#  EXOPLINES: Molecular Absorption Cross-Section Database for Brown Dwarf and
Giant Exoplanet Atmospheres

Ehsan Gharib-Nezhad Ehsan Gharib-Nezhad<EMAIL_ADDRESS>NASA Ames
Research Center, Moffett Field, CA 94035, USA  Bay Area Environmental Research
Institute, NASA Ames Research Center, Moffett Field, CA 94035, USA  School of
Molecular Sciences, Arizona State University, Tempe, AZ 85281, USA  Aishwarya
R. Iyer  School of Earth and Space Exploration Arizona State University, Tempe
AZ 85281, USA  Michael R. Line  School of Earth and Space Exploration Arizona
State University, Tempe AZ 85281, USA  Richard S. Freedman  SETI Institute,
Mountain View, CA 94035, USA  NASA Ames Research Center, Moffett Field, CA
94035, USA  Mark S. Marley  NASA Ames Research Center, Moffett Field, CA
94035, USA  Natasha E. Batalha  NASA Ames Research Center, Moffett Field, CA
94035, USA

###### Abstract

Stellar, substellar, and planetary atmosphere models are all highly sensitive
to the input opacities. Generational differences between various state-of-the-
art stellar/planetary models are primarily because of incomplete and outdated
atomic/molecular line-lists. Here we present a database of pre-computed
absorption cross-sections for all isotopologues of key atmospheric molecules
relevant to late-type stellar, brown dwarf, and planetary atmospheres: MgH,
AlH, CaH, TiH, CrH, FeH, SiO, TiO, VO, and H2O. The pressure and temperature
ranges of the computed opacities are between 10-6–3000 bar and 75–4000 K, and
their spectral ranges are 0.25–330 $\mu$m for many cases where possible. For
cases with no pressure-broadening data, we use collision theory to bridge the
gap. We also probe the effect of absorption cross-sections calculated from
different line lists in the context of Ultra-Hot Jupiter and M-dwarf
atmospheres. Using 1-D self-consistent radiative-convective thermochemical
equilibrium models, we report significant variations in the theoretical
spectra and thermal profiles of substellar atmospheres. With a 2000 K
representative Ultra-Hot Jupiter, we report variations of up to 320 and 80 ppm
in transmission and thermal emission spectra, respectively. For a 3000 K
M-dwarf, we find differences of up to 125$\%$ in the spectra. We find that the
most significant differences arise due to the choice of TiO line-lists,
primarily below 1$\mu$m. In sum, we present (1) a database of pre-computed
molecular absorption cross-sections, and (2) quantify biases that arise when
characterizing substellar/exoplanet atmospheres due to line list differences,
therefore highlighting the importance of correct and complete opacities for
eventual applications to high precision spectroscopy and photometry.

Brown dwarfs (185), Exoplanet atmospheres (487), Exoplanet atmospheric
composition (2021)

††thanks: NASA Postdoctoral Fellow

##  1 Introduction

Over the past two decades, atmospheric characterization of exoplanets and
brown dwarfs has been dramatically increasing—particularly, observations with
$HST$, $Spitzer$, various ground-based telescopes both with low to moderate
resolution spectroscopy and high-resolution cross-correlation approaches
(e.g., Madhusudhan, 2019). Additionally, with the Transiting Exoplanet Survey
Satellite ($TESS$), in conjunction with the launch of the James Webb Space
Telescope ($JWST$), we can expect hundreds of planet detections (Sullivan et
al., 2015; Louie et al., 2018; Kempton et al., 2018) followed by detailed
spectroscopic characterization of their atmospheres (Greene et al., 2016; Bean
et al., 2018). The compositional and temperature diversity of these worlds
provide a unique opportunity to gain insight into planetary atmospheric
chemical processes and formation pathways (Öberg et al., 2011; Fortney et al.,
2013; Mordasini et al., 2016; Hörst et al., 2018).

Fully capitalizing on the information encoded in a spectrum, therefore,
requires a robust model interpretation. Models used to interpret thermal
emission spectra (either from an isolated object like a brown dwarf, M-dwarf,
or directly imaged planet, or a secondary eclipse spectrum for a transiting
planet) and transmission spectra (for transiting planets) require some
combination of chemistry and radiative transfer. Self-consistent models
(either 1D or 3D) rely upon a detailed coupling between chemical processes
(e.g., thermochemical equilibrium or chemical kinetics/photochemistry),
radiative energy transport, convective/dynamical energy transport, and
cloud/haze processes to determine the atmospheric state and subsequent
observables (e.g., Marley & Robinson, 2015; Zhang, 2020, and references
therein). Retrieval models, on the other hand, are purely data-driven and
attempt to leverage large numbers of free parameters (e.g., molecular
abundances for selected species, temperature profile parameterization) to
adequately fit the observables to determine Bayesian constraints on
composition, clouds, and thermal structures (Line et al., 2014). The adequacy
of these methods, whether for predictions or parameter estimation, relies upon
accurate and complete molecular and atomic opacities.

