><td>OH<sup>+</sup></td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>PH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>PH<sub>3</sub></td><td>IR</td><td>Ex(H),HI,Th(H)</td></tr><tr><td>PN</td><td>IR</td><td>Ex(H)</td></tr><tr><td>PO</td><td>IR</td><td>Ex(H)</td></tr><tr><td>PS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>S<sub>2</sub></td><td>UV</td><td>HI</td></tr><tr><td>ScH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>SF<sub>6</sub></td><td>IR</td><td>HI,SDa,Th</td></tr><tr><td>SH</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H)</td></tr><tr><td>SiF<sub>4</sub></td><td>IR</td><td>SDa</td></tr><tr><td>SiH</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H)</td></tr><tr><td>SiH<sub>2</sub></td><td>IR</td><td>Ex(H)</td></tr><tr><td>SiH<sub>4</sub></td><td>IR</td><td>Ex(H),Th,SDa</td></tr><tr><td>SiO</td><td>IR, Vis, UV</td><td>Ex(H),Ku(H)</td></tr><tr><td>SiO<sub>2</sub></td><td>IR</td><td>Ex(H)</td></tr><tr><td>SiH</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>SiS</td><td>IR</td><td>Ex(H)</td></tr><tr><td>SO</td><td>IR, Vis, UV</td><td>Ex(H),HI</td></tr><tr><td>SO<sub>2</sub></td><td>IR</td><td>Am,Ex(H),HI</td></tr><tr><td>SO<sub>3</sub></td><td>IR</td><td>Ex(H),HI</td></tr><tr><td>TiH</td><td>Vis</td><td>Ex(H),Mo(H)</td></tr><tr><td>TiO</td><td>IR, Vis, UV</td><td>Ex(H),Mo(H),Ku(H)</td></tr><tr><td>VO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>YO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>ZnO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>ZrO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr></tbody></table>

Databases: Am=NASA Ames; Ex=ExoMol; HI=HITRAN; HT=HITEMP; Mo=MoLIST; Ku=Kurucz; SDa=TFSiCaSDa, MeCaSDa, TFMeCaSDa, GeCaSDa, SiCaSDa, ECaSDa; SM=S&MPO; Th=TheoReTS; see Table 3.

λ ranges: UV = 0.1 - 0.4 µm; Vis = 0.4 - 0.8 µm; IR ≥ 0.8 µm.
<table><caption>**Table 4** – continued</caption><thead><tr><th>Molecule</th><th>λ range</th><th>Data base</th></tr></thead><tbody><tr><td>VO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>YO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>ZnO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr><tr><td>ZrO</td><td>IR, Vis, UV</td><td>Ex(H)</td></tr></tbody></table>

*Notes.* Data bases: Am=NASA Ames; Ex=ExoMol; HI=HITRAN; HT=HITEMP; Mo=MoLLIST; Ku=Kurucz; SDa=TFSiCaSDa, MeCaSDa, TFMeCaSDa, GeCaSDa, SiCaSDa, ECaSDa; SM=S&MPO; Th=TheoReTS; see Table 3.

λ ranges: UV = 0.1–0.4 µm; Vis = 0.4–0.8 µm; IR ≥ 0.8 µm.

(Seager, Bains & Hu 2013). In the near future, the intent is for new data (new bands and new isotopologues, like for instance CH₃D in MeCaSDa) to be added to these data bases (Richard et al. 2024), and for further ones to be developed, especially for some molecules of astrophysical interest, like C₃H₆O₃ [trioxane that may be relevant for comets, see Richard, Asselin & Boudon (2022)].

These data bases contain calculated line lists for all spectral regions of these molecules that could be assigned in experimental laboratory spectra and fitted line-by-line using effective Hamiltonians and dipole moments. The data bases contain extra information, such as energy levels with all quantum numbers and eigenvectors. When available, different isotopologues data are included in each data base. The given accuracy of line positions and intensities is equal to the standard deviation of the fit; extrapolation is limited to only a few rotational quantum number values outside the existing assignment range. The data output is in the 160-character HITRAN2004 format (Rothman et al. 2005). CaSDa use some specific notations for line assignments in the case of CH₃Cl and C₂H₄ since they are based on use of a tensorial formalism similar to that of CH₄. It is also possible to compute absorption cross-sections.

**ExoMol**<fnref n="9" /> is a provider of the molecular and since 2023 also atomic data necessary for modelling spectroscopy of exoplanets (Tennyson et al. 2024b). The main data products are line lists, with the emphasis on the molecules important for exoplanetary and stellar atmospheres, but also for spectroscopy of planets, comets as well as industrial applications (see Tennyson & Yurchenko 2021). As of today, the ExoMol data base contains line lists for 92 molecules and 245 isotopologues, see Table 6 for the current snapshot of the molecular line lists available in ExoMol. Up to the ExoMol 2020 release (Tennyson et al. 2020), the emphasis had been on the completeness of the data in terms of the temperature and wavelength coverage especially aimed at lower to medium resolution exoplanetary studies, usually involving transit spectroscopy, see Table 4. ExoMol line lists are generally constructed to be accurate for resolving power *R* ≤ 10 000 (Tennyson et al. 2024b), i.e. appropriate for the *Ariel* and *JWST* missions. Higher temperatures applications with the atmospheres of hot Jupiters studied by *HST* instruments being a typical application meant that the line lists had an emphasis on completeness (Yurchenko et al. 2014). Since 2020, the focus of the ExoMol data base has shifted to high resolution (HR) applications, i.e. ground-based HR cross-correlation applications. The ExoMol line lists are currently being upgraded to the quality of the HITRAN line lists, where the underlying high-resolution data are available. Other conceptual shifts in the ExoMol data structure are the introduction of uncertainties for the line positions to enable the data users to select the lines according with their application needs; provision of UV photoab-

sorption and photodissociation cross-sections (Pezzella, Tennyson & Yurchenko 2022; Tennyson et al. 2023) (see Section 8); broadening due to pre-dissociation (Tennyson et al. 2023; Yurchenko et al. 2024c).

The ExoMol line lists are written as bzip2-compressed ascii files using the two file structure: a States file (.states) and a Transition file (.trans). The States file provides a full description of the (rovibronic) states, including the energy (cm⁻¹), total degeneracy, the total angular momentum, energy uncertainty (cm⁻¹), lifetimes, Lande g factors as well as the corresponding quantum numbers, with each entry identified by an integer number (State ID). The Transition files provide the Einstein coefficients in the following compact form: *i j A*<sub>*ij*</sub>, where *i* and *j* are the upper and lower state IDs, respectively, and *A*<sub>*ij*</sub> is a corresponding Einstein A coefficient (s⁻¹). The quantum numbers in the States file, when available, correspond to the standard spectroscopic convention for a given system, but can also include alternative conventions. This is strongly dependent on how the line lists have been produced.

As part of the ExoMol services, a number of useful tools are provided, including an online cross-sections app, some efficient programs ExoCross and PyExoCross to turn huge line lists into compact temperature and pressure-dependent cross-sections (Yurchenko, Al-Refaie & Tennyson 2018d; Zhang, Tennyson & Yurchenko 2024), molecular radiative lifetimes (Owens et al. 2023), molecular specific heats (Wang et al. 2023a), and molecular opacities in four different formats appropriate for a variety of atmospheric retrieval codes (Chubb et al. 2020b); details of the ExoMolOP opacity data base are given in Section 4. A detailed Atlas of molecular spectra computed using the ExoMol line lists can be found in Tennyson & Yurchenko (2018), see Fig. 2 as an example, where the ExoAmes (Underwood et al. 2016a) cross-sections of SO₂ are shown.

The majority of the line lists in the ExoMol data base have been produced by the ExoMol group using a combination of quantum mechanical calculations based on high-level spectroscopic models (i.e. potential energy surfaces, spin-orbit and other coupling etc.), tuned by fitting to the experimental data and the so-called post-production MARVELisation (Furtenbacher, Császár & Tennyson 2007), where some of the computed energies are replaced by experimental values (see Section 2.1.4). Apart from these ExoMol line lists (covering some 70 molecules), the ExoMol data base also hosts line lists from other data providers, including a large number of diatomics (Wang, Tennyson & Yurchenko 2020a) from the MoLLIST (Molecular Line Lists, Intensities, and Spectra) project (Bernath 2020), some of the high-temperature species from HITRAN (HF, HCl, HBr) (Li et al. 2013), and CO from Li et al. (2015). The HITEMP line list for NO (Hargreaves et al. 2019) is based on the ExoMol NOname line list (Wong et al. 2017), combined with other data.

**HITRAN and HITEMP:** The HITRAN molecular spectroscopic data base has been a go-to source of molecular data for 50 yr (Rothman 2021). HITRAN, an acronym of high-resolution transmission, was primarily established to model the radiative transfer through the Earth's atmosphere and consequently included line-by-line parameters to model the dominant terrestrial absorbers. Over the years, as observations, experiments, and analytical techniques have improved, the HITRAN data base has been regularly updated and expanded to accommodate state-of-the-art molecular parameters from the microwave through to the near UV spectral range. Papers describing quadrennial editions of the data base typically receive thousands of citations. HITRAN2020 (Gordon et al. 2022) – the most recent edition of the data base – features a compilation of line-by-line parameters, both experimentally derived and calculated,

<footnote n="9">⁹www.exomol.com</footnote>
<table><caption>**Table 5.** Calculated molecular absorption lines in the CaSDa databases.</caption><thead><tr><th>HITRAN ID</th><th>Molecule</th><th>DB name</th><th>Isotopologues</th><th>Total nb. of lines</th><th>Relevant for Ariel</th></tr></thead><tbody><tr><td>06</td><td>CH<sub>4</sub></td><td>MeCaSDa</td><td>3</td><td>12,988,898</td><td>*</td></tr><tr><td>24</td><td>CH<sub>3</sub>Cl</td><td>ChMeCaSDa</td><td>2</td><td>12,152</td><td></td></tr><tr><td>30</td><td>SF<sub>6</sub></td><td>SHeCaSDa</td><td>4</td><td>491,500</td><td></td></tr><tr><td>38</td><td>C<sub>2</sub>H<sub>4</sub></td><td>ECaSDa</td><td>1</td><td>96,397</td><td>*</td></tr><tr><td>42</td><td>CF<sub>4</sub></td><td>TFMeCaSDa</td><td>1</td><td>258,208</td><td>*</td></tr><tr><td>52</td><td>GeH<sub>4</sub></td><td>GeCaSDa</td><td>5</td><td>60,878</td><td>*</td></tr><tr><td>-</td><td>RuO<sub>4</sub></td><td>RuCaSDa</td><td>9</td><td>30,205</td><td></td></tr><tr><td>-</td><td>SiF<sub>4</sub></td><td>TFSiCaSDa</td><td>3</td><td>210,401</td><td>*</td></tr><tr><td>-</td><td>UF<sub>6</sub></td><td>UHeCaSDa</td><td>8</td><td>110,129</td><td></td></tr><tr><td>-</td><td>SiH<sub>4</sub></td><td>SiCaSDa</td><td>3</td><td>20,090</td><td>*</td></tr></tbody></table>

As part of the ExoMol services, a number of useful tools are provided, including an online cross-sections app, some efficient programs ExoCross and PyExoCross to turn huge line lists into compact temperature and pressure dependent cross-sections (Yurchenko et al. 2018; Zhang et al. 2024), molecular radiative lifetimes (Owens et al. 2023), molecular specific heats (Wang et al. 2023b) and molecular opacities for at least four atmospheric retrieval codes (Chubb et al. 2021); details of the ExoMolOP opacity database are given in Section 4. A detailed Atlas of molecular spectra computed using the ExoMol line lists can be found in Tennyson & Yurchenko (2018), see Fig. 2 as an example, where the ExoAmes (Underwood et al. 2016) cross-sections of SO₂ are shown.

The majority of the line lists in the ExoMol database have been produced by the ExoMol group using a combination of quantum mechanical calculations based on high-level spectroscopic models (i.e. potential energy surfaces, spin-orbit and other coupling etc.), tuned by fitting to the experimental data and the so-called post-production MARVELisation (Furtenbacher et al. 2007), where some of the computed energies are replaced by experimental values (see Section 2.1.4). Apart from these ExoMol line lists (covering some 70 molecules), the ExoMol database also hosts line lists from other data providers, including a large number of diatomics (Wang et al. 2020b) from the MoLLiST (Molecular Line Lists, Intensities and Spectra) project (Bernath 2020), some of the high-temperature species from HITRAN (HF, HCl, HBr) (Li et al. 2013), and CO from Li et al. (2015). The HITEMP line list for NO (Hargreaves et al. 2019) is based on the ExoMol NOname line list (Wong et al. 2017), combined with other data.

### 2.1.1.3 HITRAN and HITEMP
The HITRAN molecular spectroscopic database has been a go-to source of molecular data for 50 years (Rothman 2021). HITRAN, an acronym of high-resolution transmission, was primarily established to model the radiative transfer through the Earth's atmosphere and consequently included line-by-line parameters to model the dominant terrestrial absorbers. Over the years, as observations, experiments, and analytical techniques have improved, the HITRAN database has been regularly updated and expanded to accommodate state-of-the-art molecular parameters from the microwave through to the near UV spectral range. Papers describing quadrennial editions of the database typically receive thousands of citations. HITRAN2020 (Gordon et al. 2022) – the most recent edition of the database – features a compilation of line-by-line parameters, both experimentally-derived and calculated, for 55 molecules and

is freely available from HITRANonline<fnref n="11" />. Table 1 of Gordon et al. (2022) provides a summary of the spectral coverage and the number of lines included in HITRAN for each isotopologue of every molecule. Each transition in HITRAN includes the line position, intensity, lower-state energy, line shape parameters, and assignment information that are necessary for calculating the absorption of a transition at a given temperature and concentration. HITRAN line-by-line parameters are provided at a reference temperature of 296 K with intensities that account for the typical natural abundance on Earth. Alongside Voigt line shape parameters for air- and self-broadening (i.e., the broadening due to the terrestrial atmosphere and pure gas, respectively), recent editions of HITRAN have also accommodated parameters for high-level line shapes and broadening parameters that are applicable to planetary atmospheres other than Earth. This includes atmospheres dominated by H₂/He, CO₂ (Wilzewski et al. 2016; Tan et al. 2022), and H₂O (Tan et al. 2019). A summary of the additional broadening available via the HITRAN database is provided in Table 6.

In addition to line-by-line parameters, HITRAN also provides experimental absorption cross-sections for over 300 molecules for which no reliable quantum mechanical models exist (Kochanov et al. 2019) (see Section 2.1.3.1), collision-induced absorption data for a variety of collisional complexes (Karman et al. 2019) (see Section 5), aerosol properties (see Section 6), and water vapor continuum data (Mlawer et al. 2012) (see Section 5). HITRAN also provides auxiliary data necessary for carrying out calculations of spectra at different thermodynamic conditions, including Total Internal Partition Sums (Gamache et al. 2017; Gamache et al. 2021). The HITRAN Application Programming Interface, HAPI (Kochanov et al. 2016), allows one to efficiently download HITRAN data and carry out calculations of spectral absorption, emission, and transmission. HITRAN provides line lists for a small number of species which are considered complete up to high temperatures of around 4000–5000 K: HF, HCl, HBr, HI, and H₂ (Li et al. 2013).

