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

Katy L. Chubb1,211footnotemark: 1 Séverine Robert322footnotemark: 2 Clara
<EMAIL_ADDRESS>Sergei N. Yurchenko644footnotemark:
4 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
1University of Bristol  School of Physics  HH Wills Physics Laboratory
Tyndall Avenue  Bristol BS8 1TL  UK
2Centre for Exoplanet Science  University of St Andrews  North Haugh  St
Andrews  KY16 9SS  UK
3Royal Belgian Institute for Space Aeronomy (BIRA-IASB)  Av. Circulaire 3
1180 Uccle  Belgium
4Bard College  Institute of Astrophysics and Space Sciences  30 Campus Rd
Annandale-On-Hudson  NY 12504
5Institute of Astrophysics and Space Sciences  Rua das Estrelas  4150-762
Porto  Portugal
6Department of Physics and Astronomy  University College London  London WC1E
6BT  UK
7Observatoire de Paris  PSL Research University  61  Avenue de l’Observatoire
F-75014 Paris  France
8Lab. ICB  UMR 6303 CNRS / Université de Bourgogne  9 Av. A. Savary  BP 47870
F-21078 Dijon Cedex  France
9Institut UTINAM  UMR CNRS 6213  Université de Franche-Comté  16 Route de Gray
25030 Besançon cedex  France
10Université Paris-Saclay  CNRS  GEOPS  91405  Orsay  France
11LESIA  Paris Observatory  CNRS  PSL Univ  5 place Jules Janssen  92190
Meudon Cedex  France
12Umeå University  Department of Physics  901 87 Umeå  Sweden
13Center for Astrophysics | Harvard & Smithsonian  60 Garden Street  Cambridge  MA 02138  USA
14Space Research Institute  Austrian Academy of Sciences  Schmiedlstrasse 6
8042 Graz  Austria
15TU Graz  Fakultät für Mathematik  Physik und Geodäsie  Petersgasse 16
A-8010 Graz  Austria
16International Atomic Energy Agency  Wagramer Strasse 5  Vienna A-1400
Austria
17Université Paris Cité and Univ Paris Est Creteil  CNRS  LISA  F-75013 Paris
France
18Institute for Molecules and Materials  Radboud University  Heyendaalseweg
135  6525 AJ Nijmegen  Netherlands
19IAPS-INAF  Via Fosso del Cavaliere  100  00133  Rome  Italy
20Université de Reims Champagne-Ardenne  UMR CNRS 7331  BP 1039  F-51687
Reims Cedex 2  France
21Leibniz Institute for Plasma Science and Technology (INP)  Felix-Hausdorff-
Straße 2  17489 Greifswald  Germany
22Fakultät für Physik  Ludwig-Maximilians-Universität München  Scheinerstraße
1  D-81679 München  Germany
23School of Physical Sciences  The Open University  Walton Hall  Milton Keynes
MK7 6AA  UK
24Dipartimento di Fisica  La Sapienza Università di Roma  Piazzale Aldo Moro 5
Roma  00185  Italy
25University of Paris-Saclay and ENS Paris-Saclay  LATMOS  11 bourlevard
d’Alembert  78280 Guyancourt  France
26V.E. Zuev Institute of Atmospheric Optics SB RAS  1  Akademician Zuev Sq
Tomsk  634055 Russia
27Université Paris-Saclay  Universit’e Paris Cit’e  CEA  CNRS  AIM  91191
Gif-sur-Yvette  France
28Space Science and Astrobiology Division  NASA Ames Research Center  Moffett
Field  CA  94035 USA
29University of Oxford  Atmospheric  Oceanic and Planetary Physics  Department
of Physics  Parks Rd  Oxford OX1 3PU  UK
30J. Heyrovský Institute of Physical Chemistry  Czech Academy of Sciences
Dolejškova 2155/3  18223  Prague  Czech Republic
31Institute of Astronomy  KU Leuven  Celestijnenlaan 200D bus 2401  3001
Leuven
32CQE  IMS  Department of Chemical Engineering  Instituto Superior Técnico
Universidade de Lisboa  Portugal
33Instituto de Astrofísica de Andalucía (IAA-CSIC)  Glorieta de la Astronomía
s/n  18008  Granada  Spain
34Institut d’Astrophysique de Paris (CNRS  Sorbonne Université)  98bis Bd
Arago  75014 Paris  France
35Max-Planck-Institut für Sonnensystemforschung  Justus-von-Liebig-Weg 3
37077 Göttingen  Germany
36Division of Geological and Planetary Sciences  California Institute of
Technology  1200 E. California Blvd  Pasadena  CA  91125  USA
37SRON Netherlands Institute for Space Research  Niels Bohrweg 4  2333 CA
Leiden  the Netherlands
38Dipartimento di Fisica e Astronomia  Università degli studi di Padova
Vicolo dell’Osservatorio 3  35122 Padova  Italy
39INAF  Osservatorio Astronomico di Padova  Vicolo dell’Osservatorio 5  35122
Padova  Italy
40Martin A. Fisher School of Physics  Brandeis University  415 South St
Waltham  MA  02453  USA

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

Katy L. Chubb1,211footnotemark: 1 Séverine Robert322footnotemark: 2 Clara
<EMAIL_ADDRESS>Sergei N. Yurchenko644footnotemark:
4 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
1University of Bristol  School of Physics  HH Wills Physics Laboratory
Tyndall Avenue  Bristol BS8 1TL  UK
2Centre for Exoplanet Science  University of St Andrews  North Haugh  St
Andrews  KY16 9SS  UK
3Royal Belgian Institute for Space Aeronomy (BIRA-IASB)  Av. Circulaire 3
1180 Uccle  Belgium
4Bard College  Institute of Astrophysics and Space Sciences  30 Campus Rd
Annandale-On-Hudson  NY 12504
5Institute of Astrophysics and Space Sciences  Rua das Estrelas  4150-762
Porto  Portugal
6Department of Physics and Astronomy  University College London  London WC1E
6BT  UK
7Observatoire de Paris  PSL Research University  61  Avenue de l’Observatoire
F-75014 Paris  France
8Lab. ICB  UMR 6303 CNRS / Université de Bourgogne  9 Av. A. Savary  BP 47870
F-21078 Dijon Cedex  France
9Institut UTINAM  UMR CNRS 6213  Université de Franche-Comté  16 Route de Gray
25030 Besançon cedex  France
10Université Paris-Saclay  CNRS  GEOPS  91405  Orsay  France
11LESIA  Paris Observatory  CNRS  PSL Univ  5 place Jules Janssen  92190
Meudon Cedex  France
12Umeå University  Department of Physics  901 87 Umeå  Sweden
13Center for Astrophysics | Harvard & Smithsonian  60 Garden Street  Cambridge  MA 02138  USA
14Space Research Institute  Austrian Academy of Sciences  Schmiedlstrasse 6
8042 Graz  Austria
15TU Graz  Fakultät für Mathematik  Physik und Geodäsie  Petersgasse 16
A-8010 Graz  Austria
16International Atomic Energy Agency  Wagramer Strasse 5  Vienna A-1400
Austria
17Université Paris Cité and Univ Paris Est Creteil  CNRS  LISA  F-75013 Paris
France
18Institute for Molecules and Materials  Radboud University  Heyendaalseweg
135  6525 AJ Nijmegen  Netherlands
19IAPS-INAF  Via Fosso del Cavaliere  100  00133  Rome  Italy
20Université de Reims Champagne-Ardenne  UMR CNRS 7331  BP 1039  F-51687
Reims Cedex 2  France
21Leibniz Institute for Plasma Science and Technology (INP)  Felix-Hausdorff-
Straße 2  17489 Greifswald  Germany
22Fakultät für Physik  Ludwig-Maximilians-Universität München  Scheinerstraße
1  D-81679 München  Germany
23School of Physical Sciences  The Open University  Walton Hall  Milton Keynes
MK7 6AA  UK
24Dipartimento di Fisica  La Sapienza Università di Roma  Piazzale Aldo Moro 5
Roma  00185  Italy
25University of Paris-Saclay and ENS Paris-Saclay  LATMOS  11 bourlevard
d’Alembert  78280 Guyancourt  France
26V.E. Zuev Institute of Atmospheric Optics SB RAS  1  Akademician Zuev Sq
Tomsk  634055 Russia
27Université Paris-Saclay  Universit’e Paris Cit’e  CEA  CNRS  AIM  91191
Gif-sur-Yvette  France
28Space Science and Astrobiology Division  NASA Ames Research Center  Moffett
Field  CA  94035 USA
29University of Oxford  Atmospheric  Oceanic and Planetary Physics  Department
of Physics  Parks Rd  Oxford OX1 3PU  UK
30J. Heyrovský Institute of Physical Chemistry  Czech Academy of Sciences
Dolejškova 2155/3  18223  Prague  Czech Republic
31Institute of Astronomy  KU Leuven  Celestijnenlaan 200D bus 2401  3001
Leuven
32CQE  IMS  Department of Chemical Engineering  Instituto Superior Técnico
Universidade de Lisboa  Portugal
33Instituto de Astrofísica de Andalucía (IAA-CSIC)  Glorieta de la Astronomía
s/n  18008  Granada  Spain
34Institut d’Astrophysique de Paris (CNRS  Sorbonne Université)  98bis Bd
Arago  75014 Paris  France
35Max-Planck-Institut für Sonnensystemforschung  Justus-von-Liebig-Weg 3
37077 Göttingen  Germany
36Division of Geological and Planetary Sciences  California Institute of
Technology  1200 E. California Blvd  Pasadena  CA  91125  USA
37SRON Netherlands Institute for Space Research  Niels Bohrweg 4  2333 CA
Leiden  the Netherlands
38Dipartimento di Fisica e Astronomia  Università degli studi di Padova
Vicolo dell’Osservatorio 3  35122 Padova  Italy
39INAF  Osservatorio Astronomico di Padova  Vicolo dell’Osservatorio 5  35122
Padova  Italy
40Martin A. Fisher School of Physics  Brandeis University  415 South St
Waltham  MA  02453  USA