In this work, we focus on high-resolution (adaptive R, e.g.,
2$\times$104–2$\times$106 at 1 $\micron$) opacities with implications to
Ultra-Hot Jupiter atmospheres. Our prime candidates being TiO, VO, MgH, AlH,
CaH, TiH, CrH, FeH, and SiO–the key molecules111For further study on the
composition of these ultra-hot Jupiters and M-dwarfs, studies by Lodders &
Fegley (2006) and Visscher et al. (2010) are suggested. in such atmospheres.
In addition, we generate H2O high-resolution opacities from 500–4000 K, which
is required for modeling everything from super-Earth to M-dwarf atmospheres.
Starting with §2, we first provide an astrophysical context for the importance
of metal hydrides and oxides in substellar atmospheres. §3 provides discussion
on the current state of opacity or absorption cross-section data, highlighting
line broadening effects that are missing and how we tackle them. In §4, we
bridge the gap by providing pre-generated absorption cross-sections for the
metal hydrides and oxides in question, alongside comparisons with previous
efforts. In §5, we quantify the effect of opacity differences on transmission
and emission spectra of a representative222“representative” in this context
means a generic atmospheric case Ultra Hot Jupiter planet, followed by M-dwarf
stellar spectra in §6, and potential biases and challenges with opacities that
arise in atmospheric characterization efforts, described in §7. Finally, we
present a brief summary of our conclusions in §8. The main outcome of this
work is EXOPLINES absorption cross-section database (i.e., EXOplanet Pressure-
broadened LINES).

##  2 Astrophysical Importance

Temperature and pressure play a key role in controlling molecular and atomic
abundances that ultimately shape a spectrum (e.g., Burrows & Sharp, 1999). At
cooler temperatures ($<$200 K), solar system giants are dominated by
absorption because of methane and scattering by clouds, and photochemically
produced hydrocarbons. At warmer temperatures (300–1000 K), T-dwarfs, and many
(sub)Neptune transiting planet atmospheres are sculpted (or presumed to be
sculpted) by water, methane, ammonia, and alkali metals. Higher temperature
results in the onset of CO absorption, followed by several oxides (TiO, VO)
and hydrides (FeH, CrH, MgH, CaH), especially above 1500 K. The increasing
presence of these species as a function of temperature is what ultimately
(along with dust/condensate formation) governs the M-L-T-Y dwarf
classification sequence and their sub-types (Kirkpatrick, 2005). Furthermore,
water dissociation, the onset of H-bound/free-free, and contribution of
refractory atoms and their ions (e.g., Fe, Ti, Mg, Ca, Si) dominate
atmospheres with temperatures above $\sim$2500 K, encountered in M-dwarfs and
ultra-hot Jupiters (Lodders, 1999). Here, we highlight the importance of these
metal oxides and hydrides and their behavior in high-temperature
regimes—particularly in substellar atmospheres of M/L-type Dwarfs and highly
irradiated exoplanets.

###  2.1 Metal Oxides

M-dwarf stars (2000 K $<$ Teff $<$ 4000 K), active photospheric spots on sun-
like stars, and even highly irradiated exoplanets with similar effective
temperatures have atmospheres that are all dominated by TiO (Kirkpatrick et
al., 1991; Webber, 1971). Covering the optical spectral region between 630–900
nm, TiO plays a vital role in the proper characterization of M-dwarfs and
Ultra-Hot Jupiters. The temperature dependence of TiO governs the energy level
populations that affect the relative band-structure intensities, an essential
tool in classifying early-type M-dwarfs (Sharpless, 1956). For instance, in
spectra of M0–M3 dwarfs, the 0–0 band333In spectroscopy, the
$\nu^{\prime}-\nu^{\prime\prime}$ band refers to all rotation-vibrational
transitions between the upper vibrational level, $\nu^{\prime}$, and the lower
vibration level $\nu^{\prime\prime}$ (Bernath, 2005). (705.4 nm) is used as
the primary classification marker. The strongest TiO bands near 843 nm, 819.4
nm to 885.9 nm, and 660 to 710 nm are important indicators for M4, M6, and
late-type M8 dwarfs respectively (Sharpless, 1956; Lockwood, 1972; Ruiz et
al., 1997; Delfosse et al., 1997).