HITEMP (Rothman et al. 2010) is in principle updated alongside the HITRAN database and is specifically aimed at modelling high-temperature (≥ 1000 K) environments where HITRAN data cannot be reliably applied. This includes the atmospheres of stars, brown dwarfs, and planets at elevated temperatures, such as hot Jupiters, hot super-Earths, or Venus. At the moment HITEMP provides line lists for eight molecules (H₂O, CO₂, N₂O, CO, CH₄, NO, NO₂, OH)

<footnote n="11">¹¹ www.hitran.org</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Comparison of $^{12}$CH$_4$ cross-sections at 296 K (left) and 1500 K (right) in the far and mid-infrared regions for different data bases: MeCaSDa (Richard et al. 2020), TheoReTs (Rey et al. 2016a), the ExoMol MM line list (Yurchenko et al. 2024d), HITRAN2020 (Gordon et al. 2022), and HITEMP (Hargreaves et al. 2020).</figcaption></figure>

<table><caption>**Table 5.** Calculated molecular absorption lines in the CaSDa data bases.</caption><thead><tr><th>HITRAN ID</th><th>Molecule</th><th>DB name</th><th>Isotopologues</th><th>Total nb. of lines</th><th>Relevant for <i>Ariel</i></th></tr></thead><tbody><tr><td>06</td><td>CH<sub>4</sub></td><td>MeCaSDa</td><td>3</td><td>12 988 898</td><td>*</td></tr><tr><td>24</td><td>CH<sub>3</sub>Cl</td><td>ChMeCaSDa</td><td>2</td><td>12 152</td><td></td></tr><tr><td>30</td><td>SF<sub>6</sub></td><td>SHeCaSDa</td><td>4</td><td>491 500</td><td></td></tr><tr><td>38</td><td>C<sub>2</sub>H<sub>4</sub></td><td>ECaSDa</td><td>1</td><td>96 397</td><td>*</td></tr><tr><td>42</td><td>CF<sub>4</sub></td><td>TFMeCaSDa</td><td>1</td><td>258 208</td><td>*</td></tr><tr><td>52</td><td>GeH<sub>4</sub></td><td>GeCaSDa</td><td>5</td><td>60 878</td><td>*</td></tr><tr><td>-</td><td>RuO<sub>4</sub></td><td>RuCaSDa</td><td>9</td><td>30 205</td><td></td></tr><tr><td>-</td><td>SiF<sub>4</sub></td><td>TFSiCaSDa</td><td>3</td><td>210 401</td><td>*</td></tr><tr><td>-</td><td>UF<sub>6</sub></td><td>UHeCaSDa</td><td>8</td><td>110 129</td><td></td></tr><tr><td>-</td><td>SiH<sub>4</sub></td><td>SiCaSDa</td><td>3</td><td>20 090</td><td>*</td></tr></tbody></table>

for 55 molecules and is freely available from HITRANonline.<fnref n="10" /> table 1 of Gordon et al. (2022) provides a summary of the spectral coverage and the number of lines included in HITRAN for each isotopologue of every molecule. Each transition in HITRAN includes the line position, intensity, lower state energy, line shape parameters, and assignment information that are necessary for calculating the absorption of a transition at a given temperature and concentration. HITRAN line-by-line parameters are provided at a reference temperature of 296 K with intensities that account for the typical natural abundance on Earth. Alongside Voigt line shape parameters for air- and self-broadening (i.e. the broadening due to the terrestrial atmosphere and pure gas, respectively), recent editions of HITRAN have also accommodated parameters for high-level line shapes and broadening parameters that are applicable to planetary atmospheres other than Earth. This includes atmospheres dominated by H₂/He, CO₂ (Wilzewski et al. 2016; Tan et al. 2022), and H₂O (Tan et al. 2019). A summary of the additional broadening available via the HITRAN data base is provided in Table 7.

In addition to line-by-line parameters, HITRAN also provides experimental absorption cross-sections for over 300 molecules for which no reliable quantum mechanical models exist (Kochanov et al. 2019) (see section 2.1.3.1), collision-induced absorption data for a variety of collisional complexes (Karman et al. 2019) (see Section 5), aerosol properties (see Section 6), and water vapour continuum data (Mlawer et al. 2012) (see Section 5). HITRAN also provides

auxiliary data necessary for carrying out calculations of spectra at different thermodynamic conditions, including total internal partition sums (Gamache et al. 2017, 2021). The HITRAN Application Programming Interface, HAPI (Kochanov et al. 2016), allows one to efficiently download HITRAN data and carry out calculations of spectral absorption, emission, and transmission. HITRAN provides line lists for a small number of species which are considered complete up to high temperatures of around 4000–5000 K: HF, HCl, HBr, HI, and H₂ (Li et al. 2013).

HITEMP (Rothman et al. 2010) is in principle updated alongside the HITRAN data base and is specifically aimed at modelling high-temperature (≥1000 K) environments where HITRAN data cannot be reliably applied. This includes the atmospheres of stars, brown dwarfs, and planets at elevated temperatures, such as hot Jupiters, hot super-Earths, or Venus. At the moment HITEMP provides line lists for eight molecules (H₂O, CO₂, N₂O, CO, CH₄, NO, NO₂, OH) and is consistent with HITRAN where possible, but typically includes a substantial proportion of calculated ab initio or semi-empirical parameters. These additional lines account for hot bands, and other transitions that are negligible (i.e. extremely weak) at terrestrial temperatures and therefore not included in the HITRAN line list. While the number of lines required for each molecule can reach billions, one goal of HITEMP has been to remain practical to use in line-by-line radiative transfer calculations. Therefore, the underlying ab initio line lists are analysed and filtered to reduce the number of lines necessary for each molecule, as demonstrated for the addition of CH₄ (Hargreaves et al. 2020) to HITEMP.

<footnote n="10">¹⁰www.hitran.org</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 2.** ExoMol Spectral Atlas (Tennyson & Yurchenko 2018): Cross-sections of SO₂ computed with the ExoMol line ExoAmes (Underwood et al. 2016).</figcaption></figure>

<table><caption>**Table 6.** Reference sources for Voigt line broadening parameters available in HITRAN, in addition to air- and self-broadening which are provided for every line. W16 refers to Wilzewski et al. (2016), T19 to Tan et al. (2019), T22 to Tan et al. (2022), D18 to Dudaryonok & Lavrentieva (2018), L20 to Lavrentieva & Dudaryonok (2020), and self refers to self-broadening parameters (see Gordon et al. 2022).</caption><thead><tr><th rowspan="2">HITRAN ID</th><th rowspan="2">Molecule</th><th colspan="4">Broadening Parameters</th></tr><tr><th>H<sub>2</sub></th><th>He</th><th>H<sub>2</sub>O</th><th>CO<sub>2</sub></th></tr></thead><tbody><tr><td>1</td><td>H<sub>2</sub>O</td><td>—</td><td>—</td><td>Self</td><td>—</td></tr><tr><td>2</td><td>CO<sub>2</sub></td><td>T22</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>4</td><td>N<sub>2</sub>O</td><td>—</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>5</td><td>CO</td><td>T22</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>6</td><td>CH<sub>4</sub></td><td>—</td><td>—</td><td>T19</td><td>—</td></tr><tr><td>7</td><td>O<sub>2</sub></td><td>—</td><td>—</td><td>T19</td><td>—</td></tr><tr><td>9</td><td>SO<sub>2</sub></td><td>W16</td><td>W16</td><td>—</td><td>D18</td></tr><tr><td>11</td><td>NH<sub>3</sub></td><td>W16</td><td>W16</td><td>T19</td><td>W16</td></tr><tr><td>13</td><td>OH</td><td>T22</td><td>T22</td><td>—</td><td>—</td></tr><tr><td>14</td><td>HF</td><td>W16</td><td>W16</td><td>—</td><td>W16</td></tr><tr><td>15</td><td>HCl</td><td>W16</td><td>W16</td><td>—</td><td>W16</td></tr><tr><td>19</td><td>OCS</td><td>T22</td><td>T22</td><td>—</td><td>L20</td></tr><tr><td>20</td><td>H<sub>2</sub>CO</td><td>T22</td><td>T22</td><td>—</td><td>T22</td></tr><tr><td>23</td><td>HCN</td><td>T22</td><td>T22</td><td>—</td><td>—</td></tr><tr><td>26</td><td>C<sub>2</sub>H<sub>2</sub></td><td>W16</td><td>W16</td><td>—</td><td>W16</td></tr><tr><td>28</td><td>PH<sub>3</sub></td><td>T22</td><td>T22</td><td>—</td><td>—</td></tr><tr><td>31</td><td>H<sub>2</sub>S</td><td>T22</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>45</td><td>H<sub>2</sub></td><td>Self</td><td>—</td><td>—</td><td>—</td></tr><tr><td>52</td><td>GeH<sub>4</sub></td><td>T22</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

and is consistent with HITRAN where possible, but typically includes a substantial proportion of calculated *ab initio* or semi-empirical parameters. These additional lines account for hot bands, and other transitions that are negligible (i.e., extremely weak) at terrestrial temperatures and therefore not included in the HITRAN line list. While the number of lines required for each molecule can reach billions, one goal of HITEMP has been to remain practical to use in line-by-line radiative transfer calculations. Therefore, the underlying *ab initio* line lists are analyzed and filtered to reduce the number of lines necessary for each molecule, as demonstrated for the addition of CH₄ (Hargreaves et al. 2020) to HITEMP.

In summary, HITRAN and HITEMP both provide essential input parameters for many radiative transfer codes. These data are used for a variety of applications, including the modelling of exoplanet atmospheres at high-resolution.

#### 2.1.1.4 NASA Ames database
The database from NASA Ames uses the “Best Theory + Reliable High-Resolution Experiment (BTRHE)” strategy (Huang et al. 2021) to provide accurate and complete line lists for species such as SO₂ (5 isotopologues up to 500 K) (Huang et al. 2015, 2016), CO₂ (up to 3000 K) (Huang et al. 2023a), NH₃ (Huang et al. 2022b), N₂O (Huang et al. 2023b), OCS, CS₂ and their isotopologues. The most recent NASA Ames releases include hot line lists for the four most abundant isotopologues of CO₂ (¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O, and ¹⁶O¹²C¹⁷O) (Huang et al. 2022a) and extensive room temperature line lists for N₂O with its 12 isotopologues (Huang et al. 2023b). The ExoMol SO₂ line list (Underwood et al. 2016) was also produced jointly with NASA Ames. Some of the earlier NASA Ames line lists were formatted using the HITRAN-like line-by-line ascii format, while the more recent line lists are provided in the ExoMol-like format with two parts, states and transitions. Although these are ascii files, for transitions (Einstein coefficients and states IDs), NASA Ames uses a simple compacting scheme based on representing real numbers as integers. The line lists can be accessed online<fnref n="12" />.

#### 2.1.1.5 TheoReTS
Precise knowledge of high-energy molecular states and intensities of rovibrational transitions is essential for the modelling of various planetary atmospheres as well as for the understanding of spectral properties, even in extreme dynamical and temperature conditions. This clearly demonstrates the need of having consistent line-by-line spectroscopic databases, with a large coverage in terms of both wavelengths and temperatures. Because of their completeness, variational calculations are well designed for the modelling of planetary atmospheres, unlike traditional spectroscopic effective models for which wavenumber extrapolation beyond the range of observed data turns out very limited. Within that context, the TheoReTS (Theoretical Reims-Tomsk Spectral data) project (Rey et al. 2016b) – whose philosophy closely follows that of ExoMol (Tennyson et al. 2020) – was born in 2016¹³. For the construction of accurate variationally-computed molecular line lists allowing a

<footnote n="12">¹² https://huang.seti.org/ and https://data.nas.nasa.gov/ai3000k</footnote>