###### 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.

33footnotetext<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
##  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 $\mu$m ($\sim$ 1280 - 20,000 cm-1),
with the highest resolving power (R = 100) between 1.95 - 3.9 $\mu$m ($\sim$
2500 - 5100 cm-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 $\mu$m, 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.

Table 1: Summary of Ariel instruments and their wavelength coverage and resolving power R=$\frac{\lambda}{\Delta\lambda}$, 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). Instrument | Wavelength range ($\mu$m) | Wavenumber range (cm-1) | R=$\frac{\lambda}{\Delta\lambda}$
---|---|---|---
VISPhot | 0.5 - 0.6 | 16,667 - 20,0000 |
FGS 1 | 0.6 - 0.81 | 12,346 - 16,667 | Photometric bands
FGS 2 | 0.81 - 1.1 | 9091 - 12,346 |
NIRSpec | 1.1 - 1.95 | 5128 - 9091 | 20
AIRS Ch0 | 1.95 - 3.9 | 2564 - 5128 | 100
AIRS Ch1 | 3.9 - 7.8 | 1282 - 2564 | 30

###  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
online444https://doi.org/10.5281/zenodo.7675743. 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.

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

###  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 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
project555https://github.com/Ariel-data. 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 ($\frac{\lambda}{\Delta\lambda}$ $\gtrsim$ 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. To interpret these 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 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). 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 linelists from some of the
main spectral databases. An approximate temperature up to which the linelist
is considered complete, in terms of completeness of transition data at a given
temperature, is given; either hot ($\geq$ 1000 K) or else assumed to be
roughly Earth-temperature ($\leq$ 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 Spectroscopy666https://spec.jpl.nasa.gov/
and the Cologne database for molecular spectroscopy
(CDMS)777https://cdms.astro.uni-koeln.de/.

Atomic line list data can be obtained from various sources such as the
NIST888https://physics.nist.gov/PhysRefData/ASD/lines_form.html (Kramida et
al., 2013) and
Kurucz999https://lweb.cfa.harvard.edu/amp/ampdata/kurucz23/sekur.html;
http://kurucz.harvard.edu/atoms.html (Kurucz, 2017) databases, and the Vienna
atomic line database (VALD3)101010http://vald.astro.uu.se (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.

Table 3: An overview of some line list databases used by the (exo)planetary
atmosphere community.

Database | Type of data | Reference | Link
---|---|---|---
CaSDa | Theoretical line lists up to high temperatures | Richard et al. (2020, 2024) | https://vamdc.icb.cnrs.fr
ExoMol | Theoretical line lists up to high temperatures | Tennyson et al. (2020) | https://exomol.com
GEISA | Accurate line lists for terrestrial conditions | Jacquinet-Husson et al. (2016); Delahaye et al. (2021) | https://geisa.aeris-data.fr
HITEMP | Line lists up to high temperatures | Rothman et al. (2010) | https://hitran.org/hitemp
HITRAN | Accurate line lists for terrestrial conditions | Gordon et al. (2022) | https://hitran.org
Kurucz | Semi-empirical line lists up to high temperatures | Kurucz (1995) | http://kurucz.harvard.edu/molecules.html
MoLLIST | Laboratory line lists up to high temperatures | Bernath (2020) | https://bernath.uwaterloo.ca/molecularlists.php
NASA Ames | Semi-empirical line lists up to high temperatures |  e.g. Huang et al. (2023a) | http://huang.seti.org
NIST | Atomic line lists up to high temperatures | Kramida et al. (2013) | https://physics.nist.gov/PhysRefData/ASD/lines_form.html
S&MPO | Spectroscopy and Molecular Properties of Ozone | Tyuterev et al. (2021) | http://smpo.iao.ru
TheoReTs | Theoretical line lists up to high temperatures | Rey et al. (2016b) | https://theorets.tsu.ru
VALD3 | Atomic line lists up to high temperatures | Ryabchikova et al. (2015) | http://vald.astro.uu.se

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 $\geq$ 1000 K are labelled with (H), and all others are generally
assumed to be complete up to $\sim$ 500 K. A few exceptions are noted in the
text.

Molecule |  $\lambda$ range | Database
---|---|---
AlCl | IR, Vis, UV | Ex(H),Ku(H),Mo(H)
AlF | IR, Vis, UV | Ex(H),Ku(H),Mo(H)
AlH | IR, Vis, UV | Ex(H),Ku(H),Mo(H)
AlO | IR, Vis, UV | Ex(H)
AsH3 | IR | Ex
BeH | IR, Vis, UV | Ex(H)
C2 | IR, Vis, UV | Ex(H),Ku(H)
C2H2 | IR | Ex(H),HI
C2H4 | IR | Ex,HI,Th, SDa
C2H6 | IR | HI
C2N2 | IR | HI
C4H2 | IR | HI
C3 | IR | Ex(H)
CaF | IR, Vis, UV | Ex(H),Mo(H)
CaH | IR, Vis, UV | Ex(H),Mo(H)
CaO | IR, Vis, UV | Ex(H)
CaOH | IR,Vis | Ex(H)
CF4 | IR | HI,SDa,Th
CH | IR, Vis, UV | Ex(H),Ku(H),Mo(H)
CH+ | IR, Vis, UV | Ex(H)
CH2 | IR | Th(H)
CH3 | IR | Ex(H),Th(H)
CH3Br | IR | HI
CH3Cl | IR | Ex(H),HI,SDa,Th
CH3CN | IR | HI
CH3F | IR | Ex,HI,Th
CH3I | IR | HI
CH3OH | IR | HI
CH4 | IR, NIR | Ex(H),HI,HT(H),Th(H),SDa(H)
ClO | IR | HI
ClONO2 | IR | HI
CN | IR, Vis, UV | Ex(H),Ku(H),Mo(H)
CO | IR | Ex(H),HI,HT(H)
CO2 | IR | Am,Ex(H),HI,HT(H)
COCl2 | IR | HI
COF2 | IR | HI
CP | IR | Ex(H)
CrH | NIR | Ex(H),Mo(H)
CS | IR | Ex(H),HI
CS2 | IR | Am,HI
FeH | NIR | Ex(H),Mo(H)
GeH4 | IR | HI,SDa,Th
H2 | IR, Vis, UV | Ex(H),HI(H)
H2CO | IR | Ex(H),HI,Th
H2CS | IR | Ex(H)
H2O | IR | Ex(H),HI,HT(H)
H2O2 | IR | Ex(H),HI
H2S | IR | Ex(H),HI
H${}_{3}^{+}$ | IR | Ex(H)
H3O+ | IR | Ex(H)
HBr | IR | Ex(H),HI(H)
HCl | IR | Ex(H),HI(H)
HCN | IR | Ex(H),HI
HC3N | IR | HI
HCOOH | IR | HI
HDO | IR | Ex(H),HI
HD+ | IR | Ex(H)
HeH$+$ | IR | Ex(H)
HF | IR | Ex(H),HI(H)
HI | IR | Ex(H),HI(H)
HNO3 | IR | Ex,HI