Similar to TiO, VO is a refractory molecule in M-dwarfs and early L-dwarf
atmospheres ($\sim$L2). With strong spectral signatures between 0.6–1.5
$\micron$, metal oxides such as VO are sensitive temperature indicators in
substellar atmospheres (Cushing et al., 2005). The strength of the VO
absorption features at 1.17 and 1.22 $\micron$, combined with TiO and CaH
bands, are valuable spectroscopic youth indicators for brown dwarfs
(Kirkpatrick et al., 2006; Peterson et al., 2008).

In addition to their importance for substellar spectral and age
classification, high-temperature oxides are critical sources of opacity in the
optical wavelength region, that drive heating in the upper atmospheres of hot
Jupiters ($>$1800 K and $<$50 mbar)—essential for proper characterization of
the 1D vertical structure of the atmosphere (Hubeny et al., 2003; Fortney et
al., 2008). The presence of TiO and VO drive up stellar irradiation mean
opacity relative to the planetary thermal emission mean opacity, resulting in
a “thermal inversion” (increasing temperature with decreasing pressure) in the
planetary atmosphere. However, we note that bonafide detection of metal oxides
(TiO or VO) has remained elusive and somewhat controversial, partially due to
the inadequacy of the opacity data for these species (Merritt et al., 2020;
Nugroho et al., 2017).

In substellar atmospheres, especially at temperatures cooler than 2300 K, both
TiO and VO gradually disappear due to condensate formation (TiO into to CaTiO3
and VO turns into solid VO, Lodders (1999)). Therefore, their spectral
features are not prominent at such atmospheres at $\sim$0.7–1.2 $\micron$,
allowing for metal hydride FeH, CrH, and CaH features to present themselves.

###  2.2 Metal Hydrides

Several FeH features within the 0.7–1.3 $\micron$ range has been detected in
the late-M and L dwarfs (Kirkpatrick et al., 2000), including the 0–0 band
(known as the Wing-Ford band) at 0.985–1.02 $\micron$ (Cushing et al., 2003),
the 1–0 band at 869.2 nm in L-dwarfs (Kirkpatrick et al., 1999), the 2–0 band
at 778.6 nm, the 1–0 band at 869.2 nm, the 2–1 band at 902.0 nm (Tinney &
Reid, 1998) and the 1–2 band at 1238.9 nm bands are present in very low-mass
stars (Reid et al., 2001). Additionally, Schiavon et al. (1997) showed that
the Wing-Ford band is sensitive to surface gravity and metallicity. Similar to
FeH, CaH, CrH, and AlH all show a strong dependence on surface gravity (see
Chapter 4 in Reid & Hawley (2005)).

The CrH 0–0 (861.1 nm) and 0–1 (996.9 nm) bands along with the FeH bands (and
their ratios) serve as diagnostic indicators (Kirkpatrick et al., 1999, 2000)
for classifying the L-dwarf sub-types (see Table 6 in Kirkpatrick et al.
(1999)).

In the context of Ultra-Hot Jupiters, species like MgH, AlO, NaH, and CaO
could also drive thermal inversions depending on elemental abundance ratios
(Gandhi & Madhusudhan, 2019). Additionally, hydrides such as MgH, CrH, CaH,
and FeH although expected to be present in hot Jupiter atmospheres; the lack
of reliable detections have made it difficult to assess their true role in
governing the 1-D thermal structure.

##  3 Methodology: Molecular Absorption Cross-Sections

The absorption cross section444Both opacities and absorption cross-sections
represent the capability of species (i.e., atom, molecule, or radical) to
absorb or emit light. However, their definitions are different. Opacity
$\kappa$ is the “effective area” of one gram of an absorber (unit: cm2/gram)
to absorb/emit light while absorption cross-section $\sigma$ is the “effective
area” of one absorber (unit: cm2/molecule). These quantities are
interchangeable with $\kappa\rho$=$\sigma n$ equation, where $\rho$ is mass
density ($gram/cm^{3}$) and $n$ is number density (molecule/cm3). (hereafter
ACS) of an absorber is governed by the wavelength-dependent intensity,
position, and width of a spectral line. The line shape is typically modeled
with a Voigt profile, which is a convolution of Doppler (thermal) and pressure
(Lorentz or collisional) broadening. Uncertainties in the line positions,
strengths, and widths are ultimately what drive the uncertainties or
inadequacies in various pre-computed ACSs. Below we present the formulation of
line profile in §3.1, and then we extend our discussion on pressure-broadening
and their availability in §3.2, followed by the treatment for their
$J$-dependency and wing cut-off in §3.3-3.4. Finally, §3.5 describes the line-
list data structure, and computational details are provided in §3.6.