<footnote n="13">¹³ https://theorets.tsu.ru/ and https://theorets.univ-reims.fr/</footnote>
<table><caption>**Table 6.** An overview of the line lists provided by ExoMol, www.exomol.com</caption><thead><tr><th>Molecule</th><th>Reference</th><th>Molecule</th><th>Reference</th><th>Molecule</th><th>Reference</th></tr></thead><tbody><tr><td>AlCl</td><td>Yurchenko et al. (2023)</td><td>H<sub>2</sub>CS</td><td>Mellor et al. (2022)</td><td>NH<sub>3</sub></td><td>Coles, Yurchenko &amp; Tennyson (2019b)</td></tr><tr><td>AlF</td><td>Yousefi &amp; Bernath (2018)</td><td>H<sub>3</sub><sup>+</sup></td><td>Bowesman et al. (2023)</td><td><sup>15</sup>NH<sub>3</sub></td><td>Yurchenko et al. (2024e)</td></tr><tr><td>AlH</td><td>Yurchenko et al. (2024c)</td><td>H<sub>3</sub>O<sup>+</sup></td><td>Yurchenko et al. (2020b)</td><td>NO</td><td>Wong et al. (2017)</td></tr><tr><td>AlO</td><td>Patrascu, Tennyson &amp; Yurchenko (2015)</td><td>HBO</td><td>Li, Qin &amp; Liu (2024)</td><td>NO</td><td>Qu, Yurchenko &amp; Tennyson (2021)</td></tr><tr><td>AsH<sub>3</sub></td><td>Coles et al. (2019a)</td><td>HBr</td><td>Coxon &amp; Hajigeorgiou (2015)</td><td>NS</td><td>Yurchenko et al. (2018b)</td></tr><tr><td>BeH</td><td>Darby-Lewis et al. (2018)</td><td>HCCH</td><td>Chubb, Tennyson &amp; Yurchenko (2020a)</td><td>OCS</td><td>Owens et al. (2024b)</td></tr><tr><td>C<sub>2</sub></td><td>Yurchenko et al. (2018c)</td><td>HCl</td><td>Li et al. (2013)</td><td>OH</td><td>Brooke et al. (2016)</td></tr><tr><td>C<sub>2</sub></td><td>Brooke et al. (2013)</td><td>HCN/HNC</td><td>Barber et al. (2014)</td><td>OH<sup>+</sup></td><td>Hodges, Bittner &amp; Bernath (2018)</td></tr><tr><td>C<sub>2</sub>H<sub>4</sub></td><td>Mant et al. (2018)</td><td>HD</td><td>Amaral et al. (2019)</td><td>P<sub>2</sub>H<sub>2</sub></td><td>Owens &amp; Yurchenko (2019)</td></tr><tr><td>C<sub>3</sub></td><td>Lynas-Gray et al. (2024)</td><td>HD<sup>+</sup></td><td>Amaral et al. (2019)</td><td>PF<sub>3</sub></td><td>Mant et al. (2019)</td></tr><tr><td>CaF</td><td>Hou &amp; Bernath (2018)</td><td>HDO</td><td>Mizus et al. (in preparation)</td><td>PH</td><td>Langleben, Yurchenko &amp; Tennyson (2019)</td></tr><tr><td>CaH</td><td>Yadin et al. (2012)</td><td>HeH<sup>+</sup></td><td>Amaral et al. (2019)</td><td>PH<sub>3</sub></td><td>Sousa-Silva et al. (2015)</td></tr><tr><td>CaH</td><td>Owens et al. (2022a)</td><td>HF</td><td>Coxon &amp; Hajigeorgiou (2015)</td><td>PN</td><td>Semenov et al. (in preparation)</td></tr><tr><td>CaO</td><td>Yurchenko et al. (2016)</td><td>HNO<sub>3</sub></td><td>Pavlyuchko et al. (2015)</td><td>PO</td><td>Prajapat et al. (2017)</td></tr><tr><td>CaOH</td><td>Owens et al. (2022a)</td><td>HS</td><td>Yurchenko et al. (2018b)</td><td>PS</td><td>Prajapat et al. (2017)</td></tr><tr><td>CH</td><td>Masseron et al. (2014)</td><td>KCl</td><td>Barton et al. (2014)</td><td>ScH</td><td>Lodi, Yurchenko &amp; Tennyson (2015)</td></tr><tr><td>CH<sub>3</sub></td><td>Adam et al. (2019)</td><td>KF</td><td>Frohman, Bernath &amp; Brooke (2016)</td><td>SH</td><td>Gorman, Yurchenko &amp; Tennyson (2019)</td></tr><tr><td>CH<sub>3</sub>Cl</td><td>Owens et al. (2018b)</td><td>KOH</td><td>Owens, Tennyson &amp; Yurchenko (2021)</td><td>SiH</td><td>Yurchenko et al. (2018a)</td></tr><tr><td>CH<sub>3</sub>F</td><td>Owens et al. (2018a)</td><td>LaO</td><td>Bernath, Dodangodage &amp; Liévin (2022)</td><td>SiH<sub>2</sub></td><td>Clark et al. (2020)</td></tr><tr><td>CH<sub>4</sub></td><td>Yurchenko &amp; Tennyson (2014)</td><td>LiCl</td><td>Bittner &amp; Bernath (2018)</td><td>SiH<sub>4</sub></td><td>Owens et al. (2017)</td></tr><tr><td>CH<sup>+</sup></td><td>Pearce, Yurchenko &amp; Tennyson (2024)</td><td>LiF</td><td>Bittner &amp; Bernath (2018)</td><td>SiN</td><td>Owens et al. (2022a)</td></tr><tr><td>CH<sup>4</sup></td><td>Kefala et al. (2024)</td><td>LiH</td><td>Coppola, Lodi &amp; Tennyson (2011)</td><td>SiO</td><td>Yurchenko et al. (2022)</td></tr><tr><td>CN</td><td>Syme &amp; McKemmish (2021)</td><td>LiH<sup>+</sup></td><td>Coppola et al. (2011)</td><td>SiO</td><td>Kurucz (2011)</td></tr><tr><td>CO</td><td>Li et al. (2015)</td><td>LiOH</td><td>Owens et al. (2024a)</td><td>SiO<sub>2</sub></td><td>Owens et al. (2020)</td></tr><tr><td>CO<sub>2</sub></td><td>Yurchenko et al. (2020a)</td><td>MgF</td><td>Hou &amp; Bernath (2017)</td><td>SiS</td><td>Upadhyay et al. (2018)</td></tr><tr><td>CP</td><td>Ram et al. (2014)</td><td>MgH</td><td>Owens et al. (2022a)</td><td>SO</td><td>Brady et al. (2024)</td></tr><tr><td>CrH</td><td>Chowdhury et al. (2006)</td><td>MgH</td><td>Gharib-Nezhad, Shayesteh &amp; Bernath (2013)</td><td>SO<sub>2</sub></td><td>Underwood et al. (2016a)</td></tr><tr><td>CS</td><td>Paulose et al. (2015)</td><td>MgO</td><td>Li, Tennyson &amp; Yurchenko (2019)</td><td>SO<sub>3</sub></td><td>Underwood et al. (2016b)</td></tr><tr><td>FeH</td><td>Wende et al. (2010)</td><td>N<sub>2</sub></td><td>Western et al. (2018)</td><td>TiH</td><td>Burrows et al. (2005)</td></tr><tr><td>H<sub>2</sub></td><td>Roueff et al. (2019)</td><td>N<sub>2</sub>O</td><td>Yurchenko, Mellor &amp; Tennyson (2024a)</td><td>TiO</td><td>McKemmish et al. (2019)</td></tr><tr><td>H<sub>2</sub><sup>16</sup>O</td><td>Polyansky et al. (2018)</td><td>NaCl</td><td>Barton et al. (2014)</td><td>VO</td><td>McKemmish, Yurchenko &amp; Tennyson (2016)</td></tr><tr><td>H<sub>2</sub><sup>17,18</sup>O</td><td>Polyansky et al. (2017)</td><td>NaF</td><td>Frohman et al. (2016)</td><td>VO</td><td>Bowesman et al. (2024)</td></tr><tr><td>H<sub>2</sub>CO</td><td>Al-Refaie et al. (2015)</td><td>NaH</td><td>Rivlin et al. (2015)</td><td>YO</td><td>Yurchenko et al. (2024b)</td></tr><tr><td>H<sub>2</sub>O<sub>2</sub></td><td>Al-Refaie et al. (2016)</td><td>NaO</td><td>Mitev et al. (2022)</td><td>YO</td><td>Yurchenko et al. (2019)</td></tr><tr><td>H<sub>2</sub>S</td><td>Azzam et al. (2016)</td><td>NaOH</td><td>Owens et al. (2021)</td><td>ZrO</td><td>Perri, Taher &amp; McKemmish (2023)</td></tr><tr><td>H<sub>3</sub><sup>+</sup></td><td>Mizus et al. (2017)</td><td>NH</td><td>Perri &amp; McKemmish (2024)</td><td></td><td></td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** ExoMol Spectral Atlas (Tennyson & Yurchenko 2018): Cross-sections of SO₂ computed with the ExoMol line ExoAmes (Underwood et al. 2016a).</figcaption></figure>
complete description of the main spectral features, highly-
optimised numerical methods and symmetry tools for solv-
ing the nuclear-motion equation as well as high-level ab initio
calculations are required.

The TheoReTS line lists are simple ascii files with three
columns: *v*<sub>ij</sub>, *S*<sub>ij</sub>, *E*<sub>low</sub>. For ease of use, quantum numbers
and symmetry labels can be provided upon request using a
HITRAN-like format. In addition, variational energy levels
can be also replaced by rotation-vibration levels computed
from empirical effective Hamiltonians whose parameters are
fitted to experimental data, as in the case of methane (Rey
et al. 2018). This ensures almost the same quality as HI-
TRAN2020 (Gordon et al. 2022) for the line positions of
cold bands while many new hot bands can be accurately pre-
dicted. For the modelling of hot exoplanets and brown dwarfs,
a methane line list for the HITEMP (Hargreaves et al. 2020)
spectroscopic database was constructed using the TheoReTS
predictions (Rey et al. 2017; Wong et al. 2019). Moreover,
in order to facilitate the manipulation of the so-called quasi-
continuum formed by billions of lines (e.g. due to line lists
of heavy molecules at high-temperatures), a set of super-
lines can be generated at different temperatures to drastically
reduce the total number of lines by several orders of magni-
tude (Rey et al. 2016b).

In its current form, TheoReTS contains line lists for 9
molecules (CH4, PH3, SF6, C2H4, CF4, GeH4, SiH4, CH3F,
NF3) and 28 isotopologues. New line lists will be released in
2024, either by improving the existing ones or by including
new ones for both *semirigid* and *nonrigid molecules* (Rey
et al. 2023). Among the next candidates of primary impor-
tance – potentially relevant for the study of exoplanetary
atmospheres are CH2, CH3, NH3, H2CCN, H2NCN, CH3Cl,
C3H4, H2O2, CCl4, CH3CN or C2H6 that will be gradually
uploaded in TheoReTS. The construction of comprehensive
line lists is now being revisited using an novel methodology
developed in Reims to derive *ab initio* effective models (Rey
2022), combining the small dimensionality of the spectro-
scopic polyad models and the completeness of the variational
calculation. Fine-tuning of the *ab initio*-based spectroscopic
parameters allows matches to observed data to be made with-
out much computational effort, unlike a refinement procedure
of the PES which is generally more demanding. Effective
parameters plan to be shared in the upgraded version of The-
oReTS.

2.1.2 Laboratory spectroscopy measurements

As might be expected, the vast majority of laboratory studies
have been undertaken with terrestrial applications in mind,
and these studies form the basis for many of the line lists
discussed throughout this section. However, the experimen-
tal conditions of these studies, such as pressure and tem-
perature, are not always directly applicable to non-terrestrial
planetary environments, which means spectroscopic param-
eters derived from them have limitations when applied else-
where. Within our Solar System there are atmospheric tem-
peratures, pressures, and constituents that are beyond those
encountered in the Earth's atmosphere. Moreover, the variety
of exoplanet atmospheres that are already accessible to tran-
sit observations, via JWST observations or high-resolution
ground-based observations, and those that will be observed
by the near-future Ariel mission, mean that the experimen-
tal requirements far exceed atmospheric environments previ-

ously studied and necessitate a range of planetary-applicable
laboratory measurements to better model these observations
(Fortney et al. 2019).

2.1.2.1 Experimental data for Solar System planets Ex-
perimental data can support both the study of our Solar Sys-
tem bodies and contribute significantly to the understanding
of exoplanet spectroscopy.

The advent of the ESA Venus Express mission to Venus and the NASA/Juno and ESA/JUICE missions to the Jovian system pushed the interest on new laboratory experiments to study the properties of CO2 at high temperatures and pressures, to simulate the Venusian case, and H2 and H2+He mixtures as representative of collision induced absorption (CIA) in Jupiter's atmosphere. For example, two different experimental apparatus have been used to obtain the spectra representative of Venus (Stefani et al. 2013) and Jupiter (Snels et al. 2021), due to the different pressure and temperature values covered. In the case of Venus, CO2 spectra were obtained in the 1-10 µm spectral band (Stefani et al. 2022a,b), exploring temperature and pressure values according to a real Venus vertical profile (Seiff et al. 1985). An example is shown in Figure 3. For the Jupiter case, collision induced absorption (CIA) coefficients of H2 and H2-He were measured (see Section 5). Furthermore, empirical spectra for key absorption species observed in the atmospheres of Gas Giant planets have traditionally been implemented in retrievals when line lists were incomplete, as done for CH4 in the visible (Karkoschka 1994).

Titan, with its complex atmosphere, has motivated data-
focused experiments for decades, valuable not just for the
analysis of the Saturnine moon but for studies of the early
Earth and its exoplanetary analogues. These studies reflect the
need for spectroscopic data of hydrocarbons and other organic
molecules in nitrogen-rich environments and have already
significantly improved our understanding of the opacities and
reflectivities of haze particles such as CH3D, C2H6, and many
other Titan tholins (Khare et al. 1984b; He et al. 2022c; Hörst
et al. 2008; Vuitton et al. 2019; Hasenkopf et al. 2010; Brassé
et al. 2015).

2.1.2.2 High-temperature experimental measurements

Outside of the terrestrial temperature range measurements
are relatively sparse, but there have been some efforts to
address this for planetary applications in recent years. This
section is not meant to be a comprehensive overview of the
history of spectroscopic measurements, but instead aims to
provide a summary of recent work that highlight key tech-
niques and molecules currently being investigated for exo-
planetary applications. In particular, we focus on the spec-
tral region covered by Ariel at elevated temperatures, due
to the atmospheric temperatures found in the potential pro-
posed exoplanet target lists (Edwards et al. 2019a; Edwards
& Tinetti 2022). Laboratory studies at high temperatures, i.e.
above room temperatures and typically up to ~ 1000 K -
2000 K, using a variety of experimental techniques, have
provided crucial data for exoplanetary studies. However, ac-
quiring spectra at high temperatures is challenging, primarily
because of the physical properties of laboratory equipment,
but also due to decomposition of the sample, which can lead
to reaction products contaminating observations.

Many existing experimental line lists have been built upon
spectra recorded with Fourier transform spectrometers (FTS)
<table><caption>**Table 7.** Reference sources for Voigt line broadening parameters available in HITRAN, in addition to air- and self-broadening which are provided for every line. W16 refers to Wilzewski et al. (2016), T19 to Tan et al. (2019), T22 to Tan et al. (2022), D18 to Dudaryonok & Lavrentieva (2018), L20 to Lavrentieva & Dudaryonok (2020), and self refers to self-broadening parameters (see Gordon et al. 2022).</caption><thead><tr><th rowspan="2">HITRAN<br>ID</th><th rowspan="2">Molecule</th><th colspan="4">Broadening parameters</th></tr><tr><th>H<sub>2</sub></th><th>He</th><th>H<sub>2</sub>O</th><th>CO<sub>2</sub></th></tr></thead><tbody><tr><td>1</td><td>H<sub>2</sub>O</td><td>—</td><td>—</td><td>Self</td><td>—</td></tr><tr><td>2</td><td>CO<sub>2</sub></td><td>T22</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>4</td><td>N<sub>2</sub>O</td><td>—</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>5</td><td>CO</td><td>T22</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>6</td><td>CH<sub>4</sub></td><td>—</td><td>—</td><td>T19</td><td>—</td></tr><tr><td>7</td><td>O<sub>2</sub></td><td>—</td><td>—</td><td>T19</td><td>—</td></tr><tr><td>9</td><td>SO<sub>2</sub></td><td>W16</td><td>W16</td><td>—</td><td>D18</td></tr><tr><td>11</td><td>NH<sub>3</sub></td><td>W16</td><td>W16</td><td>T19</td><td>W16</td></tr><tr><td>13</td><td>OH</td><td>T22</td><td>T22</td><td>—</td><td>—</td></tr><tr><td>14</td><td>HF</td><td>W16</td><td>W16</td><td>—</td><td>W16</td></tr><tr><td>15</td><td>HCl</td><td>W16</td><td>W16</td><td>—</td><td>W16</td></tr><tr><td>19</td><td>OCS</td><td>T22</td><td>T22</td><td>—</td><td>L20</td></tr><tr><td>20</td><td>H<sub>2</sub>CO</td><td>T22</td><td>T22</td><td>—</td><td>T22</td></tr><tr><td>23</td><td>HCN</td><td>T22</td><td>T22</td><td>—</td><td>—</td></tr><tr><td>26</td><td>C<sub>2</sub>H<sub>2</sub></td><td>W16</td><td>W16</td><td>—</td><td>W16</td></tr><tr><td>28</td><td>PH<sub>3</sub></td><td>T22</td><td>T22</td><td>—</td><td>—</td></tr><tr><td>31</td><td>H<sub>2</sub>S</td><td>T22</td><td>T22</td><td>T19</td><td>T22</td></tr><tr><td>45</td><td>H<sub>2</sub></td><td>Self</td><td>—</td><td>—</td><td>—</td></tr><tr><td>52</td><td>GeH<sub>4</sub></td><td>T22</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

In summary, HITRAN and HITEMP both provide essential input parameters for many radiative transfer codes. These data are used for a variety of applications, including the modelling of exoplanet atmospheres at high-resolution.

**NASA Ames data base:** The data base from NASA Ames uses the 'Best Theory+Reliable High-Resolution Experiment (BTRHE)' strategy (Huang, Schwenke & Lee 2021) to provide accurate and complete line lists for species such as SO₂ (5 isotopologues up to 500 K) (Huang, Schwenke & Lee 2015, 2016), CO₂ (up to 3000 K) (Huang et al. 2023b), NH₃ (Huang et al. 2022b), N₂O (Huang, Schwenke & Lee 2023a), OCS, CS₂, and their isotopologues. The most recent NASA Ames releases include hot line lists are for the four most abundant isotopologues of CO₂ (¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O, and ¹⁶O¹²C¹⁷O) (Huang et al. 2022a) and extensive room temperature line lists for N₂O with its 12 isotopologues (Huang et al. 2023a). The ExoMol SO₂ line list (Underwood et al. 2016a) was also produced jointly with NASA Ames. Some of the earlier NASA Ames line lists were formatted using the HITRAN-like line-by-line ascii format, while the more recent line lists are provided in the ExoMol-like format with two parts, states and transitions. Although these are ascii files, for transitions (Einstein coefficients and states IDs), NASA Ames uses a simple compacting scheme based on representing real numbers as integers. The line lists can be accessed online.<fnref n="11" />

**TheoReTS:** Precise knowledge of high-energy molecular states and intensities of rovibrational transitions is essential for the modelling of various planetary atmospheres as well as for the understanding of spectral properties, even in extreme dynamical and temperature conditions. This clearly demonstrates the need of having consistent line-by-line spectroscopic data bases, with a large coverage in terms of both wavelengths and temperatures. Because of

their completeness, variational calculations are well designed for the modelling of planetary atmospheres, unlike traditional spectroscopic effective models for which wavenumber extrapolation beyond the range of observed data turns out very limited. Within that context, the TheoReTS (Theoretical Reims-Tomsk Spectral data) project (Rey et al. 2016a) — whose philosophy closely follows that of ExoMol (Tennyson et al. 2020) — was born in 2016.<fnref n="12" /> For the construction of accurate variationally computed molecular line lists allowing a complete description of the main spectral features, highly optimized numerical methods and symmetry tools for solving the nuclear-motion equation as well as high-level ab initio calculations are required.