Molecule |  $\lambda$ range | Database
---|---|---
HO2 | IR | HI
HOBr | IR | HI
HOCl | IR | HI
KCl | IR | Ex(H)
KF |  | Ex(H),Mo(H)
KOH | IR | Ex(H)
LaO | Vis,UV | Ex(H),Mo(H)
LiCl | IR | Ex(H),Mo(H)
LiF | IR | Ex(H),Mo(H)
LiH | IR | Ex(H)
LiH+ | IR | Ex(H)
LiOH | IR | Ex(H)
MgF | IR, Vis, U | Ex(H),Mo(H)
MgH | IR, Vis, U | Ex(H),Mo(H)
MgO | IR, Vis, U | Ex(H)
N2 | IR,UV | Ex(H),HI
N2O | IR | Am,Ex(H),HI,HT(H)
NaF |  | Ex(H),Mo(H)
NaH | IR, Vis, UV | Ex(H)
NaCl | IR | Ex(H)
NaO | IR, Vis, UV | Ex(H)
NaOH | IR | Ex(H)
NF3 | IR | HI,Th
NH | IR, Vis, U | Ex(H),Ku(H),Mo(H)
NH3 | IR | Ex(H),HI
NO | IR, Vis, U | Ex(H),HI,HT(H)
NO+ | IR | HI
NO2 | IR | HI,HT(H)
NS | IR | Ex(H)
O2 | IR, Vis, UV | HI
O3 | IR | HI,SM
OCS | IR | Am,Ex(H),HI
OH | IR, Vis, UV | Ex(H),HI,HT(H),Mo(H)
OH+ | IR, Vis, UV | Ex(H),Mo(H)
PH | IR, Vis, UV | Ex(H)
PH3 | IR | Ex(H),HI,Th(H)
PN | IR | Ex(H)
PO | IR | Ex(H)
PS | IR | Ex(H)
S2 | UV | HI
ScH | IR, Vis, UV | Ex(H)
SF6 | IR | HI,SDa,Th
SH | IR, Vis, UV | Ex(H),Mo(H)
SiF4 | IR | SDa
SiH | IR, Vis, UV | Ex(H),Ku(H)
SiH2 | IR | Ex(H)
SiH4 | IR | Ex(H),Th,SDa
SiO | IR, Vis, UV | Ex(H),Ku(H)
SiO2 | IR | Ex(H)
SiH | IR, Vis, UV | Ex(H)
SiS | IR | Ex(H)
SO | IR, Vis, UV | Ex(H),HI
SO2 | IR | Am,Ex(H),HI
SO3 | IR | Ex(H),HI
TiH | Vis | Ex(H),Mo(H)
TiO | IR, Vis, UV | Ex(H),Mo(H),Ku(H)
VO | IR, Vis, UV | Ex(H)
YO | IR, Vis, UV | Ex(H)
ZnO | IR, Vis, UV | Ex(H)
ZrO | IR, Vis, UV | Ex(H)

Databases: 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.
$\lambda$ ranges: UV = 0.1 - 0.4 $\mu$m; Vis = 0.4 - 0.8 $\mu$m; IR $\geq$ 0.8
$\mu$m.

####  2.1.1 Descriptions of molecular databases

##### CaSDa

The CaSDa (Calculated Spectroscopic Databases)
databases111111https://vamdc.icb.cnrs.fr (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 be 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 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.

Table 5: Calculated molecular absorption lines in the CaSDa databases. HITRAN ID | Molecule | DB name | Isotopologues | Total nb. of lines | Relevant for Ariel
---|---|---|---|---|---
06 | CH4 | MeCaSDa | 3 | 12,988,898 | *
24 | CH3Cl | ChMeCaSDa | 2 | 12,152 |
30 | SF6 | SHeCaSDa | 4 | 491,500 |
38 | C2H4 | ECaSDa | 1 | 96,397 | *
42 | CF4 | TFMeCaSDa | 1 | 258,208 | *
52 | GeH4 | GeCaSDa | 5 | 60,878 | *
– | RuO4 | RuCaSDa | 9 | 30,205 |
– | SiF4 | TFSiCaSDa | 3 | 210,401 | *
– | UF6 | UHeCaSDa | 8 | 110,129 |
– | SiH4 | SiCaSDa | 3 | 20,090 | *
Figure 1: Comparison of 12CH4 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).

##### ExoMol

ExoMol121212www.exomol.com is a provider of the molecular131313Also atomic
from 2023 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 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 $R\leq 1000$ (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-1), total degeneracy, the total angular momentum, energy
uncertainty (cm-1), 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: $i\;\;j\;\;A_{ij}$, 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.

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.

Figure 2: ExoMol Spectral Atlas (Tennyson & Yurchenko, 2018): Cross-sections
of SO2 computed with the ExoMol line ExoAmes (Underwood et al., 2016).

##### 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 HITRANonline141414www.hitran.org. 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.

HITRAN |  | Broadening Parameters
---|---|---
ID | Molecule | H2 | He | H2O | CO2
1 | H2O | $-$ | $-$ | Self | $-$
2 | CO2 | T22 | T22 | T19 | T22
4 | N2O | $-$ | T22 | T19 | T22
5 | CO | T22 | T22 | T19 | T22
6 | CH4 | $-$ | $-$ | T19 | $-$
7 | O2 | $-$ | $-$ | T19 | $-$
9 | SO2 | W16 | W16 | $-$ | D18
11 | NH3 | W16 | W16 | T19 | W16
13 | OH | T22 | T22 | $-$ | $-$
14 | HF | W16 | W16 | $-$ | W16
15 | HCl | W16 | W16 | $-$ | W16
19 | OCS | T22 | T22 | $-$ | L20
20 | H2CO | T22 | T22 | $-$ | T22
23 | HCN | T22 | T22 | $-$ | $-$
26 | C2H2 | W16 | W16 | $-$ | W16
28 | PH3 | T22 | T22 | $-$ | $-$
31 | H2S | T22 | T22 | T19 | T22
45 | H2 | Self | $-$ | $-$ | $-$
52 | GeH4 | T22 | $-$ | $-$ | $-$
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).

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),
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, 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 ($\gtrsim$
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 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.

##### 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 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., 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 online151515https://huang.seti.org/
and https://data.nas.nasa.gov/ai3000k.

##### 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
2016161616https://theorets.tsu.ru/ and https://theorets.univ-reims.fr/. For
the construction of accurate variationally-computed molecular line lists
allowing a complete description of the main spectral features, highly-
optimised 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: $\nu_{ij}$,
$S_{ij}$, $E_{low}$. 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 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 magnitude
(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 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 anovel 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. However,
the experimental conditions of these 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 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 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).

##### 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 $\mu$m 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).

Figure 3: Measured spectra of CO2 at different temperatures and pressures
relevant to the atmosphere of Venus, from Stefani et al. (2013).

##### 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 techniques and molecules
currently being investigated for exoplanetary applications. In particular, we
focus on the spectral region covered by Ariel at elevated temperatures, due to
the atmospheric temperatures found in the potential proposed exoplanet target
lists (Edwards et al., 2019a; Edwards & Tinetti, 2022). Laboratory studies at
high temperatures, i.e. above room temperatures and typically up to $\sim$
1000 K - 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, 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 ($\lesssim$ 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., $\Delta\nu$
$<$ 1.0$\times$10-6 cm-1). More recently, frequency combs have enabled highly
accurate spectroscopic studies to be acquired over moderately large spectral
regions, which can now include whole vibrational bands. For example, comb
spectroscopy has been used for measurements of high-temperature spectra of H2O
(Schroeder et al., 2017; Rutkowski et al., 2018), CH4 (Malarich et al., 2021),
and CO2 (Cole et al., 2023) in the 6250–7570 cm-1 range. Water spectra
measured in a pre-mixed methane/air flat flame (Rutkowski et al., 2018) were
assigned using the MARVELised POKAZATEL line list, while H2O (Schroeder et
al., 2017) and CH4 (Malarich et al., 2021) spectra measured in a range of
temperatures and sub-atmospheric pressures were used to assess the accuracy of
current editions of HITRAN and HITEMP databases. The CO2 spectra were measured
at pressures up to 25 bar to test and improve line mixing models and their
temperature dependence (Cole et al., 2023). Another development relevant for
high-temperature applications is the optical-optical double resonance
spectroscopy with continuous-wave pump and comb probe, which allows
measurement and assignment of hot-band transitions with sub-Doppler resolution
without the need to heat the sample (Foltynowicz et al., 2021b; Silva de
Oliveira et al., 2024). This technique has so far been used to measure and
assign hot band transitions in the 3$\nu$3 $\leftarrow$ $\nu$3 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 for more details on frequency comb spectroscopy.

Broadband FTS measurements of high-temperature gases enclosed in a heated tube
cell (up to $\sim$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). 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
($\sim$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 (Es-sebbar & 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).

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).

##### 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 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 room
temperature line lists have already been used to update the databases, namely
the $\nu_{4}$ band region (3000–3160 cm-1) of CH3I (Sadiek et al., 2020) and
the $\nu_{1}$+$\nu_{3}$ band region (2110–2200 cm-1) of CS2 (Karlovets et al.,
2020) were used in updates to the HITRAN2020 database (Gordon et al., 2022),
and the $\nu_{6}$ and $\nu_{4}$ band region (1250–1380 cm-1) of H2CO measured
by Germann et al. (2024) was used to improve the accuracy of the ExoMol line
list for H2CO (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 (CH3NO2), naphtalene (C10H8), adamantane (C10H16), and
hexamethylenetetramine (C6N4H12) (Spaun et al., 2016), and vinyl bromide
(CH2CHBr) (Changala et al., 2016) in the 2850–3070 cm-1 range, as well as the
buckminster fullerene (C60) in the 1180–1190 cm-1 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+ 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 CH2OO Criegee intermediate (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$\leftarrow$0 and 4$\leftarrow$0 bands of CO (Mondelain et al., 2015) and the
$\nu_{3}$ 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 $\mu$m band of O2.