###  3.1 Line-width

The conventional form of the spectral line shape is the Voigt profile, which
is a convolution of Doppler and Lorentz profiles. Doppler broadening is
governed by the temperature, molecular mass, and also the transition energy,
and its half-width at half-maximum width (HWHM), ${\it\Gamma}_{\mathrm{D}}$,
may be given by (Buldyreva et al., 2011):

$\Gamma_{\mathrm{D}}=3.581\times 10^{-7}\sqrt{\frac{T}{M}}\ \nu$ (1)

where $M$ is absorbers molecular mass in amu (atomic mass unit), $T$ is the
temperature (in K), and $\nu$ is the line position in wavenumber (cm-1).

Lorentz line profile is controlled by the magnitude of the interaction between
the absorber and broadening gas species, and the Lorentz HWHM,
${\it\Gamma}_{\mathrm{L}}$, depends on the temperature and the broadening
species and can be described by

$\centering\Gamma_{\mathrm{L}}=\sum_{b}\Big{(}\frac{T}{296\mathrm{K}}\Big{)}^{-n_{T,b}}\;\gamma_{{\mathrm{L},b}}\;p_{\mathrm{b}}\@add@centering$
(2)

where $\gamma_{\mathrm{L,b}}$ is the Lorentz coefficient of an absorber (HWHM,
unit: cm-1/bar), $p_{\mathrm{b}}$ is the broadener partial pressure (unit:
bar), and $n_{\mathrm{T},b}$ is the temperature-dependence coefficient, which
is dimensionless. Both $\gamma_{\mathrm{L,b}}$ and $n_{\mathrm{T},b}$ are
controlled by broadener–absorber interaction and the quantum properties of
absorbing molecules.

Quantifying $\gamma_{\mathrm{L},b}$ and $n_{\mathrm{T},b}$ coefficients for
the metal hydrides/oxides in question (e.g., TiO, VO, MgH, etc.) are
challenging aspects of ACS calculations because there is not any laboratory or
computational measurements have been done to determine their
$\gamma_{\mathrm{L},b}$ and $n_{\mathrm{T},b}$ coefficients555More precisely,
we could find only one spectroscopic measurement of AlH in H2 gas by Watson &
Hull (1936). Their measured $\gamma_{\mathrm{L}}$ is 0.24 cm-1/atm, which
looks much larger than the available H2-broadening data for other well-known
absorbers. Given the limitation in pressure gauges, spectrometers, and
thermometers in their measurements in the 1930s, we decided not to use their
number..

###  3.2 Estimating the Lorentz Coefficient

Theoretically determining the Lorentz coefficient is quite challenging because
it depends on molecular quantum properties such as total rotational angular
momentum666In fact, each transition has its corresponding rotational and
vibrational quantum numbers and molecular symmetries, which are controlling
the Lorentz coefficient and hence the spectral line-width., molecular
symmetries, and environmental conditions like temperature and the background
gas broadener composition. For TiO, VO, TiH, CrH, the Lorentz coefficients
have been estimated up to low $J$ quantum numbers (given in Table 1) for H2/He
atmospheres. These estimations are based on the similarity between the
molecular symmetry or dipole moments that these absorbers have with the
available Lorentz coefficients (e.g., Freedman et al., 2014; Chubb et al.,
2020)777For instance, Chubb et al. (2020) used HCN broadening coefficients for
computing the ACS data of CaH, CrH, SiO, TiO, and VO absorbers, as well as HF
broadening coefficients data for FeH and TiH.). In reality, we do not have
enough or even a single measurement for the metal hydries/oxides in this study
(except H2O) at any temperature (see §7 for the challenges we are dealing with
these opacities).