The TheoReTS line lists are simple ascii files with three columns: *v*<sub>ij</sub>, *S*<sub>ij</sub>, *E*<sub>low</sub>. For ease of use, quantum numbers and symmetry labels can be provided upon request using a HITRAN-like format. In addition, variational energy levels can be also replaced by rotation-vibration levels computed from empirical effective Hamiltonians whose parameters are fitted to experimental data, as in the case of methane (Rey et al. 2018). This ensures almost the same quality as HITRAN2020 (Gordon et al. 2022) for the line positions of cold bands while many new hot bands can be accurately predicted. For modelling hot exoplanets and brown dwarfs, a methane line list for the HITEMP (Hargreaves et al. 2020) spectroscopic data base was constructed using the TheoReTS predictions (Rey, Nikitin & Tyuterev 2017; Wong et al. 2019). Moreover, in order to facilitate the manipulation of the so-called quasi-continuum formed by billions of lines (e.g. due to line lists of heavy molecules at high-temperatures), a set of super-lines can be generated at different temperatures to drastically reduce the total number of lines by several orders of magnitude (Rey et al. 2016a).

In its current form, TheoReTS contains line lists for nine molecules (CH₄, PH₃, SF₆, C₂H₄, CF₄, GeH₄, SiH₄, CH₃F, NF₃) and 28 isotopologues. New line lists will be released in 2024, either by improving the existing ones or by including new ones for both *semirigid* and *non-rigid molecules* (Rey et al. 2023). Among the next candidates of primary importance — potentially relevant for the study of exoplanetary atmospheres are CH₂, CH₃, NH₃, H₂CCN, H₂NCN, CH₃Cl, C₃H₄, H₂O₂, CCl₄, CH₃CN, or C₂H₆ that will be gradually uploaded in TheoReTS. The construction of comprehensive line lists is now being revisited using a novel methodology developed in Reims to derive ab initio effective models (Rey 2022), combining the small dimensionality of the spectroscopic polyad models and the completeness of the variational calculation. Fine-tuning of the ab initio-based spectroscopic parameters allows matches to observed data to be made without much computational effort, unlike a refinement procedure of the PES which is generally more demanding. Effective parameters plan to be shared in the upgraded version of TheoReTS.

## 2.1.2 Laboratory spectroscopy measurements

As might be expected, the vast majority of laboratory studies have been undertaken with terrestrial applications in mind, and these studies form the basis for many of the line lists discussed throughout this section. Laboratory studies not only provide empirical measurements of critical parameters such as line positions, intensities, broadening coefficients, and temperature dependencies (e.g. see Gordon et al. 2022, which overviews experimental works included for HITRAN2020), but they are also used to refine and develop theoretical models, they are essential for constraining calculated parameters,

<footnote n="11">¹¹https://huang.seti.org/ and https://data.nas.nasa.gov/ai3000k</footnote>

<footnote n="12">¹²https://theorets.tsu.ru/ and https://theorets.univ-reims.fr/</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 3.** Measured spectra of CO₂ at different temperatures and pressures relevant to the atmosphere of Venus, from Stefani et al. (2013).</figcaption></figure>

and typically span the infrared region. These measurements provide relatively wide spectral coverage (e.g., multiple vibrational modes) at high spectral resolution (≤ 0.01 cm⁻¹) sufficient for accurate retrievals of planetary conditions. Complementary to FTS, cavity ring down spectrometers (CRDS) are capable of providing similar frequency accuracy to FTS, but the increased effective path provided by the cavity results in much higher sensitivity for weak transitions and is well-suited to 'window' regions of molecular absorption. Laser-based techniques, for example, have been able to probe limited spectral regions at even higher resolutions comparable with millimeter rotational studies (e.g., Δν < 1.0×10⁻⁶ cm⁻¹). More recently, frequency combs have enabled highly accurate spectroscopic studies to be acquired over moderately large spectral regions, which can now include whole vibrational bands. For example, comb spectroscopy has been used for measurements of high-temperature spectra of H₂O (Schroeder et al. 2017; Rutkowski et al. 2018), CH₄ (Malarich et al. 2021), and CO₂ (Cole et al. 2023) in the 6250–7570 cm⁻¹ range. Water spectra measured in a pre-mixed methane/air flat flame (Rutkowski et al. 2018) were assigned using the MARVELised POKAZATEL line list, while H₂O (Schroeder et al. 2017) and CH₄ (Malarich et al. 2021) spectra measured in a range of temperatures and sub-atmospheric pressures were used to assess the accuracy of current editions of HITRAN and HITEMP databases. The CO₂ spectra were measured at pressures up to 25 bar to test and improve line mixing models and their temperature dependence (Cole et al. 2023).

Another development relevant for high-temperature applications is the optical-optical double resonance spectroscopy with continuous-wave pump and comb probe, which allows measurement and assignment of hot-band transitions with sub-Doppler resolution without the need to heat the sample (Foltynowicz et al. 2021b; Silva de Oliveira et al. 2024). This technique has so far been used to measure and assign hot band transitions in the 3ν₃ ← ν₃ range of CH₄ (Foltynowicz et al. 2021a; Silva de Oliveira et al. 2024), finding good agreement with the TheoReTS predictions (Rey et al. 2014a; Hargreaves et al. 2020). See Section 2.1.2.3 for more details on frequency comb spectroscopy.

Broadband FTS measurements of high-temperature gases enclosed in a heated tube cell (up to ~1500 K) can provide essential testing of line lists (Bharadwaj & Modest 2007; Alberti et al. 2015). Such measurements have also provided valuable absorption cross-sections when line lists have been insufficient for planetary studies (e.g., Nassar & Bernath 2003, for CH₄). In addition, high-enthalpy sources (Georges et al. 2019) and oxyacetylene torches with temperatures up to 3000 K (Coheur et al. 2005), or time-resolved spectroscopy in glow discharges (Pastorek et al. 2022, and references therein), can be used to investigate combustion environments and non-local thermodynamic equilibrium (non-LTE) conditions (Dudás et al. 2023). While FTS measurements combined with tube furnaces apparatus have formed the bulk of many studies at high temperatures, often laser based analyses are used in high-temperature remote sensing applications of combustion processes (Tancin et al. 2020).
and they are often used directly as is the case for absorption cross-section measurements (see Section 2.1.3). However, the experimental conditions of many studies, such as pressure and temperature, are not always directly applicable to non-terrestrial planetary environments, which means spectroscopic parameters derived from them have limitations when applied elsewhere. Within our Solar System there are atmospheric temperatures, pressures, and constituents that are beyond those encountered in the Earth's atmosphere. Moreover, the variety of exoplanet atmospheres that are already accessible to transit measurements, via JWST observations or high-resolution ground-based observations (and those that will be observed by the near-future Ariel mission), mean that the experimental requirements far exceed atmospheric environments previously studied and necessitate a range of planetary-applicable laboratory measurements to better model these observations (Fortney et al. 2019).

The value of experimental spectroscopy for characterizing planetary atmospheres cannot be overstated. However, this section is not meant to be a comprehensive overview of the history of spectroscopic works, but instead aims to provide a summary of recent experimental measurements that highlight key techniques, spectroscopic parameters, and molecules currently being investigated for planetary applications.

**Experimental data for Solar System planets:** Experimental data can support both the study of our Solar System bodies and contribute significantly to the understanding of exoplanet spectroscopy.

The advent of the ESA Venus Express mission to Venus and the NASA/Juno and ESA/JUICE missions to the Jovian system pushed the interest on new laboratory experiments to study the properties of CO₂ at high temperatures and pressures, to simulate the Venusian case, and H₂ and H₂+He mixtures as representative of collision induced absorption (CIA) in Jupiter's atmosphere. For example, two different experimental apparatus have been used to obtain the spectra representative of Venus (Stefani et al. 2013) and Jupiter (Snels et al. 2021), due to the different pressure and temperature values covered. In the case of Venus, CO₂ spectra were obtained in the 1–10 µm spectral band (Stefani et al. 2022a, b), exploring temperature and pressure values according to a real Venus vertical profile (Seiff et al. 1985). An example is shown in Fig. 3. For the Jupiter case, CIA coefficients of H₂ and H₂-He were measured (see Section 5). Furthermore, empirical absorption cross-sections for key absorption species observed in the atmospheres of Gas Giant planets have traditionally been implemented in retrievals when line lists were incomplete, as done for CH₄ in the visible (Karkoschka 1994). Moreover, numerous experimental measurements of broadening parameters applicable to planetary atmospheres (e.g. H₂, He, CO₂, and H₂O) and their temperature dependencies have been combined into functional forms by Wilzewski et al. (2016) and Tan et al. (2022) to populate these parameters in spectroscopic data bases.

Titan, with its complex atmosphere, has motivated data-focused experiments for decades (e.g. McKellar 1989; de Vanssay et al. 1995; Curtis et al. 2008; Sung et al. 2013; Hewett et al. 2020), valuable not just for the analysis of the Saturnine moon but for studies of the early Earth and its exoplanetary analogues. These studies reflect the need for spectroscopic data of hydrocarbons and other organic molecules in nitrogen-rich environments and have already significantly improved our understanding of the opacities of CH₃D and C₂H₆ for instance (Hörst, Vuitton & Yelle 2008; Vuitton et al. 2019; He et al. 2022b).

**High-temperature experimental measurements:** Experimental measurements are relatively sparse outside of the terrestrial temperature range, but there have been some efforts to address this for planetary applications in recent years. In particular, we focus on the

spectral region covered by Ariel at elevated temperatures, due to the atmospheric temperatures found in the proposed exoplanet target lists (Edwards et al. 2019b; Edwards & Tinetti 2022). Laboratory studies at high temperatures consistent with hot planetary atmospheres (i.e. above room temperatures and typically up to ~1000–2000 K), using a variety of experimental techniques, have provided crucial data for exoplanetary studies. However, acquiring spectra at high temperatures is challenging, primarily because of the physical properties of laboratory equipment, but also due to decomposition of the sample molecule, which can lead to reaction products contaminating observations.

Many existing experimental line lists have been built upon spectra recorded with Fourier transform spectrometers (FTS) and typically span the infrared region. These measurements provide relatively wide spectral coverage (e.g. multiple vibrational modes) at high spectral resolution (≤0.01 cm⁻¹). It is common to couple Fourier transform spectrometers with cells capable of reaching elevated temperatures. Analyses from these measurements have provided new insight for line positions (Hargreaves, Li & Bernath 2012, for NH₃), intensities (Georges et al. 2019, for CH₄), line shape parameters (Delahaye et al. 2016, for H₂O), and absorption cross-sections (Beale, Hargreaves & Bernath 2016, for C₃H₈) sufficient for accurate retrievals of planetary conditions. Complementary to FTS, cavity ring down spectrometers (CRDS) are capable of providing similar frequency accuracy to FTS, but the increased effective path provided by the cavity results in much higher sensitivity for weak transitions. This high sensitivity makes CRDS well-suited to weaker ‘window’ regions of molecular absorption that are difficult to study with other methods. For example, line parameters obtained for weak CH₄ transitions in the NIR (Campargue et al. 2023) can be included in spectroscopic data bases directly or used to refine line positions in future iterations of an initio line lists. Moreover, CRDS measurements enable constraints to be applied to the water vapour continuum (Koroleva et al. 2023a), which is essential for accounting for the total water absorption through long path lengths (see Section 5). Laser-based techniques, for example, have been able to probe limited spectral regions at even higher resolutions comparable with millimetre rotational studies (e.g. Δν < 1.0×10⁻⁶ cm⁻¹). More recently, frequency combs have enabled highly accurate spectroscopic studies to be acquired over moderately large spectral regions, which can now include whole vibrational bands. For example, comb spectroscopy has been used for measurements of high-temperature spectra of H₂O (Schroeder et al. 2017; Rutkowski et al. 2018), CH₄ (Malarich et al. 2021), and CO₂ (Cole et al. 2023) in the 6250–7570 cm⁻¹ range. Water spectra measured in a pre-mixed methane/air flat flame (Rutkowski et al. 2018) were assigned using the MARVELised POKAZATEL line list, while H₂O (Schroeder et al. 2017) and CH₄ (Malarich et al. 2021) spectra measured in a range of temperatures and sub-atmospheric pressures were used to assess the accuracy of current editions of HITRAN and HITEMP data bases. The CO₂ spectra were measured at pressures up to 25 bar to test and improve line mixing models and their temperature dependence (Cole et al. 2023). Another development relevant for high-temperature applications is the optical–optical double resonance spectroscopy with continuous-wave pump and comb probe, which allows measurement and assignment of hot-band transitions with sub-Doppler resolution without the need to heat the sample (Foltynowicz et al. 2021b; Silva de Oliveira et al. 2024). This technique has so far been used to measure and assign hot band transitions in the 3ν₃ ← ν₃ range of CH₄ (Foltynowicz et al. 2021a; Oliveira et al. 2024), finding good agreement with the TheoReTS predictions (Rey, Nikitin & Tyuterev 2014b; Hargreaves et al. 2020). See Section 2.1.2 for a detailed
Combining laser spectroscopy techniques with shock-tube apparatus enables sensitive measurements at higher temperatures and pressures (Ding et al. 2019; Strand et al. 2019; Tancin & Goldenstein 2021; Chakraborty et al. 2024), which can be difficult to reach with tube furnaces. In addition, these techniques can also be combined with frequency combs to provide accurate high-temperature measurements that cover broad spectral ranges (Pinkowski et al. 2021; Malarich et al. 2021).

Spectroscopic studies of atomic transitions and diatomic molecules at high temperatures have historically taken advantage of the Sun's photosphere (~5800 K). For example, telluric-free, high-resolution Solar spectra recorded from orbiting satellites have been used to extend laboratory studies, as done for CH (Melen et al. 1989; Colin & Bernath 2010), NH (Ram & Bernath 2010), and OH (Melen et al. 1995; Bernath & Colin 2009; Civiš et al. 2023). A recent review of middle-to-near IR emission spectra of four simple astrophysically relevant molecular radicals, OH, NH, CN and CH, was given by Civiš et al. (2023). In addition, key diatomic species that characterise spectra of brown dwarfs are also expected to be present in exoplanet atmospheres. Lines list have been developed for these molecules by analysing archived high-temperature, high resolution spectra, such as carried out for FeH (Hargreaves et al. 2010), and MgH (Shayesteh et al. 2007; Gharib-Nezhad et al. 2013; Hinkle et al. 2013; Owens et al. 2022a), and TiO (Cameron & Bernath 2022).

Water is a key molecule for our atmosphere, and has been prominent in exoplanet observations since early transmission spectra (Tinetti et al. 2007; Swain et al. 2009). The water line lists discussed above have relied on numerous experimental studies to determine assignments. Indeed, some of the current theoretical line lists of H₂O suitable for high temperature analyses have their origin in earlier works that identified water on the Sun (Wallace et al. 1995; Polyansky et al. 1997; Viti et al. 1998). Some examples of recent high-temperature water vapor studies that use FTS (Zobov et al. 2008; Alberti et al. 2015), scanned laser spectroscopy (Melin & Sanders 2018; Melin et al. 2020) and frequency comb studies (Schroeder et al. 2017; Rutkowski et al. 2018) have all helped to refine and validate H₂O line lists.