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. Molecule | Range [cm-1] | Range [$\mu$m] | Method | T [K] | Reference
---|---|---|---|---|---
H2O | 6800–7200 | 1.39 - 1.47 | DCS | 296-1300 | Schroeder et al. (2017)
| 6250–6670 | 1.50 - 1.60 | CE FTS | 1950 | Rutkowski et al. (2018)
CO2 | 5064–5126 | 1.95 - 1.97 | CE Vernier | RT | Siciliani de Cumis et al. (2018)
| 6800–7000 | 1.43 - 1.47 | DCS | 495-977 | Cole et al. (2023)
N2O | 1250–1310 | 7.63 - 8.00 | FTS | RT | Hjältén et al. (2021)
CO | 6310–6365 | 1.57 - 1.58 | CE VIPA | RT | Kowzan et al. (2017)
CH4 | 2900–3050 | 3.28 - 3.45 | DCS | RT | Baumann et al. (2011)
| 5870–6130 | 1.63 - 1.70 | DCS | RT | Zolot et al. (2013)
| 6770–7570 | 1.32 - 1.48 | DCS | 296-1000 | Malarich et al. (2021)
| 5900-6100 | 1.64 - 1.69 | OODR | 111 | Foltynowicz et al. (2021a)
|  |  |  | RT | Silva de Oliveira et al. (2024)
13CH4 | 1250–1380 | 7.25 - 8.00 | FTS | RT | Germann et al. (2022)
14CH4 | 2910–3110 | 3.22 - 3.44 | PAS | RT | Karhu et al. (2019)
H2CO | 1250–1380 | 7.25 - 8.00 | FTS | RT | Germann et al. (2024)
H13CN | 6390–6535 | 1.53 - 1.56 | DCS | RT | Coddington et al. (2008)
C2H2 | 6430–6630 | 1.51 - 1.56 | DCS | RT | Zolot et al. (2013)
CH3I | 2930–3160 | 3.16 - 3.41 | FTS | RT | Sadiek et al. (2020)
|  |  |  |  | Hjältén et al. (2023)
CS2 | 2110–2200 | 4.55 - 4.74 | DCS | RT | Karlovets et al. (2020)
HfF+ | 11500–13000 | 0.77 - 0.87 | CE VIPA | 823 | Cossel et al. (2012)
CH3NO2 | 2940–3090 | 3.24 - 3.40 | CE FTS | 10-20 | Spaun et al. (2016)
CH2CHBr | 3023–3033 | 3.30 - 3.31 | CE FTS | 10-20 | Changala et al. (2016)
DOCO | 2380–2750 | 3.64 - 4.20 | CE FTS | RT | Bui et al. (2018)
C60 | 1180–1190 | 8.40 - 8.47 | CE FTS | 150 | Changala et al. (2019)
CH2OO | 1217–1287 | 7.77 - 8.22 | VIPA | RT | Luo (2020)
CH2Br2 | 2960–3120 | 3.21 - 3.38 | FTS | RT | Sadiek et al. (2023)
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. Molecule | Band | Range [cm-1] | Range [$\mu$m] | Method | Reference
---|---|---|---|---|---
H${}_{2}^{16}$O | (013 $\leftarrow$ 000) | 12,621 - 12,665 | 0.789 - 0.792 | CRDS | Chen et al. (2018)
| (101 $\leftarrow$ 000) | 7164 - 7185 | 1.391 - 1.396 | CRDS | Kassi et al. (2018)
| (200 $\leftarrow$ 000) | 7000 - 7350 | 1.36 - 1.43 | NICE-OHMSa | Tóbiás et al. (2020); Diouf et al. (2022)
H217O | (200 $\leftarrow$ 000)b | 7228 - 7289 | 1.37 - 1.38 | NICE-OHMS | Melosso et al. (2021)
H218O | (200 $\leftarrow$ 000) | 7000 - 7350 | 1.36 - 1.43 | NICE-OHMSa | Diouf et al. (2021)
Six H2O isotopologues | Several | 8041 – 8633 | 1.15 - 1.24 | CRDS | Koroleva et al. (2023)
12C16O2 | (30012 $\leftarrow$ 00001) | 6170 – 6370 | 1.57 - 1.62 | CRDS | Reed et al. (2021)
| (30013 $\leftarrow$ 00001) |  |  |  |
| (30012 $\leftarrow$ 00001) | 6170 – 6370 | 1.57 - 1.62 | CRDS | Guo et al. (2021)
| (20012 $\leftarrow$ 00001) | 4830 – 5010 | 1.99 - 2.07 | CRDS | Fleurbaey et al. (2023)
| (20013 $\leftarrow$ 00001) |  |  |  |
| (01111 $\leftarrow$ 01101) | 2306 – 2312 | 4.33 - 4.34 | CRSS | Galli et al. (2013)
14C16O2 | (00011 $\leftarrow$ 00001) | 2190 – 2250 | 4.44 - 4.57 | CRDS | Galli et al. (2011)
N2O | 3$\nu_{1}$ | 6518 - 6578 | 1.52 - 1.53 | CRDS | Liu et al. (2019)
| 3$\nu_{1}$ | 6518 - 6578 | 1.52 - 1.53 | DAS | Iwakuni (2022)
| $\nu_{3}$ | 2190 – 2210 | 4.52 - 4.57 | DAS | Knabe et al. (2013)
| $\nu_{3}$ | 2130 - 2270 | 4.41 - 4.69 | CRSS | Ting et al. (2014)
| $\nu_{1}$ | 1250 - 1310 | 7.63 - 8.00 | DAS | AlSaif et al. (2018)
Several N2O isotopologues | - | 8320 – 8620 | 1.16 - 1.20 | CRDS | Karlovets et al. (2021, 2022)
CO | (3 $\leftarrow$ 0) | 6170 - 6420 | 1.56 - 1.62 | CRDS | Mondelain et al. (2015)
| (3 $\leftarrow$ 0) | 6170 - 6420 | 1.56 - 1.62 | CRDS | Wang et al. (2021)
| (4 $\leftarrow$ 0) | 8206 - 8465 | 1.18 - 1.22 | CRDS | Mondelain et al. (2015)
CH4 | 2$\nu_{3}$ | 6015 – 6115 | 1.64 - 1.66 | CRDS | Votava et al. (2022)
| $\nu_{3}$ | 2890 - 3120 | 3.21 - 3.46 | CEAS | Okubo et al. (2011); Abe et al. (2013)
| $\nu_{3}$ | 2890 - 3120 | 3.21 - 3.46 | CRSS | Kocheril et al. (2018)
O2 | (0,0) | 7800 – 7960 | 1.26 - 1.28 | CRDS | Fleurbaey et al. (2021)
H13CN | 2$\nu_{3}$ | 6390 – 6536 | 1.53 - 1.56 | CRSS | Hrabina et al. (2022)
D2H+ | $\nu_{1}$ | 2588 – 2930 | 3.41 - 3.86 | NICE-VMS | Markus et al. (2019)
CHF3 | $\nu_{5}$ | 1156 - 1160 | 8.62 - 8.65 | CRSS | Vicentini et al. (2020)
CH3OH | $\nu_{5}$ | 970 - 973 | 10.29 - 10.30 | CRSS | Santagata et al. (2019)
Benzene | $\nu_{11}$ | 675 - 689 | 14.5 - 14.8 | DAS | Lamperti et al. (2020)

####  2.1.3 Alternative parameterisations

##### 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).

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 $\sim$2500–5000 cm-1 ($\sim$2 - 4 $\mu$m) 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 $\sim$ 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
sufide (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)171717https://www.astrochem.org/pahdb/, offering
extensive data on thousands of PAHs, although primarily for the identification
within interstellar emission spectra rather than for their detection in
exoplanetary atmospheres.

##### 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 PGOPHER
(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 $\mu$m 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), TixOy (Jeong
et al., 2000) and (MgO)x (Chen et al., 2014).

####  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$\times$10-5 \-
100 bar, and temperatures $\sim$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 SiO2, 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, 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 ExoMol, 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 C2H2 (Chubb et al., 2018a), TiO (McKemmish et al., 2017),
H2CS (Mellor et al., 2023), C2 (Furtenbacher et al., 2016; McKemmish et al.,
2020), CaOH (Wang et al., 2020a), H2S (Chubb et al., 2018b), NH3 (Al-Derzi et
al., 2015; Furtenbacher et al., 2020), AlO (Bowesman et al., 2021), H2CO (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 PH3. Due to new laboratory data becoming available, the MARVEL process
for improving the accuracy of theoretial 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?