Small polyatomic molecules such as ammonia and methane can have complex infrared spectra when observed at high resolution, and spectroscopic analyses at high temperatures provide opportunities for extending assignments (Barton et al. 2015). Simplified empirical line lists have been produced by analysing multiple measurements at a variety of different temperatures, as done for NH₃ (Hargreaves et al. 2012) and CH₄ (Beale et al. 2017; Ghysels et al. 2018; Malarich et al. 2021). Furthermore, the experimental absorption cross-sections can themselves become a vital tool in validating high temperature line lists (Wong et al. 2019). Measurements of absorption cross-sections up to temperatures of 1600 K (Essebbar & Farooq 2014; Alrefae et al. 2014; Wong et al. 2019), become particularly necessary for molecules when no complete line lists exists (also Section 2.1.3.1).

Each edition of the HITRAN database incorporates a substantial proportion of experimentally-derived parameters and readers are directed toward the paper describing HITRAN2020 (Gordon et al. 2022, and references therein) for a summary of relevant spectroscopic experimental studies that apply to molecules given in Table 4. In addition, it should be noted that the MARVEL (measured active rotation-vibration

energy levels) methodology (Furtenbacher et al. 2007) (see Section 2.1.4), which is used to empirically correct energy levels of *ab initio* line lists (e.g., Yurchenko et al. 2022), is built upon an extensive survey of experimental measurements, and readers are also directed to each work for a summary of relevant literature.

It is worth stressing that experimental measurements can be particularly challenging for reactive (or toxic) species, especially at high temperatures, which can limit the availability of parameters. In most cases, the absolute intensities are not available experimentally for species and therefore relying on the theory is the only option. It is therefore not uncommon for some spectroscopic parameters, including intensities (and associated lifetimes) as well as pressure-broadening (Tan et al. 2022), to be based only on limited laboratory measurements for some molecules (e.g., H₂ broadening of CO₂).

### 2.1.2.3 Spot-light: Frequency comb-based spectroscopy

This section presents a deeper dive into different aspects of frequency comb spectroscopy with the emphasis on its potential for providing spectroscopic data for exoplanetary spectroscopic studies.

Recent advancements in frequency comb sources and comb-based spectroscopic techniques have provided new opportunities for broadband precision molecular spectroscopy. The combination of large bandwidth, high spectral resolution, and high frequency accuracy provided by frequency combs make them ideal sources for high-precision measurements of spectroscopic molecular parameters. As mentioned above, such high-resolution measurements are an essential component to improving the accuracy of theoretically derived line lists (see Sections 2.1.2.2 and 2.1.4). Frequency combs can either be used directly as a light source for broadband high-resolution spectroscopy (which is referred to as direct frequency comb spectroscopy) or as references to calibrate the frequency axis of tunable-laser-based spectrometers (referred to as comb-referenced spectroscopy). While the simultaneous spectral coverage of most frequency combs cannot yet compete with incoherent sources, the spectral resolution of comb-based spectrometer is orders of magnitude better than that of an FTS spectrometer based on an incoherent light source, allowing the measurement of undistorted line profiles at low pressures with sub-MHz accuracy on line positions. Moreover, the spectral and spatial coherence of the combs make possible the use of path length enhancement methods, such as multi-pass cells and cavities, to increase the absorption sensitivity and detect weak absorption bands. Comb-referenced cavity-enhanced tunable-laser-based spectrometers provide even better absorption sensitivity and - when combined with saturation spectroscopy - line positions with kHz accuracy.

Below we give an overview of precision measurements using direct frequency comb spectroscopy and comb-referenced spectroscopy, with a focus on measurements that led to new line lists or substantial improvement of existing ones for different molecules. We note that an exhaustive coverage of all measurements involving frequency combs is beyond the scope of this work.

Table 7 summarises a selection of experimental line lists obtained from measurements using different direct frequency comb spectroscopy techniques. Most of these measurements were performed at room temperature using direct absorption in multi-pass cells or enhancement cavities. Three of the
<figure><img src="image_6.png" /><figcaption>Figure 3. Measured spectra of CO₂ at different temperatures and pressures relevant to the atmosphere of Venus, from Stefani et al. (2013).</figcaption></figure>

spotlight overview of frequency comb spectroscopy for planetary applications.

In addition to providing measurements of line positions, intensities, and line shape parameters, broad-band FTS measurements of high-temperature gases enclosed in a heated tube cell (up to ~1500 K) can also provide essential testing of the accuracy of current line lists available in the literature, such as for the CO₂ line list in HITEMP (Bharadwaj & Modest 2007; Alberti et al. 2015). Such measurements have also provided valuable absorption cross-sections that can be used for atmospheric characterization when line lists have been incomplete for planetary studies (e.g. Nassar & Bernath 2003, for CH₄). In addition, spectra obtained from high-enthalpy sources (Georges et al. 2019) and oxyacetylene torches with temperatures up to 3000 K (Coheur et al. 2005), or time-resolved spectroscopy in glow discharges (Pastorek et al. 2022, and references therein), can be used to investigate combustion environments and non-local thermodynamic equilibrium (non-LTE) conditions (Dudás et al. 2023). Spectroscopic parameters obtained from these studies can then be used to constrain theoretical line lists, improving the accuracy throughout. While FTS measurements combined with tube furnaces apparatus have formed the bulk of many studies at high temperatures, often laser based analyses are used in high-temperature

remote sensing applications of combustion processes (Tancin et al. 2020). Combining laser spectroscopy techniques with shock-tube apparatus enables sensitive measurements at higher temperatures and pressures (Ding, Strand & Hanson 2019; Strand et al. 2019; Tancin & Goldenstein 2021; Chakraborty et al. 2024), which can be difficult to reach with tube furnaces. In addition, these techniques can also be combined with frequency combs to provide accurate measurements at high-temperature that cover broad spectral ranges, such as recent investigations for the line-positions of CH₄ (Pinkowski et al. 2021; Malarich et al. 2021).

Spectroscopic studies of atomic transitions and diatomic molecules at high temperatures have historically taken advantage of the Sun's photosphere (~5800 K), providing accurate line positions. For example, telluric-free, high-resolution Solar spectra recorded from orbiting satellites have been used to extend laboratory studies, as done for CH (Melen et al. 1989; Colin & Bernath 2010), NH (Ram & Bernath 2010), and OH (Melen et al. 1995; Bernath & Colin 2009; Civiš et al. 2023); similarly Barton, Yurchenko & Tennyson (2013) used extensive sunspot spectra due to Campbell et al. (1995) to help create an extensive SiO line list. This can provide key measurements of spectral lines positions for molecules that are difficult to measure in the laboratory. A recent review of middle-to-near IR emission spectra
room temperature line lists have already been used to up-
date the databases, namely the $v_4$ band region (3000–3160 $cm^{-1}$) of CH$_3$I (Sadiek et al. 2020) and the $v_1+v_3$ band re-
gion (2110–2200 $cm^{-1}$) of CS$_2$ (Karlovets et al. 2020) were
used in updates to the HITRAN2020 database (Gordon et al.
2022), and the $v_6$ and $v_4$ band region (1250–1380 $cm^{-1}$)
of H$_2$CO measured by Germann et al. (2024) was used to
improve the accuracy of the ExoMol line list for H$_2$CO (Al-
Refaie et al. 2015; Al-Derzi et al. 2021).

To study complex molecules, whose spectra are unresolved at room temperature, buffer gas cooling has been implemented to reduce the number of populated rotational and vibrational states. Combining buffer gas cooling with cavity-enhanced comb spectroscopy allowed the measurement of rotationally resolved spectra of nitromethane (CH$_3$NO$_2$), naphthalene (C$_{10}$H$_8$), adamantane (C$_{10}$H$_{16}$), and hexamethylenetetramine (C$_6$N$_4$H$_{12}$) (Spaun et al. 2016), and vinyl bromide (CH$_2$CHBr) (Changala et al. 2016) in the 2850–3070 $cm^{-1}$ range, as well as the buckminster fullerene (C$_{60}$) in the 1180–1190 $cm^{-1}$ range (Changala et al. 2019).

Cavity-enhanced comb spectroscopy has also been com-
bined with velocity-modulation to measure four bands of a
molecular ion HfF⁺ in the 11500–13000 $cm^{-1}$ range (Cossel
et al. 2012). Finally, the time-resolved capabilities of comb
spectroscopy have been used to measure high-resolution
spectra of trans- and cis-DOCO transients (products of the
OD + CO reaction) in the OD stretch region 2380–2750
$cm^{-1}$ (Bui et al. 2018), as well as the pressure broadening of
absorption lines of the short-lived CH$_2$OO Criegee interme-
diate (Luo 2020) in the 1217–1287 $cm^{-1}$ range.

Table 8 summarises a selection of experimental line lists obtained from measurements using different comb-referenced spectroscopy techniques. Many works using comb-referenced cavity-enhanced techniques in the near-infrared provided transition frequencies for overtone and combination bands with kHz level accuracy for e.g., H₂O (Chen et al. 2018; Kassi et al. 2018; Tóbiás et al. 2020), CO₂ (Reed et al. 2021; Guo et al. 2021; Fleurbaey et al. 2023), CO (Mondelain et al. 2015; Wang et al. 2021) and CH₄ (Votava et al. 2022). In the mid-infrared, sub-MHz and kHz level accuracy was obtained for the fundamental bands of CH₄ (Kocheril et al. 2018), N₂O (Knabe et al. 2013; Ting et al. 2014; AlSaif et al. 2018), CHF₃ (Vicentini et al. 2020), and CH₃OH (Santagata et al. 2019) using saturation and Doppler-broadened spectroscopy in absorption cells, and for CH₄ using sub-Doppler cavity-enhanced spectroscopy (Okubo et al. 2011; Abe et al. 2013). Three of these works have already been used for updating the databases and are included as part of HITRAN2020 (Gordon et al. 2022). This includes line positions for the 3↔0 and 4↔0 bands of CO (Mondelain et al. 2015) and the $v_3$ region of CH₄ (Abe et al. 2013), with the work of Fleurbaey et al. (2021) included in a fit for line positions of the 1.27 µm band of O₂.

2.1.3 Alternative parameterisations

**2.1.3.1 Absorption cross-section measurements** Determining an accurate line list for a large proportion of known molecules is not practical, or possible, due to the complexity of assigning congested spectra (Sousa-Silva et al. 2019; Zapata Trujillo & McKemmish 2022a,b, 2023). In such instances, numerous individual lines typically blend into unresolved spectral bands. However, these molecules can still

form strong detectable features in atmospheric spectra, and their spectroscopic signatures are required in retrieval frameworks for detection, in addition to improving the retrieval accuracy of planetary characteristics or other atmospheric species. To provide this necessary data, it is common practice to carefully measure experimental absorption cross-sections. These measurements are required to cover the expected temperature and pressure conditions of the appropriate planetary atmosphere, as well as including the appropriate broadening gases (e.g., H₂, He, N₂, etc) at a resolution that provides sufficient details.

Cross-sections are not just restricted to the infrared or visible wavelength regions; many valuable cross-sections which cover the UV region are regularly employed in Earth observations, for example. There are many cross-sections included in the HITRAN database that cover the UV and visible regions, such as SO₂ and O₃. While this section will mainly discuss infrared and visible absorption cross-sections due to the relevance for Ariel, UV absorption cross-sections are also important for exoplanet atmosphere models used to inform our understanding of observed planets. UV cross-sections also have special continuum features related to photodissociation and photoabsorption effects; see Section 8 where we discuss these separately.

The Pacific Northwest Nation Laboratory (PNNL) produced a large catalogue (Sharpe et al. 2004) of infrared absorption cross-sections for many chemical compounds recorded at 1.0 atm with a Fourier transform spectrometer at temperatures of 5, 25 and 50°C. Species included compounds that were difficult to measure in the laboratory. These cross-sections are no longer available from PNNL directly, but the majority of these measurements are now included as part of the HITRAN database (Gordon et al. 2022). The HITRAN database provides experimental absorption cross-sections of over 300 molecules (Kochanov et al. 2019), in addition to the line-by-line molecules described above. HITRAN also regularly expands the available data with each new edition (Gordon et al. 2022).

It should be noted that many chemical compounds have been measured due to signatures appearing in Earth observation measurements. For example, chlorine-containing compounds (e.g., chlorofluorocarbons) are intensely monitored because their reactions in the atmosphere lead to the depletion of stratospheric ozone. Therefore, the temperature and pressure coverage of absorption cross-sections is regularly expanded for improved accuracy of retrievals, for example, using Fourier transform measurements of the molecule contained in a cold cell (Harrison 2018).

Other planets of the Solar System (and their moons) contain many trace gases, which are typically retrieved using experimental absorption cross-sections. For example, Titan, with its rich hydrocarbon atmosphere, requires cross-section measurements of nitrogen broadened species at low temperatures (e.g., Sung et al. 2013, 2018; Vuitton et al. 2019). Similarly, H₂ and He broadened measurements are required for the Jovian planets (e.g., Sung et al. 2016a; Dodangodage et al. 2020). It is expected that some of these species will be present at elevated temperatures in warm Gas Giant exoplanetary atmospheres (Fleury et al. 2023), therefore recent studies have also provided experimental absorption cross-sections at elevated temperatures (e.g., Alrefae et al. 2014; Hargreaves et al. 2015; Beale et al. 2016; Venot et al. 2018; Bernath & Fernando 2021; Adil et al. 2023).
of four simple astrophysically relevant molecular radicals, OH, NH, CN, and CH, was given by Civiš et al. (2023). In addition, key diatomic species that characterize spectra of brown dwarfs are also expected to be present in exoplanet atmospheres. These molecules are challenging for theoretical calculations, and measurements of line positions and intensities are essential for improving models. Semi-empirical line lists have been developed for these molecules by analysing archived high-temperature, high resolution spectra, such as carried out for FeH (Hargreaves et al. 2010), and MgH (Shayesteh et al. 2007; Gharib-Nezhad et al. 2013; Hinkle et al. 2013; Owens et al. 2022a), and TiO (Cameron & Bernath 2022). These semi-empirical works have often been directly implemented into brown dwarf (Bailey & Kedziora-Chudczer 2012) and exoplanet (Mukherjee et al. 2023) atmospheric models to improve characterization.

Water is a key molecule for our atmosphere, and has been prominent in exoplanet observations since early transmission spectra (Tinetti et al. 2007; Swain et al. 2009). The water line lists discussed above have relied on numerous experimental studies to accurately determine spectroscopic parameters (e.g. positions, intensities, line shapes, broadening coefficients, pressure shifts, temperature dependencies), and to refine assignments. Indeed, some of the current theoretical line lists of H₂O suitable for high temperature analyses have their origin in earlier works that identified new transitions of high-temperature water vapour on the Sun (Wallace et al. 1995; Polyansky et al. 1997; Viti et al. 1998). Some examples of recent high-temperature water vapour studies that use FTS (Zobov et al. 2008; Alberti et al. 2015), scanned laser spectroscopy (Melin & Sanders 2018; Melin, Sanders & Nasir 2020) and frequency comb studies (Schroeder et al. 2017; Rutkowski et al. 2018) have all helped to refine spectroscopic parameters for H₂O line lists and to constrain ab initio calculations. Hot (1723 K) laboratory studies have also been used to test and confirm the accuracy of the available line lists (Melin et al. 2020).

Small polyatomic molecules such as ammonia and methane can have complex infrared spectra when observed at high resolution, and spectroscopic analyses at high temperatures provide opportunities for extending rovibrational assignments (Barton et al. 2015). Simplified empirical line lists have been produced by analysing multiple measurements at a variety of different temperatures, as done for NH₃ (Hargreaves et al. 2012) and CH₄ (Beale et al. 2017; Ghysels et al. 2018; Malarich et al. 2021). These simplified line lists lack spectroscopic assignments but constitute empirical line positions, intensities, and lower state energies, and are capable of reproducing the experimental spectra over the temperature range of the studies and can be used to characterize brown dwarf and exoplanet atmospheres. Analyses of these line lists can then be performed to determine line assignments and constrain calculated parameters. Furthermore, the measured spectra can be converted into experimental absorption cross-sections (Wong et al. 2019) that can themselves be used as input data to planetary models in place of line lists, or can be used to compared the accuracy of multiple high temperature line lists as done for CH₄ (Hargreaves et al. 2020). Measurements of absorption cross-sections up to temperatures of 1600 K (Alrefae, Es-sebbar & Farooq 2014; Es-sebbar & Farooq 2014; Wong et al. 2019), become particularly necessary for molecules when no complete line lists exists (also Section 2.1.3).

Each edition of the HITRAN data base incorporates a substantial proportion of experimentally derived parameters and readers are directed towards the paper describing HITRAN2020 (Gordon et al. 2022, and references therein) for a summary of relevant spectroscopic experimental studies that apply to molecules given in Table 4. In addition, it should be noted that the MARVEL (measured active

rotation-vibration energy levels) methodology (Furtenbacher et al. 2007) (see Section 2.1.4), which is used to empirically correct energy levels of ab initio line lists (e.g. Yurchenko et al. 2022), is built upon an extensive survey of experimental measurements, and readers are also directed to each work for a summary of relevant literature.

It is worth stressing that experimental measurements can be particularly challenging for reactive (or toxic) species, especially at high temperatures, which can limit the availability of parameters. In most cases, the absolute intensities are not available experimentally for species and therefore relying on the theory is the only option. It is therefore not uncommon for some spectroscopic parameters, including intensities (and associated lifetimes) as well as pressure-broadening (Tan et al. 2022), to be based only on limited laboratory measurements for some molecules (e.g. H₂ broadening of CO₂).

**Spot-light: frequency comb-based spectroscopy:** This section presents a deeper dive into different aspects of frequency comb spectroscopy with the emphasis on its potential for providing spectroscopic data for exoplanetary spectroscopic studies.

Recent advancements in frequency comb sources and comb-based spectroscopic techniques (Gohle et al. 2007; Foltynowicz et al. 2011; Maslowski et al. 2016; Kowzan et al. 2016; Coddington, Newbury & Swann 2016; Changala et al. 2016; Weichman et al. 2019; Ycas et al. 2018; Krzempek et al. 2019; Muraviev, Konnov & Vodopyanov 2020; Foltynowicz et al. 2021b) have provided new opportunities for broad-band precision molecular spectroscopy. The combination of large bandwidth, high spectral resolution, and high frequency accuracy provided by frequency combs make them ideal sources for high-precision measurements of spectroscopic molecular parameters. Such high-resolution measurements are an essential component to improving the accuracy of theoretically derived line lists (see Sections 2.1.2 and 2.1.4). Frequency combs can either be used directly as light sources for broad-band high-resolution spectroscopy (which is referred to as direct frequency comb spectroscopy) or as references to calibrate the frequency axis of tunable-laser-based spectrometers (referred to as comb-referenced spectroscopy). While the simultaneous spectral coverage of most frequency combs cannot yet compete with incoherent sources, the spectral resolution of comb-based spectrometers is orders of magnitude better than that of an FTS spectrometer based on an incoherent light source, allowing the measurement of undistorted line profiles at low pressures with sub-MHz accuracy on line positions. Moreover, the spectral and spatial coherence of the combs make possible the use of path length enhancement methods, such as multi-pass cells (Adler et al. 2010b) and cavities (Adler et al. 2010a), to increase the absorption sensitivity and detect weak absorption bands. Comb-referenced cavity-enhanced tunable-laser-based spectrometers provide even better absorption sensitivity and – when combined with saturation spectroscopy – line positions with kHz accuracy.

Below we give an overview of precision measurements using direct frequency comb spectroscopy and comb-referenced spectroscopy, with a focus on measurements that led to new line lists or substantial improvement of existing ones for different molecules. We note that an exhaustive coverage of all measurements involving frequency combs is beyond the scope of this work.

Table 8 summarizes a selection of experimental line lists obtained from measurements using different direct frequency comb spectroscopy techniques. Most of these measurements were performed at room temperature using direct absorption in multipass cells or enhancement cavities. Many of the works provided also line intensities, and pressure broadening and shift parameters. Three of the room temperature line lists have already been used to update the data bases, namely the v₄ band region (3000–3160 cm⁻¹) of
<table><caption>**Table 7.** Molecular line lists obtained from direct frequency comb spectroscopy measurements using different methods: DCS - dual comb spectroscopy; FTS - Fourier transform spectroscopy; Vernier - Vernier spectroscopy; VIPA - spectrometers based on virtually imaged phased array; PAS - photoacoustic spectroscopy; OODR - optical-optical double resonance spectroscopy; CE - cavity enhanced. The spectral coverage and temperature range are also indicated; RT - room temperature.</caption><thead><tr><th>Molecule</th><th>Range [cm<sup>-1</sup>]</th><th>Range [µm]</th><th>Method</th><th>T [K]</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="2">H<sub>2</sub>O</td><td>6800-7200</td><td>1.39 - 1.47</td><td>DCS</td><td>296-1300</td><td>Schroeder et al. (2017)</td></tr><tr><td>6250-6670</td><td>1.50 - 1.60</td><td>CE FTS</td><td>1950</td><td>Rutkowski et al. (2018)</td></tr><tr><td rowspan="2">CO<sub>2</sub></td><td>5064-5126</td><td>1.95 - 1.97</td><td>CE Vernier</td><td>RT</td><td>Siciliani de Cumis et al. (2018)</td></tr><tr><td>6800-7000</td><td>1.43 - 1.47</td><td>DCS</td><td>495-977</td><td>Cole et al. (2023)</td></tr><tr><td>N<sub>2</sub>O</td><td>1250-1310</td><td>7.63 - 8.00</td><td>FTS</td><td>RT</td><td>Hjältén et al. (2021)</td></tr><tr><td>CO</td><td>6310-6365</td><td>1.57 - 1.58</td><td>CE VIPA</td><td>RT</td><td>Kowzan et al. (2017)</td></tr><tr><td rowspan="4">CH<sub>4</sub></td><td>2900-3050</td><td>3.28 - 3.45</td><td>DCS</td><td>RT</td><td>Baumann et al. (2011)</td></tr><tr><td>5870-6130</td><td>1.63 - 1.70</td><td>DCS</td><td>RT</td><td>Zolot et al. (2013)</td></tr><tr><td>6770-7570</td><td>1.32 - 1.48</td><td>DCS</td><td>296-1000</td><td>Malarich et al. (2021)</td></tr><tr><td>5900-6100</td><td>1.64 - 1.69</td><td>OODR</td><td>111</td><td>Foltynowicz et al. (2021a)</td></tr><tr><td rowspan="2"><sup>13</sup>CH<sub>4</sub></td><td>1250-1380</td><td>7.25 - 8.00</td><td>FTS</td><td>RT</td><td>Silva de Oliveira et al. (2024)</td></tr><tr><td>2910-3110</td><td>3.22 - 3.44</td><td>PAS</td><td>RT</td><td>Germann et al. (2022)</td></tr><tr><td>H<sub>2</sub>CO</td><td>1250-1380</td><td>7.25 - 8.00</td><td>FTS</td><td>RT</td><td>Karhu et al. (2019)</td></tr><tr><td>H<sup>13</sup>CN</td><td>6390-6535</td><td>1.53 - 1.56</td><td>DCS</td><td>RT</td><td>Coddington et al. (2008)</td></tr><tr><td>C<sub>2</sub>H<sub>2</sub></td><td>6430-6630</td><td>1.51 - 1.56</td><td>DCS</td><td>RT</td><td>Zolot et al. (2013)</td></tr><tr><td>CH<sub>3</sub>I</td><td>2930-3160</td><td>3.16 - 3.41</td><td>FTS</td><td>RT</td><td>Sadiek et al. (2020)</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Hjältén et al. (2023)</td></tr><tr><td>CS<sub>2</sub></td><td>2110-2200</td><td>4.55 - 4.74</td><td>DCS</td><td>RT</td><td>Karlovets et al. (2020)</td></tr><tr><td>HfF<sup>+</sup></td><td>11500-13000</td><td>0.77 - 0.87</td><td>CE VIPA</td><td>823</td><td>Cossel et al. (2012)</td></tr><tr><td>CH<sub>3</sub>NO<sub>2</sub></td><td>2940-3090</td><td>3.24 - 3.40</td><td>CE FTS</td><td>10-20</td><td>Spaun et al. (2016)</td></tr><tr><td>CH<sub>2</sub>CHBr</td><td>3023-3033</td><td>3.30 - 3.31</td><td>CE FTS</td><td>10-20</td><td>Changala et al. (2016)</td></tr><tr><td>DOCO</td><td>2380-2750</td><td>3.64 - 4.20</td><td>CE FTS</td><td>RT</td><td>Bui et al. (2018)</td></tr><tr><td>C<sub>60</sub></td><td>1180-1190</td><td>8.40 - 8.47</td><td>CE FTS</td><td>150</td><td>Changala et al. (2019)</td></tr><tr><td>CH<sub>2</sub>OO</td><td>1217-1287</td><td>7.77 - 8.22</td><td>VIPA</td><td>RT</td><td>Luo (2020)</td></tr><tr><td>CH<sub>2</sub>Br<sub>2</sub></td><td>2960-3120</td><td>3.21 - 3.38</td><td>FTS</td><td>RT</td><td>Sadiek et al. (2023)</td></tr></tbody></table>

The limited number of specific temperature and pressure conditions measured as absorption cross-sections makes them less flexible than line lists. However, techniques have been developed to interpolate between measurements with polynomial coefficients (Buehler et al. 2022) as well as producing pseudo-line lists (Steffens et al. 2023). Each technique does not identify quantum mechanical transitions, as is the case for spectroscopic line lists (see earlier in Section 2), but instead empirical parameters are determined that can reproduce the absorption cross-section intensity over the range of measurements. However, care should be taken when extrapolating these techniques to conditions beyond those used from the initial studies.

Ariel will cover the ~2500–5000 cm⁻¹ (~2 - 4 µm) region at a resolving power of 100 (see Table 1), which spans the spectral range where key molecular functional groups (e.g., C-H stretch at ~3000-3300 cm⁻¹) exhibit strong absorption. The majority of the absorption cross-sections described above and included in HITRAN have spectral features within this region. Some of these molecules have already been proposed as biosignatures (Zhan et al. 2021) or technosignatures (Haqq-Misra et al. 2022), due to their distinct spectral features and limited pathways for synthesis. Indeed, it was in this spectral range that the recent tentative detection of dimethyl sulfide (DMS or (CH₃)₂S) was made from transit spectra of K2-18b recorded using JWST (Madhusudhan et al. 2023) and absorption cross-sections in HITRAN.

**Polycyclic aromatic hydrocarbons (PAHs)** and tholins are known to contribute significantly to the optical properties of Solar System planetary spectra (Abdel-Shafy & Mansour 2016; Zhao et al. 2018). They have an optical slope similar to

cloud/hazes, potentially causing a degeneracy in the interpretation of spectral data caused by aerosols (see Section 6, and, for example, Figure 1 of Ercolano et al. (2022)). Ercolano et al. (2022) explore the detectability of PAHs observed with Ariel (Tinetti et al. 2018) and Twinkle Edwards et al. (2019b), finding there is a possibility of detection. Dubey et al. (2023) investigate the formation processes of various PAHs on the thermalised atmospheres of hot Jupiter exoplanets, and found that planets with an effective temperature of around 1300 K are the most promising targets for investigating PAHs, particularly for atmospheres with a high carbon-to-oxygen ratio (C/O) and high metallicity. A follow-up study by Grübel et al. (MNRAS, submitted) focuses on the inter-comparison of different cloud/haze, PAHs and Tholin models while retrieving the best case scenario for a particular planet, Wasp-6 b. The cross-sections presented by Ercolano et al. (2022), based on calculations of Draine & Li (2007), represent a combined effect observed from a collection of crystalline PAHs. These cross-sections are consistent with observations of the interstellar medium (ISM) and thus presumably originate from a diverse PAH mixture. Given the sheer amount of different molecules, they currently represent the most convenient way to implement PAHs in atmospheric retrievals. The NASA Ames PAH IR Spectral Database is a source of cross-section data for PAHs (Boersma et al. 2014; Bauschlicher et al. 2018; Mattioda et al. 2020)<fnref n="14" />, offering extensive data on thousands of PAHs, although primarily for the identification within in-