  1. 1.

ExoMol: at the time of writing, the following line lists are in progress by
the ExoMol project (see Section 2.1.1), 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: N2O, C3, HCN, HOD;
triatomics (electronic): HCN; larger polyatomic (IR): C2H2, C2H6. MARVEL
studies for N2O isotopologues (see Tennyson et al. (2024) for
14N${}_{2}^{16}$O), CO2 (see Ibrahim et al. (2024); Alatoom et al. (2024), CO,
HCN/HNC, HCO+, BH and 15NH3 are being performed as well as updates to 14NH3,
HCCH, and inevitably, water.

  2. 2.

TheoReTS: line lists for several species including CH2, CH3, NH3, H2CCN,
H2NCN, CH3Cl, C3H4, H2O2, CCl4, CH3CN or C2H6 are being worked on, and will be
gradually uploaded to the TheoReTS database (see Section 2.1.1).

  3. 3.

CaSDa: the CaSDa database is working on producing new data for the existing
species listed in Table 5, including new bands and new isotopologues (e.g. for
CH3D). They also plan to develop new line lists for species such as SiH4 and
C3H6O3 (see Section 2.1.1).

  4. 4.

NASA Ames: line lists for sulphur-bearing species OCS and CS2 (see Section
2.1.1).

  5. 5.

HITRAN and HITEMP: Work toward the next edition of the HITRAN database is
underway, which will include works highlighted in the HITRAN2020 paper (Gordon
et al., 2022) and additional recent literature. Examples include expanding the
3800-4800 cm-1 region of NH3, the addition of new molecules

  6. 6.

Non-LTE conditions: although most studies of exoplanet atmospheres assume
species to be in local thermodynamic equilibrium (LTE), effects arising from
non-LTE conditions are known to be important in Earth’s upper atmosphere, as
well as in the atmospheres of other Solar System planets. In the most accurate
treatment, non-LTE radiative transfer calculations determine the populations
of all the atomic and molecular states involved by considering the relevant
species’ rates with respect to radiative decay and collisional excitation, de-
excitation as well as potentially ionization and other processes (Wright et
al., 2022). However, complete data sets are rarely available for this purpose;
even for the Non-LTE of H atoms, some of the collisional data are not so well
known. In particular, data for collisions of H atoms with heavy particles
(atoms/molecules) are lacking (Muñoz & Schneider, 2019). Studies such as
Wright et al. (2022) are working towards improving data and models for non-LTE
effects in exoplanet atmospheres. An upcoming paper (García Muñoz et al.,
Icarus, 2024, in review) also considers non-LTE effects and emphasises the
importance of H2O-H2O excitation collisions, especially for the vibrational
modes of the molecule.

  7. 7.

Vibrational modes of molecular clusters: vibrational spectra from DFT
calculations are in progress for species such as (TiO)n clusters up to $n$ =
10 and (SiO)n clusters up to $n$ = 20 (Lecoq-Molinos, in prep.).

  8. 8.

Quantum computing approaches: ab initio line list parameters are currently
calculated using modern high-performance computers, particularly crucial for
line lists containing millions to billions of transitions. However, the
algorithms used can become computationally intensive and time consuming,
scaling with the complexity of the molecule and temperature coverage. Quantum
computers could be an alternative solution, even though fault-tolerant quantum
computers are unlikely to be available in the immediate future. Variational
Quantum Algorithms (VQAs) and, in particular, Variational Quantum Eigensolvers
(QVEs) are promising class of algorithms to estimate the eigenstates and the
corresponding eigenvalues of a given Hamiltonian (Cerezo et al., 2020). This
kind of technology demonstrates the potential, from a theoretical point of
view, to describe the electronic structure of complex molecules faster. In the
near future, a quantum speedup would be ideal to describe precise line lists
(Innan et al., 2023).

###  2.4 Data needs: What’s missing and urgent?

  1. 1.

Species occurring in JWST studies: the recent potential detection of CS2 in
the exoplanetary atmosphere of TOI-270d (Holmberg & Madhusudhan, 2024; Benneke
et al., 2024) is an example of molecules requiring improvement of the spectral
coverage of associated molecular data. SO2 was recently observed in the
atmosphere of hot gas giant exoplanet WASP-39 b (Tsai et al., 2023; Powell et
al., 2024), with theoretical studies such as Janssen et al. (2023) predicting
the importance of sulphur species in hot rocky exoplanet atmospheres also.
These studies highlight the need for line lists of sulphur species such as CS2
up to high temperatures.

  2. 2.

Ti- and V-bearing species: Hoeijmakers et al. (2020) predict significant
concentrations of gas-phase TiO2, VO2, and TiS in the atmosphere of hot
Jupiter exoplanet WASP-121b. These could be important absorbers which
currently do not have available accurate ro-vibrational line lists.

  3. 3.

Species relevant to lava planets: recent studies suggested that modelling the
atmospheric properties of hot-Super Earth (lava) exoplanets require different
types species to be considered, including KOH, NaOH, SiO2, CaOH, FeO, MgO,
MgOH (Schaefer et al., 2012; Tennyson & Yurchenko, 2017; Mahapatra et al.,
2017). There have therefore been calls for line lists for these species
spanning the IR and visible spectral region. We note these calls have been
somewhat addressed and there are now available line lists from ExoMol for KOH
and NaOH (Owens et al., 2021), SiO2 (Owens et al., 2020), CaOH (Owens et al.,
2022b), MgO (Li et al., 2019). Theoretically, FeO is particularly challenging;
there are more than fifty low-lying electronic states (Sakellaris et al.,
2011; Tennyson & Yurchenko, 2017).

  4. 4.

Carbon and hydrocarbon species: for example, C3 which can be important for
high-temperature carbon atmospheres (Aringer et al., 2009) and for which an
ExoMol line list is nearing completion (Lynas-Gray et al., 2024), or C4H which
is considered to be important in the upper atmosphere of low-metallicity
objects (Bilger et al., 2013). Martin-Drumel et al. (2023) report recent
laboratory work on the infrared spectra of C3, with a combined fit of
available infrared and optical laboratory data performed using the PGOPHER
(Western, 2017) package. Allene and propyne, CH3C2H, are isomers of one
another which have both been detected on Titan (Lombardo et al., 2019; Nixon
et al., 2013). Propene has also been observed on Earth (Blake et al., 1996),
and is expected on Saturn (Moses et al., 2000). There are some known cross-
sections for propene (Bernath et al., 2023), including some hosted by the
HITRAN database (Sung et al., 2018), but not a line list.

  5. 5.

PAHs: can be important for Earth and Titan-like atmospheres (López-Puertas et
al., 2013). As previously mentioned, one of the main sources of PAH cross-
sections is the NASA Ames PAH database (Boersma et al., 2014; Bauschlicher et
al., 2018; Mattioda et al., 2020)181818https://www.astrochem.org/pahdb/, which
is tailored for characterising species in the cold temperatures of the ISM. To
be able to fully comprehend the abundance and role of PAHs on exoplanets,
there is a need for new PAH opacities to be calculated or measured over a
broad parameter space of environmental conditions and easily implementable for
retrieval applications. This necessity extends beyond the infrared spectrum,
as the availability of temperature-dependent UV cross-sections is quite
limited (see Section 8 for the availability of UV PAH photionisation and
photoabsorption cross-sections).

  6. 6.

Species relevant to Archean atmospheres: another special type of exoplanetary
atmosphere with special data requirements are archean atmospheres,
necessitating line lists for species including HC3N (Rimmer et al., 2019,
2021).

  7. 7.

Molecular ions: Bourgalais et al. (2020) performed laboratory experiments to
help identify ions observable by Ariel in the upper atmospheres of sub-
Neptunes. Their results pointed towards H3O+ and H${}_{3}^{+}$ being the most
promising. Partly as a consequence of this study ExoMol provides line lists
for H3O+ (Yurchenko et al., 2020) and H${}_{3}^{+}$ (Mizus et al., 2017;
Bowesman et al., 2023). The ExoMol database also provides lines lists for a
number of other ions including CH+ (Pearce et al., 2024), OH+ Hodges & Bernath
(2017); Hodges et al. (2018) and HeH+ (Amaral et al., 2019). Other potentially
important ions for which there are no suitable line lists at present include
HCO+, N2H+ and H2O+, as well as NO+ which is the dominant molecular ion in the
Earth’s ionosphere.

  8. 8.

Radicals: such as OH, HO2, C2H, CH2, C3H3, NH2, N2H3 are known to be important
on Earth (Seinfeld & Pandis, 2016), Mars (McElroy & Donahue, 1972), Titan
(Wilson & Atreya, 2004), and other planetary atmospheres (Catling & Kasting,
2017).

  9. 9.