<footnote n="14">¹⁴ https://www.astrochem.org/pahdb/</footnote>
<table><caption>**Table 8.** Molecular line lists obtained from direct frequency comb spectroscopy measurements using different methods: DCS – dual comb spectroscopy; FTS – Fourier transform spectroscopy; Vernier – Vernier spectroscopy; VIPA – spectrometers based on virtually imaged phased array; PAS – photoacoustic spectroscopy; OODR – optical-optical double resonance spectroscopy; CE – cavity enhanced. The spectral coverage and temperature range are also indicated; RT – room temperature. All works listed here provided line positions, and some, indicated in the 'Parameters' column, provided also intensities, S, self, air, and reaction matrix broadening parameters, γself, γair, γp, and self shift parameters, δself.</caption><thead><tr><th>Molecule</th><th>Range (cm<sup>-1</sup>)</th><th>Range (μm)</th><th>Method</th><th>T (K)</th><th>Parameters</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="2">H<sub>2</sub>O</td><td>6800–7200</td><td>1.39–1.47</td><td>DCS</td><td>296–1300</td><td>γself, γair</td><td>Schroeder et al. (2017)</td></tr><tr><td>6250–6670</td><td>1.50–1.60</td><td>CE FTS</td><td>1950</td><td>S</td><td>Rutkowski et al. (2018)</td></tr><tr><td rowspan="2">CO<sub>2</sub></td><td>5064–5126</td><td>1.95–1.97</td><td>CE Vernier</td><td>RT</td><td>S, γself</td><td>Siciliani de Cumis et al. (2018)</td></tr><tr><td>6800–7000</td><td>1.43–1.47</td><td>DCS</td><td>495–977</td><td>line mixing</td><td>Cole et al. (2023)</td></tr><tr><td>N<sub>2</sub>O</td><td>1250–1310</td><td>7.63–8.00</td><td>FTS</td><td>RT</td><td>–</td><td>Hjältén et al. (2021)</td></tr><tr><td rowspan="2">CO</td><td>6310–6365</td><td>1.57–1.58</td><td>CE VIPA</td><td>RT</td><td>γself, δself</td><td>Kowzan et al. (2019)</td></tr><tr><td>2040–2230</td><td>4.48–4.90</td><td>FTS</td><td>RT</td><td>–</td><td>Nishiyama et al. (2024)</td></tr><tr><td rowspan="5">CH<sub>4</sub></td><td>1250–1380</td><td>7.25–8.00</td><td>FTS</td><td>RT</td><td>S</td><td>Germann et al. (2022)</td></tr><tr><td>2900–3050</td><td>3.28–3.45</td><td>DCS</td><td>RT</td><td>–</td><td>Baumann et al. (2011)</td></tr><tr><td>5870–6130</td><td>1.63–1.70</td><td>DCS</td><td>RT</td><td>–</td><td>Zolot et al. (2013)</td></tr><tr><td>5900–6100</td><td>1.64–1.69</td><td>OODR</td><td>111</td><td>–</td><td>Foltynowicz et al. (2021a)</td></tr><tr><td>5910–5980</td><td>1.67–1.69</td><td>OODR</td><td>RT</td><td>–</td><td>Oliveira et al. (2024)</td></tr><tr><td rowspan="2"><sup>13</sup>CH<sub>4</sub></td><td>6770–7570</td><td>1.32–1.48</td><td>DCS</td><td>296–1000</td><td>γself, δself</td><td>Malarich et al. (2021)</td></tr><tr><td>1250–1380</td><td>7.25–8.00</td><td>FTS</td><td>RT</td><td>S</td><td>Germann et al. (2022)</td></tr><tr><td><sup>14</sup>CH<sub>4</sub></td><td>2910–3110</td><td>3.22–3.44</td><td>PAS</td><td>RT</td><td>–</td><td>Karhu et al. (2019)</td></tr><tr><td>H<sub>2</sub>CO</td><td>1250–1380</td><td>7.25–8.00</td><td>FTS</td><td>RT</td><td>S</td><td>Germann et al. (2024)</td></tr><tr><td>H<sup>13</sup>CN</td><td>6390–6535</td><td>1.53–1.56</td><td>DCS</td><td>RT</td><td>S</td><td>Guay, Genest & Fleisher (2018)</td></tr><tr><td>C<sub>2</sub>H<sub>2</sub></td><td>6430–6630</td><td>1.51–1.56</td><td>DCS</td><td>RT</td><td>–</td><td>Zolot et al. (2013)</td></tr><tr><td rowspan="2">CH<sub>3</sub>I</td><td>3000–3160</td><td>3.16–3.3</td><td>FTS</td><td>RT</td><td>S</td><td>Sadiek et al. (2020)</td></tr><tr><td>2930–3160</td><td>3.16–3.57</td><td>FTS</td><td>RT</td><td>S</td><td>Hjältén, Foltynowicz & Sadiek (2023)</td></tr><tr><td>CS<sub>2</sub></td><td>2110–2200</td><td>4.55–4.74</td><td>DCS</td><td>RT</td><td>S</td><td>Karlovets et al. (2020)</td></tr><tr><td>HfF<sup>+</sup></td><td>11 500–13 000</td><td>0.77–0.87</td><td>CE VIPA</td><td>823</td><td>–</td><td>Cossel et al. (2012)</td></tr><tr><td>CH<sub>3</sub>NO<sub>2</sub></td><td>2940–3090</td><td>3.24–3.40</td><td>CE FTS</td><td>10–20</td><td>–</td><td>Spaun et al. (2016)</td></tr><tr><td>CH<sub>2</sub>CHBr</td><td>3023–3033</td><td>3.30–3.31</td><td>CE FTS</td><td>10–20</td><td>–</td><td>Changala et al. (2016)</td></tr><tr><td>DOCO</td><td>2380–2750</td><td>3.64–4.20</td><td>CE FTS</td><td>RT</td><td>–</td><td>Bui et al. (2018)</td></tr><tr><td>C<sub>60</sub></td><td>1180–1190</td><td>8.40–8.47</td><td>CE FTS</td><td>150</td><td>–</td><td>Changala et al. (2019)</td></tr><tr><td>CH<sub>2</sub>OO</td><td>1217–1287</td><td>7.77–8.22</td><td>DCS</td><td>RT</td><td>γp</td><td>Luo (2020)</td></tr><tr><td>CH<sub>2</sub>Br<sub>2</sub></td><td>2960–3120</td><td>3.21–3.38</td><td>FTS</td><td>RT</td><td>–</td><td>Sadiek et al. (2023)</td></tr></tbody></table>

CH<sub>3</sub>I (Sadiek et al. 2020) and the v<sub>1</sub>+v<sub>3</sub> band region (2110–2200 cm<sup>-1</sup>) of CS<sub>2</sub> (Karlovets et al. 2020) were used in updates to the HITRAN2020 data base (Gordon et al. 2022), and the v<sub>6</sub> and v<sub>4</sub> band region (1250–1380 cm<sup>-1</sup>) of H<sub>2</sub>CO measured by Germann et al. (2024) was used to improve the accuracy of the ExoMol line list for H<sub>2</sub>CO (Al-Refaie et al. 2015; Al-Derzi et al. 2021).

To study complex molecules, whose spectra are unresolved at room temperature, buffer gas cooling has been implemented to reduce the number of populated rotational and vibrational states. Combining buffer gas cooling with cavity-enhanced comb spectroscopy allowed the measurement of rotationally resolved spectra of nitromethane (CH<sub>3</sub>NO<sub>2</sub>), naphtalene (C<sub>10</sub>H<sub>8</sub>), adamantane (C<sub>10</sub>H<sub>16</sub>), and hexamethylenetetramine (C<sub>6</sub>N<sub>4</sub>H<sub>12</sub>) (Spaun et al. 2016), and vinyl bromide (CH<sub>2</sub>CHBr) (Changala et al. 2016) in the 2850–3070 cm<sup>-1</sup> range, as well as the buckminster fullerene (C<sub>60</sub>) in the 1180–1190 cm<sup>-1</sup> range (Changala et al. 2019).

Cavity-enhanced comb spectroscopy has also been combined with velocity-modulation to measure four bands of a molecular ion HfF<sup>+</sup> in the 11 500–13 000 cm<sup>-1</sup> range (Cossel et al. 2012). Finally, the time-resolved capabilities of comb spectroscopy have been used to measure high-resolution spectra of trans- and cis-DOCO transients (products of the OD+CO reaction) in the OD stretch region 2380–2750 cm<sup>-1</sup> (Bui et al. 2018), as well as the pressure broadening of absorption lines of the short-lived CH<sub>2</sub>OO Criegee intermediate (Luo 2020) in the 1217–1287 cm<sup>-1</sup> range.

Table 9 summarizes a selection of experimental line lists obtained from measurements using different comb-referenced spectroscopy

techniques. Many works using comb-referenced cavity-enhanced techniques in the near-infrared provided transition frequencies for overtone and combination bands with kHz level accuracy for, e.g. H<sub>2</sub>O (Chen et al. 2018; Kassi et al. 2018; Tóbiás et al. 2020, 2024), CO<sub>2</sub> (Guo et al. 2021; Reed et al. 2021; Fleurbaey et al. 2023), CO (Mondelain et al. 2015; Wang et al. 2021), and CH<sub>4</sub> (Votava et al. 2022). In the mid-infrared, sub-MHz and kHz level accuracy was obtained for the fundamental bands of CH<sub>4</sub> (Kocheril et al. 2018), N<sub>2</sub>O (Knabe et al. 2013; Ting et al. 2014; AlSaif et al. 2018), CHF<sub>3</sub> (Vicentini et al. 2020), and CH<sub>3</sub>OH (Santagata et al. 2019) using saturation and Doppler-broadened spectroscopy in absorption cells, and for CH<sub>4</sub> using sub-Doppler cavity-enhanced spectroscopy (Okubo et al. 2011; Abe et al. 2013). Three of these works have already been used for updating the data bases and are included as part of HITRAN2020 (Gordon et al. 2022). This includes line positions for the 3 ← 0 and 4 ← 0 bands of CO (Mondelain et al. 2015) and the v<sub>3</sub> region of CH<sub>4</sub> (Abe et al. 2013), with the work of Fleurbaey et al. (2021) included in a fit for line positions of the 1.27 µm band of O<sub>2</sub>. Line intensities were provided only by a couple of works using CRDS in the Doppler-limited regime, since saturation spectroscopy often does not yield absolute intensities.

### 2.1.3 Alternative parametrizations

**Absorption cross-section measurements:** Determining an accurate line list for a large proportion of known molecules is not practical, or possible, due to the complexity of assigning congested
<table><caption>**Table 8.** Molecular line lists obtained from comb-referenced spectroscopy measurements using different methods: CRDS - cavity ring down spectroscopy; NICE-OHMS - noise-immune cavity enhanced optical heterodyne molecular spectroscopy; CRSS - comb-referenced saturation spectroscopy, DAS - direct absorption spectroscopy; CEAS - cavity enhanced absorption spectroscopy, NICE-VMS - noise-immune cavity enhanced velocity modulation spectroscopy; The spectral coverage of each is also indicated.</caption><thead><tr><th>Molecule</th><th>Band</th><th>Range [cm<sup>-1</sup>]</th><th>Range [µm]</th><th>Method</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="3">H<sub>2</sub><sup>16</sup>O</td><td>(013 &larr; 000)</td><td>12,621 - 12,665</td><td>0.789 - 0.792</td><td>CRDS</td><td>Chen et al. (2018)</td></tr><tr><td>(101 &larr; 000)</td><td>7164 - 7185</td><td>1.391 - 1.396</td><td>CRDS</td><td>Kassi et al. (2018)</td></tr><tr><td>(200 &larr; 000)</td><td>7000 - 7350</td><td>1.36 - 1.43</td><td>NICE-OHMS<sup>a</sup></td><td>Tóbiás et al. (2020); Diouf et al. (2022)</td></tr><tr><td>H<sub>2</sub><sup>17</sup>O</td><td>(200 &larr; 000)<sup>b</sup></td><td>7228 - 7289</td><td>1.37 - 1.38</td><td>NICE-OHMS</td><td>Melosso et al. (2021)</td></tr><tr><td>H<sub>2</sub><sup>18</sup>O</td><td>(200 &larr; 000)</td><td>7000 - 7350</td><td>1.36 - 1.43</td><td>NICE-OHMS<sup>a</sup></td><td>Diouf et al. (2021)</td></tr><tr><td>Six H<sub>2</sub>O isotopologues</td><td>Several</td><td>8041 - 8633</td><td>1.15 - 1.24</td><td>CRDS</td><td>Koroleva et al. (2023)</td></tr><tr><td rowspan="5"><sup>12</sup>C<sup>16</sup>O<sub>2</sub></td><td>(30012 &larr; 00001)</td><td>6170 - 6370</td><td>1.57 - 1.62</td><td>CRDS</td><td>Reed et al. (2021)</td></tr><tr><td>(30013 &larr; 00001)</td><td></td><td></td><td></td><td></td></tr><tr><td>(30012 &larr; 00001)</td><td>6170 - 6370</td><td>1.57 - 1.62</td><td>CRDS</td><td>Guo et al. (2021)</td></tr><tr><td>(20012 &larr; 00001)</td><td>4830 - 5010</td><td>1.99 - 2.07</td><td>CRDS</td><td>Fleurbay et al. (2023)</td></tr><tr><td>(20013 &larr; 00001)</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="5"><sup>14</sup>C<sup>16</sup>O<sub>2</sub></td><td>(01111 &larr; 01101)</td><td>2306 - 2312</td><td>4.33 - 4.34</td><td>CRSS</td><td>Galli et al. (2013)</td></tr><tr><td>(00011 &larr; 00001)</td><td>2190 - 2250</td><td>4.44 - 4.57</td><td>CRDS</td><td>Galli et al. (2011)</td></tr><tr><td>N<sub>2</sub>O</td><td>3ν<sub>1</sub></td><td>6518 - 6578</td><td>1.52 - 1.53</td><td>CRDS</td><td>Liu et al. (2019)</td></tr><tr><td>3ν<sub>1</sub></td><td>6518 - 6578</td><td>1.52 - 1.53</td><td>DAS</td><td>Iwakuni (2022)</td></tr><tr><td>ν<sub>3</sub></td><td>2190 - 2210</td><td>4.52 - 4.57</td><td>DAS</td><td>Knabe et al. (2013)</td></tr><tr><td rowspan="5">CH<sub>4</sub></td><td>ν<sub>3</sub></td><td>2130 - 2270</td><td>4.41 - 4.69</td><td>CRSS</td><td>Ting et al. (2014)</td></tr><tr><td>ν<sub>1</sub></td><td>1250 - 1310</td><td>7.63 - 8.00</td><td>DAS</td><td>AlSaif et al. (2018)</td></tr><tr><td>ν<sub>3</sub></td><td>6015 - 6115</td><td>1.16 - 1.20</td><td>CRDS</td><td>Karllovets et al. (2021, 2022)</td></tr><tr><td>ν<sub>3</sub></td><td>2890 - 3120</td><td>3.21 - 3.46</td><td>CEAS</td><td>Mondelain et al. (2015)</td></tr><tr><td>ν<sub>3</sub></td><td>2890 - 3120</td><td>3.21 - 3.46</td><td>CRSS</td><td>Wang et al. (2021)</td></tr><tr><td>O<sub>2</sub></td><td>(0,0)</td><td>7800 - 7960</td><td>1.26 - 1.28</td><td>CRDS</td><td>Mondelain et al. (2015)</td></tr><tr><td>H<sup>13</sup>CN</td><td>2ν<sub>3</sub></td><td>6390 - 6536</td><td>1.53 - 1.56</td><td>CRSS</td><td>Votava et al. (2022)</td></tr><tr><td>D<sub>2</sub>H<sup>+</sup></td><td>ν<sub>1</sub></td><td>2588 - 2930</td><td>3.41 - 3.86</td><td>NICE-VMS</td><td>Okubo et al. (2011); Abe et al. (2013)</td></tr><tr><td>CHF<sub>3</sub></td><td>ν<sub>5</sub></td><td>1156 - 1160</td><td>8.62 - 8.65</td><td>CRSS</td><td>Kocheril et al. (2018)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>ν<sub>5</sub></td><td>970 - 973</td><td>10.29 - 10.30</td><td>CRSS</td><td>Okubo et al. (2011); Abe et al. (2013)</td></tr><tr><td>Benzene</td><td>ν<sub>11</sub></td><td>675 - 689</td><td>14.5 - 14.8</td><td>DAS</td><td>Lamperti et al. (2020)</td></tr></tbody></table>

terstellar emission spectra rather than for their detection in exoplanetary atmospheres.

**2.1.3.2 Vibrational frequency calculations** The computation of a full ro-vibrational line list for one species can be very time consuming, and often takes years to produce. There has thus been work on computing the vibrational spectra for a large number of species, and then adding rotational sub-structure (for example using software such as PGO-PHER (Western 2017)), in order to indicate where prominent spectral features are expected. Root mean square errors of such computations are typically on the order of 15 - 25cm⁻¹ (Zapata Trujillo & McKemmish 2022b), with higher order computational chemistry or laboratory-derived data required to be incorporated for higher accuracies. There are some notable absorption features in the observed spectra of some exoplanet atmospheres, for example in WASP-39b's atmosphere at 4.56 µm as observed by JWST (Alderson et al. 2023), which have yet to be identified among the species with available ro-vibrational spectra. There is benefit in identifying potential species or types of species which could fit such features, which could then give incentive for more detailed work into the full ro-vibrational spectra. The computation of such vibrational frequencies for large numbers of molecules

is facilitated by studies into the best practice for appropriate model chemistry choices for harmonic frequency calculations, such as Zapata Trujillo & McKemmish (2022b, 2023). VIBFREQ1295 (Zapata Trujillo & McKemmish 2022a) is a database of vibrational frequency calculations. RASCALL (Rapid Approximate Spectral Calculations for ALL) (Sousa-Silva et al. 2019) is an approach which can simulate spectra consisting of approximate band centres and qualitative intensities for a huge number of species. The approximate spectra for a large number of phosphorus-bearing species was computed by Zapata Trujillo et al. (2021), building upon the RASCALL database by using quantum chemistry to improve on the accuracy of the approximate spectra for these species.

In addition, computations are available which focus on the vibrational spectra of nanoclusters, such as (TiO₂)ₙ, which can be important for exoplanet atmosphere models or observations in the IR (Sindel et al. 2023). Vibrational frequencies of other nanoclusters have been computed, such as (VO)ₙ up to n = 10 (Lecoq-Molinos et al. 2024), (VO₂)ₙ up to n = 10 (Lecoq-Molinos et al. 2024), (V₂O₅)ₙ up to n = 4 (Lecoq-Molinos et al. 2024), TiₓOᵧ (Jeong et al. 2000) and (MgO)ₓ (Chen et al. 2014).