Line lists extending into the UV: for all major species such as, H2O, CO2, CO,
OH, CH4, HCN, N2, NH3, C2H2, C2H4, C2H6, H${}_{3}^{+}$, H${}_{2}^{+}$, H3O+,
OH+, SO, SH, H2S, SO2, OCS, S2, CS. See Section 8 for further discussion on UV
photoabsorption and photodissociation data.

  10. 10.

Isotopologues: Very recently Lew et al. (2024) used JWST to detect
isotopologues of CO. Similar studies have been performed on cool stars from
the ground (Pavlenko et al., 2020b, a); such isotope-resolved studies have the
potential to provide a lot of extra information about atmospheres. Some atoms
have more than one isotope with relatively large terrestrial abundances, e.g.
Cl is 75% 35Cl and 25% 37Cl. In other cases, isotopic abundances can be very
different from Solar abundances, e.g. Mg and C. The importance of H means that
even if deuterium (D) is a minor fraction, D containing molecules such HD, HOD
and CH3D can be highly abundant. We note that all these species have different
symmetry to the parent (unsubstituted) molecule which means that the spectra
of the two species differ significantly. The ExoMol data base provides line
lists for HOD (Voronin et al., 2010) and the weak IR spectrum of HD (Amaral et
al., 2019), while CH3D has been considered by Theorets (Rey et al., 2014b).
Lines for isotopically subsituted species which do not break their symmetry
are straight forward to compute given a spectroscopic model for the parent
molecule, and this done routinely by ExoMol; methods to improve the accuracy
of these line lists have been developed (Polyansky et al., 2017; McKemmish et
al., 2024). A list of natural (terrestrial) abundances of various species
included in the HITRAN database can be found
online191919https://hitran.org/docs/iso-meta/, as well as elemental isotopic
compositions from NIST202020http://physics.nist.gov/Comp.

  11. 11.

Vibrational modes of molecular clusters: Köhn et al. (2021) point out that the
onset of cloud formation may be observable through vibrational bands of
(TiO2)4, (TiO2)5, and (TiO2)6, potentially via the Mid-Infrared Instrument on
JWST or the Extremely Large Telescope’s mid-IR imager, but more complete line-
list data are required first. We note that the full quantum chemical
computation of line lists for such large clusters is challenging, and so may
require computations of vibrational frequencies only, at least as a starting
point. There is some discussion on this in Section 2.1.3. We note some
vibrational data for TiO2 nanoclusters have recently been computed (Sindel et
al., 2023).

##  3 Line shapes: molecular and atomic

###  3.1 Theoretical approaches to line-shape parameters: Molecules

The Voigt profile. In order to simulate a spectrum of a single molecule at a
given pressure and temperature, three main components are required; line
position, line intensity and line profile. In this section, the latter is
reviewed. The most popular line profile used in the majority of atmospheric
applications (and beyond) is the Voigt profile. It refers to the so-called
“intermediate” pressure regime and accounts for collision (pressure) and
Doppler (thermal motion) broadenings considered as statistically independent
processes and has been the standard for high-resolution line-by-line modelling
of infrared molecular absorption (Armstrong, 1967). The Voigt profile
represents a convolution of the associated Lorentzian and Gaussian profiles,
representing the collisional and Doppler effects, and tends to these two
shapes in the limiting cases of high and low gas densities, respectively. The
Voigt profile has no closed analytical form and is often related to the
complex probability function. Several special numerical algorithms exist in
the literature for efficient evaluation of the Voigt profile (Humblicek, 1982;
Kuntz, 1997), see the recent computational and numerical comparison by Zhang
et al. (2024); some numerical approaches allow one to take advantage of the
convolution of the entire spectrum at once (van den Bekerom & Pannier, 2021).
While for the Doppler contribution, the corresponding (half) line width
$\gamma_{\rm D}$ is a simple function of the molecular mass, gas temperature
and the line positions (frequency):

$\gamma_{\rm
D}=\sqrt{\frac{2N_{A}k_{B}T\ln{2}}{M}}\frac{\tilde{\nu}_{fi}}{c},$ (1)

there is no simple analytic description of the line (half) width $\gamma_{\rm
L}$, defining the Lorentzian contribution, at least in the general case. The
molecular parameters $\gamma_{\rm L}$ strongly depend on the system (the
molecule and the perturbing partner), as well as on the gas conditions, i.e.
pressure and temperature. Together with the line positions $\tilde{\nu}$,
transition probabilities (e.g. oscillator strength $gf$ or Einstein $A$
coefficients), the Lorentzian width (usually half-width-at-maximum, or HWHM)
$\gamma_{\rm L}$ are an integral part of spectroscopic databases. They are
typically obtained empirically either through direct measurements with
different level of parametric modelling or semi-empirically, where a more
sophisticated theory tuned to available experimental data is involved such as,
e.g., the semi-empirical approaches (Bykov et al., 2004) representing a
simplification of the Robert-Bonamy formulae to Anderson-type expressions with
fitted correction-factor parameters or modified complex Robert-Bonamy
calculations (Ma et al., 2007) with adjusted atom-atom interaction parameters.
Application of fully first-principles methods are currently limited to simple
system or low temperatures (Wcisło et al., 2021).

The pressure-broadening of spectral lines corresponding to pure rotational
(microwave, MW) and rovibrational (infrared, IR) transitions is mainly
governed by inelastic collisions (De Lucia & Green, 1988) and exhibit (except
for light perturbers such as hydrogen and helium) strongly pronounced
dependence on the rotational quantum number $J$.

Apart from the line broadening effect, collisions also affect the line
positions by introducing the so-called line shift $\delta$. These are also
provided by the spectroscopic databases, especially those focusing on high
resolution applications, such as terrestrial, planetary (Sung & Varanasi,
2005), Solar and in some cases stellar, but so far have not featured very much
in the low-mid resolution spectroscopy of exoplanets, as would be applicable
to the Ariel mission. It is also noteworthy that ro-vibrational line shifts
are typically smaller than the associated line widths by some orders of
magnitude.

In the context of the Ariel mission, the temperature and pressure dependencies
of line widths are crucial. For Voigt line widths $\gamma$ (in cm-1atm-1), the
following power law is almost always assumed:

$\gamma(T)=\gamma_{0}(T_{\rm ref},P_{\rm ref})\left(\frac{T}{T_{\rm
ref}}\right)^{n}\frac{P}{P_{\rm ref}},$ (2)

where $T_{\rm ref}$ and $P_{\rm ref}$ are some reference temperature and
pressure (e.g., 1 atm and $296$ K, respectively). Then the parameters
$\gamma_{0}$ (reference value of HWHM) and $n$ (temperature exponents) are
tabulated by the databases for each perturber. This model works quite well for
many molecular systems but for a given set of parameters it can deviate when a
description of a large range of temperatures is required.

The Lorentzian (and therefore Voigt) profile is known to fail in the far wings
leading to significant accumulated overestimation of the opacity at high
pressure. As a work-around, a cut-off the far wings at some distance from the
centre of the line is applied. The common standards are to use a 25 cm-1 cut-
off, employed by HITRAN, ExoMol and now also by MAESTRO (Molecules and Atoms
in Exoplanet Science: Tools and Resources for Opacities) (Gharib-Nezhad et
al., 2024). A detailed analysis of line-wing profiles and cutoffs in the
context of exoplanet atmospheres, including the Voigt profile, can be found in
Gharib-Nezhad et al. (2024).

Beyond the Voigt line profile. Recent experimental studies powered by the
development of experimental techniques in the last few decades have
demonstrated the importance of a departure of the line shape description from
the simple Voigt profile model, at least for high resolution applications.
This motivated the spectroscopic databases also to provide parameters for more
accurate profile models. One of such departures is due to the effect of
collisional (Dicke) line narrowing.

The line narrowing can be described either as a reduction of the Doppler
component (velocity-changing collisions resulting in molecular confinement) or
the dependence of the collisional relaxation rates on the relative molecular
speed. In the first case, velocity-changing collisions are often considered as
strong (no memory effects, Maxwell-Boltzmann re-distribution of velocities
after each collision) and the most frequently used associated profile is that
of Rautian & Sobel’man (1966, 1967), although the soft-collision model (light
perturbers, many collisions required to modify significantly the active-
molecule velocity) developed by Galatry (1961) is used by some researchers
too. In the second case, the speed-dependence (SD) of the collisional
relaxation rates dominates the line narrowing and the corresponding models
forming the so-called Speed-Dependent Voigt (SDV) profiles. The most accurate
description of the dependence on the absolute absorber’s speed (Berman, 1972;
Pickett, 1980) is by the hypergeometric confluent function (hgSDV model),
which however, leads to high computational costs. As a more practical
approach, a modification of hgSDV based on the mean quadratic speed (Rohart et
al., 1994; Köhler et al., 1995; Rohart et al., 2007) is used (qSDV model,
often referred to as simply SDV), for which an efficient numerical-calculation
algorithm is available (Boone et al., 2007).

Both mechanisms, with the velocity-changing collisions and with the speed
dependence viewed as independent, are accounted for in “combined” line-shape
models, such as Speed-Dependent Rautian (SDR) or Speed-Dependent Galatry (SDG)
profiles. The partial correlation of these effects is considered by the
partially Correlated quadratic-Speed-Dependent Hard-Collision profile
(pCqSDHCP), developed by Tran et al. (2013) (called the Hartmann-Tran profile
or HTP profile) and recommended for high resolution spectroscopy in a IUPAC
Technical Report (Tennyson et al., 2014). Parameters for this advanced profile
have been incorporated into the HITRAN database (Gordon et al., 2022) since
2016 for the hydrogen molecule as well as some transitions of water vapor and
molecular oxygen. The line narrowing effects, being routinely used in high-
resolution terrestrial and planetary applications, have not been considered in
the mainstream exoplanetary spectroscopic studies yet, and likely first
requires studies to demonstrate the impact of such line profiles on different
atmospheric models.

Another important deficiency of the common line profile methodology used in
spectral modelling is due to the breakdown of the isolated lines
approximation. This phenomenon, also caused by molecular collisions, is
associated with the so-called line-mixing or line-interference effect. While
the line narrowing effects are mostly noticeable at lower pressure (well below
1 atm for most gases), line-mixing usually becomes relevant at higher pressure
when individual lines start to broaden and overlap. Line-mixing effects can be
especailly significant in the line wings regions where intensity is never
truly zero, and there is always some degree of overlapping with others lines.
Because of this effect, the intensity in the wings of a band falls off faster
than predicted by the sum of Lorentzians (see figures in Hartmann et al.,
2010). To a lesser extent, the troughs between individual lines or branches
can also be affected. In practice, as stated above, cross-sections
calculations employ sums of Voigt profiles with certain wing cut-offs, say
$\pm 25$ cm-1 from line centres. Such treatment bypasses a proper account of
line-mixing and prevents overestimation of absorption away from band centres
which would come from addition of billions of line wings (recall that the
wings of the Voigt profile fall off as Lorentzians $\propto\omega^{-2}$ and
not exponentially). However, such cut-offs may lead to another non-physical
situation, where the calculated cross-sections between strong bands end up
being exactly zero. In reality, line-mixing would cause a sub-Lorentzian shape
that far enough from strong absorption bands would contribute to continuum
absorption (see Section 5 for a discussion on continuum absorption). An in-
depth discussion of wing cut-offs is presented in Gharib-Nezhad et al. (2024).
An empirical method of far-wing corrections involving $\chi$-factors is
discussed in the following sections.

At higher pressure where even line cores significantly overlap, line-mixing
can lead to a noticeable intensity redistribution within a branch or an entire
band. This is known to happen for closely spaced lines in Q-branches and band
heads even at sub-atmospheric pressures, and these features may appear
stronger and more narrow than one would expect from the sum of isolated lines.
This presents potential interest for more reliable confirmation of molecular
species’ detection, where features like these are often the most noticeable.
The case of very high pressure has been considered before in order to describe
the deep venusian atmosphere (Filippov et al., 2013; Buldyreva et al., 2013).
In such conditions, the rotational structure is entirely collapsed and the
band shape differs significantly from the sum of individual spectral lines.
This is relevant to modelling of radiative transfer in hot dense atmospheres.

Proper analysis of line-mixing is complicated, and usually a perturbative
approach is taken on a band-by-band basis for the most intense bands. At
present, line-mixing is not typically implemented in suites for producing
opacities for exoplanetary atmospheric retrievals, although these effects may
become more important with newer instruments that can probe high-pressure
regions of around 1 - 10 bar.

Calculations of line widths and shifts. The needs of MW/IR pressure-broadened
line widths and pressure-induced line shifts for atmospheric applications
motivated an extensive development of theoretical methods. The most developed
and commonly accepted hypothesis of the impact approximation completed by
various choices for the translational dynamics gave birth to semi-classical
(Anderson, 1949; Tsao & Curnutte, 1962), classical (Gordon, 1966), and
quantum-mechanical (Baranger, 1958a; Shafer & Gordon, 1973) approaches.
Besides, there exist statistical approaches, e.g. Margenau (1935), whose two-
particle static limit is the opposite case to the impact approximation. Static
limit works well for low molecular velocities (negligible rate of change of
intermolecular interactions) and is applicable at large frequency detunings,
i.e. in the far spectral wings which are hardly observable at IR wavelegths.
Therefore, approaches based on the impact approximation remain major tools for
predicting collisional line-shape parameters. High computational cost and
absence of refined potential-energy surfaces (PES) set limits to the use of
quantum-mechanical methods as soon as polyatomic/“exotic” molecular pairs
and/or high temperatures are concerned.

Quantum-mechanical approaches. The most rigorous method, close coupling (CC),
is usually applied to predict parameters of purely rotational transitions at
room temperature, and only some studies address hot environments. Such data,
provided the vibrational contribution to line-broadening is small, can
technically be reused for other lines in the infrared. Certain simplifications
of this formalism, such as the coupled-states (CS) approximation (used, for
example, in Thibault et al., 2011), the infinite-order sudden (IOS)
approximation (Goldflam et al., 1977), and the nearest neighbour Coriolis
coupling (NNCC) (Yang et al., 2018; Selim et al., 2022) can make calculations
more manageable while preserving the accuracy in the high-temperature limit
for most lines in the band. The main issue of quantum-mechanical approaches at
higher temperatures is that the number of rotational functions needed to
construct a complete basis grows too fast, making calculations of the
scattering matrix impractical. A useful feature of quantum-mechanical
approaches is that they allow estimating parameters of beyond-Voigt profiles
mentioned above. Semiclassical approaches can provide the Lorentzian component
of the profile, and with some extra work, the speed-dependence parameters. If
all the parameters of the extended Hartmann-Tran profile are required, one
could employ the generalised Hess approach along with CC for the scattering
matrix computation. This has been done recently for H2 and HD with helium as
the perturber (Wcisło et al., 2021; Stankiewicz et al., 2021) up to 1000 K.

Semi-classical approaches. The need for accurate potential energy surfaces
(PES) and long-time statistics accumulation also disadvantage purely classical
computations. As a result, advanced semi-classical approaches are typically
employed, such as the formalism of Robert and Bonamy (Robert & Bonamy, 1979)
and its fully complex implementation (Lynch et al., 1996) further supplied by
exact trajectories (Buldyreva et al., 1999), a corrected average over the
perturber’s states (Antony et al., 2006; Ma et al., 2007) and an account for
line coupling (Ma et al., 2013). In cases where large volumes of line-shape
data are to be produced with a minimal CPU cost, the semi-empirical method
(Bykov et al., 2004) is used which represents a simplification of the Robert-
Bonamy expressions to the Anderson-Tsao-Curnutte forms with a correction
factor with empirically fitted parameters. Although some experimental values
are necessary, the adjusted model parameters are practically temperature-
independent and can be used for calculations at other required temperatures
(not too low to keep the validity of the trajectory notion).

Machine Learning. Given the high volume of line broadening data that is
required to model the effects of various different exoplanet compositions,
machine learning appears to provide a practical approach to the problem.
Recently Guest et al. (2024) have complete an initial machine learning study
of air-broadening based on data in the HITRAN database. Studies which look at
the effect of changing the broadener are underway.

UV and visible frequency ranges. Spectra which involve transitions between
electronic states (i.e. rotation-vibration-electronic or rovibronic
transitions), typically between the ground and an excited electronic state,
occur, with some exceptions, in the UV and/or visible region. In these cases,
the line broadening due to predissociative effects can dominate the
collisional (pressure) broadening by some orders of magnitude. These
broadening are caused by the associated lifetimes of quasi-bound transitions
decreased. A new data format has recently been proposed to capture (Tennyson
et al., 2023) and use (Yurchenko et al., 2023) the predissociative line
broadening in spectroscopic databases.