<footnote><sup>a</sup>: Assisted with spectroscopic networks</footnote>

<footnote><sup>b</sup>: Hyperfine-resolved</footnote>
<table><caption>**Table 9.** Molecular line lists obtained from comb-referenced spectroscopy measurements using different methods: CRDS – cavity ring down spectroscopy; NICE-OHMS – noise-immune cavity enhanced optical heterodyne molecular spectroscopy; CRSS – comb-referenced saturation spectroscopy, DAS – direct absorption spectroscopy; CEAS – cavity enhanced absorption spectroscopy, NICE-VMS – noise-immune cavity enhanced velocity modulation spectroscopy. The spectral coverage of each is also indicated.</caption><thead><tr><th>Molecule</th><th>Band</th><th>Range (cm<sup>-1</sup>)</th><th>Range (µm)</th><th>Method</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="3">H<sub>2</sub><sup>16</sup>O</td><td>(013 ← 000)</td><td>12 621-12 665</td><td>0.789-0.792</td><td>CRDS</td><td>Chen et al. (2018)</td></tr><tr><td>(101 ← 000)</td><td>7164-7185</td><td>1.391-1.396</td><td>CRDS</td><td>Kassi et al. (2018)</td></tr><tr><td>(200 ← 000)</td><td>7000-7350</td><td>1.36-1.43</td><td>NICE-OHMS<sup>a</sup></td><td>Tóbiás et al. (2020), Diouf et al. (2022)<br>Tóbiás et al. (2024)</td></tr><tr><td>H<sub>2</sub><sup>17</sup>O</td><td>(200 ← 000)<sup>b</sup></td><td>7228-7289</td><td>1.37-1.38</td><td>NICE-OHMS</td><td>Melosso et al. (2021)</td></tr><tr><td>H<sub>2</sub><sup>18</sup>O</td><td>(200 ← 000)</td><td>7000-7350</td><td>1.36-1.43</td><td>NICE-OHMS<sup>a</sup></td><td>Diouf et al. (2021), Tóbiás et al. (2024)</td></tr><tr><td>H<sub>2</sub>O<sup>c</sup></td><td>Several<sup>d</sup></td><td>8041-8633</td><td>1.15-1.24</td><td>CRDS</td><td>Koroleva et al. (2023b)</td></tr><tr><td rowspan="4"><sup>12</sup>C<sup>16</sup>O<sub>2</sub></td><td>(30012 ← 00001)</td><td>6170-6370</td><td>1.57-1.62</td><td>CRDS</td><td>Reed et al. (2021)</td></tr><tr><td>(30013 ← 00001)</td><td></td><td></td><td>CRDS</td><td>Guo et al. (2021)</td></tr><tr><td>(30012 ← 00001)<sup>d</sup></td><td>6170-6370</td><td>1.57-1.62</td><td>CRDS</td><td>Fleurbaey et al. (2023)</td></tr><tr><td>(20012 ← 00001)</td><td>4830-5010</td><td>1.99-2.07</td><td>CRDS</td><td></td></tr><tr><td rowspan="2"><sup>14</sup>C<sup>16</sup>O<sub>2</sub></td><td>(01111 ← 01101)</td><td>2306-2312</td><td>4.33-4.34</td><td>CRSS</td><td>Galli et al. (2013)</td></tr><tr><td>(00011 ← 00001)</td><td>2190-2250</td><td>4.44-4.57</td><td>CRDS</td><td>Galli et al. (2011)</td></tr><tr><td rowspan="5">N<sub>2</sub>O</td><td>3v<sub>1</sub></td><td>6518-6578</td><td>1.52-1.53</td><td>CRDS</td><td>Liu et al. (2019)</td></tr><tr><td>3v<sub>1</sub></td><td>6518-6578</td><td>1.52-1.53</td><td>DAS</td><td>Iwakuni (2022)</td></tr><tr><td>v<sub>3</sub></td><td>2190-2210</td><td>4.52-4.57</td><td>DAS</td><td>Knabe et al. (2013)</td></tr><tr><td>v<sub>3</sub></td><td>2130-2270</td><td>4.41-4.69</td><td>CRSS</td><td>Ting et al. (2014)</td></tr><tr><td>v<sub>1</sub></td><td>1250-1310</td><td>7.63-8.00</td><td>DAS</td><td>AlSaif et al. (2018)</td></tr><tr><td>N<sub>2</sub>O<sup>e</sup></td><td>–<sup>d</sup></td><td>8320-8620</td><td>1.16-1.20</td><td>CRDS</td><td>Karlovets et al. (2021), Karlovets et al. (2022)</td></tr><tr><td rowspan="4">CO</td><td>(7 ← 0)<sup>d</sup></td><td>14300-14500</td><td>0.689-0.699</td><td>CRDS</td><td>Balashov et al. (2023)</td></tr><tr><td>(3 ← 0)</td><td>6170-6420</td><td>1.56-1.62</td><td>CRDS</td><td>Mondelain et al. (2015)</td></tr><tr><td>(3 ← 0)</td><td>6170-6420</td><td>1.56-1.62</td><td>CRDS</td><td>Kowzan et al. (2017)</td></tr><tr><td>(3 ← 0)</td><td>6170-6420</td><td>1.56-1.62</td><td>CRDS</td><td>Wang et al. (2021)</td></tr><tr><td rowspan="3">CH<sub>4</sub></td><td>(4 ← 0)<sup>d</sup></td><td>8206-8465</td><td>1.18-1.22</td><td>CRDS</td><td>Bordet, Kassi &amp; Campargue (2021)</td></tr><tr><td>2v<sub>3</sub></td><td>6015-6115</td><td>1.64-1.66</td><td>CRDS</td><td>Votava et al. (2022)</td></tr><tr><td>v<sub>3</sub></td><td>2890-3120</td><td>3.21-3.46</td><td>CEAS</td><td>Okubo et al. (2011), Abe et al. (2013)</td></tr><tr><td rowspan="2">O<sub>2</sub></td><td>v<sub>3</sub></td><td>2890-3120</td><td>3.21-3.46</td><td>CRSS</td><td>Kocheril et al. (2018)</td></tr><tr><td>B band<sup>d</sup></td><td>14 539-14 550</td><td>0.687-0.688</td><td>CRDS</td><td>Domysławska et al. (2020)</td></tr><tr><td rowspan="2">H<sup>13</sup>CN</td><td>(0,0)<sup>d</sup></td><td>7800-7960</td><td>1.26-1.28</td><td>CRDS</td><td>Fleurbaey et al. (2021)</td></tr><tr><td>2v<sub>3</sub></td><td>6390-6536</td><td>1.53-1.56</td><td>CRSS</td><td>Hrabina et al. (2022)</td></tr><tr><td>D<sub>2</sub>H<sup>+</sup></td><td>v<sub>1</sub></td><td>2588-2930</td><td>3.41-3.86</td><td>NICE-VMS</td><td>Markus, Kocheril &amp; McCall (2019)</td></tr><tr><td>CHF<sub>3</sub></td><td>v<sub>5</sub></td><td>1156-1160</td><td>8.62-8.65</td><td>CRSS</td><td>Vicentini et al. (2020)</td></tr><tr><td>CH<sub>3</sub>OH</td><td>v<sub>5</sub></td><td>970-973</td><td>10.29-10.30</td><td>CRSS</td><td>Santagata et al. (2019)</td></tr><tr><td>Benzene</td><td>v<sub>11</sub></td><td>675-689</td><td>14.5-14.8</td><td>DAS</td><td>Lamperti et al. (2020)</td></tr></tbody></table>

spectra (Sousa-Silva, Petkowski & Seager 2019; Zapata Trujillo & McKemmish 2022a, b, 2023). In such instances, numerous individual lines typically blend into unresolved spectral bands. However, these molecules can still form strong detectable features in atmospheric spectra, and their spectroscopic signatures are required in retrieval frameworks for detection, in addition to improving the retrieval accuracy of planetary characteristics or other atmospheric species. To provide this necessary data, it is common practice to carefully measure experimental absorption cross-sections. These measurements are required to cover the expected temperature and pressure conditions of the appropriate planetary atmosphere, as well as including the appropriate broadening gases (e.g. H₂, He, N₂, etc) at a resolution that provides sufficient details.

Cross-sections are not just restricted to the infrared or visible wavelength regions; many valuable cross-sections which cover the UV region are regularly employed in Earth observations, for example. There are many cross-sections included in the HITRAN data base that cover the UV and visible regions, such as SO₂ and O₃. While this section will mainly discuss infrared and visible absorption cross-sections due to the relevance for *Ariel*, UV absorption cross-sections are also important for exoplanet atmosphere models used to

inform our understanding of observed planets. UV cross-sections also have special continuum features related to photodissociation and photoabsorption effects; see Section 8 where we discuss these separately.

The Pacific Northwest Nation Laboratory (PNNL) produced a large catalogue (Sharpe et al. 2004) of infrared absorption cross-sections for many chemical compounds recorded at 1.0 atm with a Fourier transform spectrometer at temperatures of 5, 25, and 50°C. Species included compounds that were difficult to measure in the laboratory. These cross-sections are no longer available from PNNL directly, but the majority of these measurements are now included as part of the HITRAN data base (Gordon et al. 2022). The HITRAN data base provides experimental absorption cross-sections of over 300 molecules (Kochanov et al. 2019), in addition to the line-by-line molecules described above. HITRAN also regularly expands the available data with each new edition (Gordon et al. 2022).

It should be noted that many chemical compounds have been measured due to signatures appearing in Earth observation measurements. For example, chlorine-containing compounds (e.g. chlorofluorocarbons) are intensely monitored because their reactions in the atmosphere lead to the depletion of stratospheric ozone. Therefore,

<footnote><sup>a</sup>: Assisted with spectroscopic networks; <sup>b</sup>: Hyperfine-resolved; <sup>c</sup>: Six isotopologues; <sup>d</sup>: Intensities provided; <sup>e</sup>: Five isotopologues</footnote>
### 2.1.4 How high-resolution laboratory spectroscopy can help improve the accuracy of theoretically computed line lists

There are several ways in which laboratory spectroscopy can contribute to the data needs of exoplanetary atmospheric studies, some of which are already in active use and some require more investment. The most common and efficient methodology of the production of spectroscopic data is semi-empirical, in which molecular spectra are first measured at given laboratory conditions (temperature, pressures, wavelength range etc), analysed and then inter- or extrapolated to conditions dictated by the retrieval frameworks. A typical example illustrating the need for such extrapolations is that most of the existing experimental molecular spectra have been recorded at, or close to, the ambient atmospheric conditions on Earth, i.e. room temperature and pressure, and for specific spectroscopic ranges dictated by the experimental setup. A typical retrieval procedure, on the other hand, requires a broad range of temperatures, pressures and wavelengths, on dense grids of the corresponding values (for example, pressures between at least $1×10^{-5}$ - 100 bar, and temperatures ~100 K - 3000 K). This is achieved by representing the experimental data in some functional forms, so-called spectroscopic models, of different complexity and extrapolation power.

This is a powerful, well established procedure, which is however very hungry for experimental data. Some molecules have almost no spectra measured, especially those corresponding to extreme conditions such as suggested for the atmospheres of the so-called Lava planets, including $SiO_2$, KOH, NaOH and MgOH (Schaefer et al. 2012; Tennyson & Yurchenko 2017). Apart from the mainstream atmospheric molecules, such as those described in Section 2.1.2.2, with relatively accessible spectra, there is a serious lack of analysed laboratory spectra for a large number of molecules at higher temperatures and lower wavelengths.

The so-called effective Hamiltonians (such as used by CaSDa) based on Taylor-type expansions with respect to the angular momenta with a large set of empirical spectroscopic constants provide very accurate description of the experimental spectra (usually recorded at room temperature) but with rather limited extrapolation power (e.g. to higher temperatures and especially to higher energies). These methods usually benefit from an extensive rotational coverage of individual vibrational bands in a given spectroscopic regions and thus are ideally suitable for the analysis of the FTS-like broad band techniques, as mentioned above. The so-called empirically adjusted *ab initio* techniques (employed by Exo-Mol, ThoReTS and NASA Ames) are based on the empirical refinement of the underlying inter-nuclear *ab initio* spectroscopic properties, e.g. potential energy surfaces (PES). These methods hugely benefit from analysed laboratory data (line positions and energies), ideally with an extensive coverage of the vibrational excitations at the lowest rotational excitations to minimise the coupling between the rotational and vibrational degrees of freedom. Put simply, experimental information on vibrations is especially important to increase the quality of the extrapolation of the empirical model, while the rotational information is more useful for interpolation and benchmarking of the models. These type of empirical techniques are less accurate than effective Hamiltonians when it comes to matching the experiment, but are very powerful when extrapolating to higher temperatures and even higher energies.

The MARVEL (measured active rotation-vibration energy levels) (Furtenbacher et al. 2007) process involves analysing high-accuracy laboratory measured spectra to get out experimentally-determined energy levels. These energy levels are then used in theoretically computed line lists to improve the accuracy of all transitions which involve those levels. In the case of the ExoMol database, the MARVEL process has been applied to molecular line lists for species such as $C_2H_2$ (Chubb et al. 2018a), TiO (McKemmish et al. 2017), $H_2CS$ (Mellor et al. 2023), $C_2$ (Furtenbacher et al. 2016; McKemmish et al. 2020), CaOH (Wang et al. 2020a), $H_2S$ (Chubb et al. 2018b), $NH_3$ (Al-Derzi et al. 2015; Furtenbacher et al. 2020), AlO (Bowesman et al. 2021), $H_2CO$ (Al-Derzi et al. 2021; Germann et al. 2024), $H_3^+$ (Bowesman et al. 2022), OCS (Xu & Tennyson 2023) as well as ongoing efforts to refine the line list of $PH_3$. Due to new laboratory data becoming available, the MARVEL process for improving the accuracy of theoretical line lists need to be assessed periodically. The opacities computed from line lists therefore also ideally need recomputing periodically, as the accuracy and coverage of line lists improve (see Section 4).

Regardless of the method used to improve the accuracy of theoretically computed line lists, their key common feature is the strong dependence on experimental laboratory data. Even the best modern *ab initio* methods, except perhaps of very limited systems, do not have the required quality to be used in atmospheric applications and need to be either completely constructed from scratch, such as for the Effective Hamiltonians, by fitting the corresponding expansion, so-called spectroscopic, parameters or refined, such as for the *ab initio* methods, by fitting the corresponding analytic descriptions of the spectroscopic models to the experimental data.

Our general appeal to the experimental spectroscopists who would like to engage with exoplanetary atmospheric studies is to talk to the atmospheric modelers about their direct needs in terms of the species, temperature and wavelength coverage and also talk to the line list providers about their needs in terms of the vibrational and rotational coverage.

## 2.2 Data used by retrieval codes

Owing to the importance of the line lists for atmospheric retrievals, it would not be an exaggeration to say that all, or close to all, the line lists discussed throughout this section, have already been or are in the process of being included in the main (exo-)planetary retrieval frameworks. It is the usual practice of exoplanetary atmospheric modelers to implement new line lists or important updates into their retrieval programs periodically; this usually involves building molecular opacities in the form of cross-sections or k-tables. Details on opacities used in various retrieval codes can be found in Section 4.

## 2.3 What's being worked on?

(i) ExoMol: at the time of writing, the following line lists are in progress by the ExoMol project (see Section 2.1.1.2), either as new species or improvements/updates to existing line lists; diatomics: OH, PN, CO, CH, CS, $OH^+$, $NO^+$, NiH, CrH, AlF, BH, ZrS; triatomics in IR: $N_2O$, $C_3$, HCN, HOD; triatomics (electronic): HCN; larger polyatomic (IR): $C_2H_2$,