In the case of rovibronic transitions between bound low-lying vibrational
levels of electronic states, available measurements show no well pronounced
$J$-dependencies in the collisional broadening of rovibronic transitions. The
absence of rotational dependence of the collisional (pressure) broadening
means that rotational energy transfer is of minor importance and the
broadening parameters are mainly influenced by elastic collisions. For such
transitions line widths and line shifts have the same orders of magnitude. As
mentioned by Margenau (1936), lines of rovibronic (bound-bound) transitions
are broadened and shifted similarly to atomic lines of a similar type and a
similar energy jump. Indeed, the first theoretical approaches to pressure-
induced line widths/shifts used the model of a classical oscillating radiator
whose phase is modified during collision by a random amount, leading thus, via
Fourier-integral analysis, to a “dispersion” (Lorentz) profile. For example,
Lindholm (1945) and Foley (1946) successfully developed such theories. Foley
(1946), in particular, argued that non-adiabatic effects are small for atoms
due to large gaps between their electronic levels but can occur for molecular
IR transitions because of similar energy differences between the rotational
levels of the radiator and perturber. Detailed analyses of some representative
one-term interactions (dipole-dipole, quadrupole-quadrupole and dispersive) in
the framework of phase-shift theory were made by Mizushima (1951) who also
considered velocity averaging and derived line-width and line-shift
expressions (intended for microwave transitions) with explicit temperature
dependencies. These expressions served as a basis for the power law of Eq.
(2). Later, Hindmarsh et al. (1967) accounted additionally for short-range
repulsive forces via a Lennard-Jones 12-6 potential model but for simplicity
conducted their derivation with the mean-thermal-velocity approximation.
Temperature dependence of collisional broadening and shifts of atomic and
molecular rovibronic lines has been also addressed by Cybulski et al. (2013).
Quantum-mechanical adiabatic approaches were initiated by Jablonski (1937,
1945) who assumed the gas to be a very large “molecule” and calculated the
stationary states of internal motion. A unified model relying on the Franck-
Condon principle and containing both impact and quasistatic limits was
proposed by Szudy & Baylis (1975). The authors retrieved the expressions of
Lindholm (1945) and Foley (1946) in the classical limit and suggested also a
first-order correcting term leading to line shapes with an asymmetry effect.

When there is an interaction with one or more dissociative states, i.e.,
predissociations, the broadening can vary significantly due to a variation in
the lifetimes of the excited states. The broadening in this case is a
manifestation of such interaction with the continuum. The extent of the line
broadening (or lifetime of the state in question) derives from the strength of
the predissociation, i.e., the strength of the coupling between the bound
excited states and the dissociative states. Typically non-radiative lifetimes
of electronically excited states are ca. 10-8s which result in widths of
$5\times 10^{-4}$ cm-1. For lifetimes of $10^{-13}$ s the linewidth will be 50
cm-1 which will result in the rotational structure disappearing. For
nonradiative lifetimes shorter than $10^{-15}$ s, the vibrational structure
disappears and will resemble a continuum. These types of predissociation-
induced line broadenings have been well documented experimentally for over
half a century (see chapter 7.4.2 in Léfebvre-Brion & Field (2004)).

###  3.2 Theoretical approaches to line-shape parameters: Atoms

The broadening of alkali lines by rare gases is a problem which has been
extensively investigated in experimental and theoretical work (Allard &
Kielkopf, 1982; Burrows & Volobuyev, 2003; Allard et al., 2016, 2019; Peach et
al., 2020; Allard et al., 2023, 2024). A theory of spectral line broadening
has been developed to calculate neutral atom spectra given the interaction and
transition moments for relevant states of the radiating atom with other atoms
in its environment. Within this framework it is possible to compute the
complete spectrum with a unified approach. Unlike impact theories of line
broadening which predict a Lorentzian line or the approximation methods of
Szudy & Baylis (1975, 1996) the unified theory of Allard et al. (1999)
provides an accurate spectrum from the line centre to the extreme wing.
Complete details and the derivation of the theory are given by Allard et al.
(1999). The approach is based on quantum theory of spectral line shapes by
Baranger (1958b, c) with an adiabatic representation to include the degeneracy
of atomic levels.

The spectrum $I(\Delta\omega)$ can be written as the Fourier transform (FT) of
the dipole autocorrelation function $\Phi$(s),

$I(\Delta\omega)=\frac{1}{\pi}\,Re\,\int^{+\infty}_{0}\Phi(s)e^{-i\Delta\omega
s}ds\;,$ (3)

where $\Delta\omega$ is the angular frequency difference from the unperturbed
centre of the spectral line. The autocorrelation function $\Phi$(s) is
calculated with the assumptions that the radiator is stationary in space, the
perturbers are mutually independent, and in the adiabatic approach the
interaction potentials give contributions that are scalar additive. This last
simplifying assumption allows the total profile $I(\Delta\omega)$ to be
calculated when all the perturbers interact, as the FT of the $N^{\rm th}$
power of the autocorrelation function $\phi$(s) of a unique atom-perturber
pair. Therefore,

$\Phi(s)=(\phi(s))^{N}\;,$ (4)

that is to say, the interperturber correlations are neglected. For a perturber
density $n_{p}$,

$\Phi(s)=e^{-n_{p}g(s)},$ (5)

where decay of the autocorrelation function with time leads to atomic line
broadening. When $n_{p}$ is high, the spectrum is evaluated by computing the
FT of Eq. (5). The real part of $n_{p}g(s)$ damps $\Phi(s)$ for large $s$ but
this calculation is not feasible when extended wings have to be computed at
low density because of the very slow decrease of the autocorrelation function.
An alternative is to use the expansion of the spectrum $I(\Delta\omega)$ in
powers of the density described in Royer (1971). For the implementation of
alkali lines perturbed by helium and molecular hydrogen in atmosphere codes,
the line opacity is calculated by splitting the profile into a core component
described with a Lorentzian profile, and the line wings computed using an
expansion of the autocorrelation function in powers of density. The impact
approximation determines the asymptotic behavior of the unified line shape
correlation function. In this way the results are applicable to a more general
line profile and opacity evaluation for the same perturbers at any given layer
in the photosphere or planetary atmosphere.

In Allard et al. (2019) the use of a density expansion in the opacity tables
is reviewed. When the expansion is stopped at the first order it is equivalent
to the one-perturber approximation. Previous opacity tables were constructed
to third order allowing us to obtain line profiles up to
$N_{He}$/$N_{H2}$=$10^{19}$ cm-3. The new tables are constructed to a higher
order allowing line profiles to $N_{\rm He}$/$N_{{\rm H}_{2}}$=$10^{21}$ cm-3.

###  3.3 State of the art - Data availability

####  3.3.1 Molecular line profiles

Voigt parameters: it is now recognised in the (exo-)atmospheric community that
Earth’s conditions with the oxygen and nitrogen as the main collisional
broadeners are not default ones, especially for hot Jupiter exoplanets, where
hydrogen and helium dominate molecular collisions. Although, as noted below,
broadening parameters are becoming available for a small number of systems
which deviate from the Voigt profile, the vast majority of available data are
for Voigt broadening parameters. Even so, collisional broadening parameters
which are required for computing Voigt profiles are missing or incomplete for
a larger number of the relevant molecules (see Section 2) and are therefore in
practice substituted by crude “guestimates” when generating molecular
opacities for the subsequent use in the radiative transfer calculations.
Indeed, computing opacities without line profiles is meaningless, i.e.
“something” is always better than “nothing”, but the errors involved are
usually difficult to quantify. The impact of using incorrect broadening
parameters was shown by Niraula et al. (2022, 2023) to impact retrieved
exoplanet properties.

HITRAN now includes different broadening species applicable to planetary
atmospheres, as shown in Table 6. The addition of these parameters to the
database is carried out by searching the literature for accurate experimental
measurements, which can be fit to a rotationally-dependent function (see
Wilzewski et al., 2016; Tan et al., 2019, 2022). This enables the functions to
be applied to the high-temperature lines lists of databases such as ExoMol and
HITEMP. These broadeners are representative of the typical species in the
(exo-)atmosphere under study: a mix of H2 and He for gas giants, CO2 for rocky
planets and H2O for tropical atmospheric scenarios (or water-dominated
atmospheres). The temperature dependence of line broadening parameters has
also recently been under investigation. Indeed line shapes are described by
different parameters such as the pressure broadening and pressure shift
coefficients and their respective dependence on temperature; this applies to
both molecules and atoms. The species and broadeners for which Voigt
broadening parameters are currently available in the ExoMol database can be
found online212121https://exomol.com/data/data-types/broadening_coefficients/.
A complete set of air-broadening parameters have been generated using machine
learning (Guest et al., 2024) and a large number of broadening parameters
based on the theory of Buldyreva et al. (2022) have also been added recently.

Empirical $\chi$-factor corrections: Solar System applications have shown that
the Voigt profile, tending to a Lorentz profile with increasing pressure, is
not applicable for high-pressure conditions where a sub-Lorentzian profile
needs to be used (Bézard et al., 2011). The pressure is so high in the lower
layers of the atmosphere that the line-interference (intensity-transfer, also
called line mixing) effects, in particular line (and, therefore, band) wings,
need to be accurately modeled. For now, the band shapes obtained in the
impact-approximation (Markov) limit of collisional-broadening theory (which is
invalid for large detunings from the band centre) are empirically corrected
via so-called $\chi$-factors, as, e.g., Tonkov et al. (1996); Bézard et al.
(2011) for CO2 on Venus and the recent confirmation by laboratory measurements
(Mondelain et al., 2022, 2023). Empirical $\chi$-factor corrections were also
used to model far-wing absorption for CO2 at high pressures and temperatures
(Tran et al., 2011; Cole et al., 2023), CH4 (Tran et al., 2011) and H2O (Tran