Due to the lack of $\gamma_{\mathrm{L},b}$ and $n_{\mathrm{T},b}$
coefficients, we used the classical collision theory by Anderson (1949) in
order to estimate the Lorentz coefficient using the following equation (see
§A.1 for further discussion):

$\gamma_{\mathrm{L,b}}=0.0567\ (T\mu)^{-1/2}\ \sigma_{\mathrm{col,b}}$ (3)

where $\mu$ is the reduced mass of the absorber-broadener pair in amu,
$\sigma_{\rm{col,b}}$ is the collision cross-section in $\AA^{2}$ of the
broadener b, and $\gamma_{\mathrm{L,b}}$ is in cm-1/atm. In this equation, the
collision (or scattering) cross section, $\sigma_{\rm{col,b}}$ is a
fundamental factor, that connects collisions in the microscopic world into the
spectral linewidth. For further details, see studies by Odashima et al. (1989)
and Gierszal et al. (1998) that have used this approach to calculate the
collision cross section from the laboratory-measured Lorentz line width. In
addition, Cappelletti et al. (2005) have shown a good agreement between the
experimental and computed pressure-broadening coefficients of C2H2–Ar system.

Even though Eq. 3 is derived from the collision theory, it has some
limitations and errors such as ideal gas assumption and also possible
inaccuracy in the computed collision cross-section data from ab-initio
methods. Hence, this equation and the calculated pressure-broadening
coefficients will not fulfill the lack of laboratory measurements or
theoretical calculations. For example, the modified semi-classical Robert
Bonamy theory (Robert & Bonamy, 1979; Ma et al., 2007) have been successfully
implemented to calculate the half-width and line shift of H2O and CO absorbers
in different broadening gases (e.g., Gamache & Vispoel, 2018; Vispoel et al.,
2020), and so similar studies are required for these molecules in question.

Note that the assumption of 0.5 for the temperature-dependence coefficient,
$n_{\mathrm{T,b}}$ at Eq. 3 is based on the kinetic theory, while laboratory
measurements of other species suggest $n_{\mathrm{T,b}}$ can vary from
0.2–1.2. In turn, $n_{\mathrm{T,b}}$ can strongly depend on the broadener and
$J$ quantum number (e.g., CH4 in different broadening gas that have shown in
table 5 by Gharib-Nezhad et al. (2019)), or $n_{\mathrm{T,b}}$ may be roughly
constant with $J$ (e.g., CO-self/air broadening by Devi et al. (2012)). Wagner
et al. (2005) have measured the effect of H2O-air mixture and found that
$n_{\mathrm{T,b}}$ can also be negative number. Table 2 represents the
collected collision cross sections, $\sigma_{col}$ for CaH and SiO absorbers
for H2 or He broadeners where available for $J_{\mathrm{lower}}$=0. In
addition, the AlH $\gamma_{\mathrm{L,b}}$ coefficient is assumed to be equal
to the CO broadening coefficient because of their similar dipole moments (we
adopt this approach from Freedman et al. (2014) and Chubb et al. (2020)
approaches.)

###  3.3 Estimating the Behavior of Pressure-Broadening Coefficients and Their
Dependence on $J$ Quantum Numbers

The calculated or estimated Lorentz coefficients, $\gamma_{\mathrm{L}}(J)$
depend on $J$ quantum numbers. To understand the behavior of
$\gamma_{\mathrm{L}}(J)$ for all $J$s, we need to consider two issues: 1) the
degree or rate of the $\gamma_{\mathrm{L}}(J)$ decrease with $J$ (or
$\frac{\partial\gamma}{\partial J}$), and 2) an equation that can extrapolate
these $J$-dependence behavior without becoming negative or increasing sharply.

The first issue can be tackled by comparing the $J$-dependence behavior of the
available $\gamma_{\mathrm{L}}(J)$ coefficients of diatomic molecules with H2
and He broadening. For example, the Lorentz coefficient of CO molecule (with
low dipole moment) has a smooth decrease with high $J$s (Devi et al., 2004;
Régalia-Jarlot et al., 2005; Mantz et al., 2005). In contrast, for absorbers
with large dipole moments such as HCl–H2 and HCl–He systems,
$\gamma_{\mathrm{L}}(J)$ value drop noticeably according to the laboratory
measurements done by Toth et al. (1970), Li et al. (2018), Babrov et al.
(1960) (see Fig. 1). All the metal hydrides and oxides in question (except
AlH) have large dipole moments, and for the lack of any other information we
assume that their $J$-dependency may decrease similar to HCl. However, one
should keep in mind that dipole moment values are not major factors in the
rotational dependence of the broadening parameters. Detailed discussion on the
reason for $J$-dependence of spectral lines is provided by Hartmann et al.
(2021) (chapter 3) and Renaud et al. (2018). The second issue may be solved by
using the proposed equation by the HITRAN group888https://www.hitran.org
(e.g., see Gordon et al., 2017, and their upcoming paper, Gordon et. al.
2021). As part of their group efforts, Tan et al. (2019) have examined the
fitting accuracy of the available pressure-broadening coefficients for water
as a broadener and several terrestrial key absorbers (e.g., CO, CO2, CH4); and
they suggested the fourth‐order Pad$\acute{e}$ approximant as the most
reliable prediction of the Lorentz $J$-dependency. Fourth‐order Pad$\acute{e}$
equation provides a smooth decrease of $\gamma_{\mathrm{L}}$ with $J$ and has
the following form:

$\gamma_{\mathrm{L}}(J)=\frac{a_{0}+a_{1}J+a_{2}J^{2}+a_{3}J^{3}}{1+b_{1}J+b_{2}J^{2}+b_{3}J^{3}+b_{4}J^{4}}$
(4)

where $a_{0}$ to $a_{3}$ and $b_{1}$ to $b_{4}$ are the fitting coefficients.
$J$ is also the lower total angular quantum number. Besides, we applied the
following constraints to this equation to avoid negative numbers of
$\gamma_{\mathrm{L}}$ as well as follow a sharp $J$-dependency for absorbers
with large dipole moments (i.e., MgH, CaH, CrH, FeH, TiH):

$\displaystyle\gamma_{\mathrm{L}}(J=10)=\sim 0.5\gamma_{\mathrm{L}}(J=0)$ (5)
$\displaystyle\gamma_{\mathrm{L}}(J=40)=\sim 0.1\gamma_{\mathrm{L}}(J=0)$
$\displaystyle\mathrm{if}\
\gamma_{\mathrm{L}}(J>40)<0=>\gamma_{\mathrm{L}}(J)=\gamma_{\mathrm{L}}^{min}-(\frac{1}{J}*\gamma_{\mathrm{L}}^{min})$

An example of the calculated broadening coefficients for the metal
hydrides/oxides in question is presented in Fig. 2. Additionally,, the
Fourth‐order Padè coefficients for all the absorbers in this study are listed
in Table 3 and are valid up to $J$=500.

###  3.4 Wing cut-off

Wing cut-off is an important challenge in fully and accurately computing the
opacity continuum (see §7). Given the lack of sufficient pressure broadening
data for these species and the huge computational time, the Voigt profile is
implemented in various pre-computed opacity data. The current method to deal
with this non-Lorentzian behavior of the Voigt profile is either using
absolute wavenumber such as 100 cm-1 (e.g., MacDonald, 2019) or just using
multiplication of the Voigt profile (e.g., 200 to 500 of Voigt HWHM) (e.g.,
Chubb et al., 2020; Freedman et al., 2014).

Note that several laboratory and theoretical studies have shown that non-Voigt
behavior provides a more accurate opacity continuum (e.g., Ngo et al., 2012).
For example, Hartmann et al. (2002) have recorded the 3.3 $\micron$ spectrum
of CH4 in H2 bath gas and have shown that the Voigt behavior is valid up to 25
cm-1 from the line center. Inspiring by their results, we decide to use
absolute number for the wing cut-off as follow: 30 cm-1 for $P\leq 200$ bar
and 150 cm-1 for $P>200$ bar. We noticed that Mollière et al. (2019) have
considered this method as well in calculating their opacities.

It is worth mentioning that we did not use the multiplication factor of the
Voigt linewidth because for a generic spectral line at low-to-moderate
pressure and at the infrared spectral region with small wavenumber (such as
$P<$10-3 bar at $<$1000 cm-1), the 500$\times$Voigt-half-width will be less
than 10cm-1 which is not sufficiently high value for the wing cut-off
according to the results by Hartmann et al. (2002). Additionally, for high
pressures (such as $P>$100bar), this 500$\times$Voigt-HWHM is a large number
even larger than 500 cm-1 which results in an extreme overestimation.

###  3.5 Line List

A typical line-list data contains all of the necessary ingredients to generate
ACSs, such as line positions, intensities, rotational and vibrational quantum
assignments, electronic assignments, and also various pressure-broadening and
pressure-shift values where available. The completeness and accuracy of line-
lists are a key focus of both laboratory and ab initio studies. In this work,
we use the latest version of line list data provided by the ExoMol group
(Tennyson et al., 2020), summarized in Table 4.

###  3.6 Computational Details

We employ the ExoCross999github.com/Trovemaster/exocross/wiki code developed
by Yurchenko et al. (2018) to compute the temperature-dependent line strengths
and the Voigt profile (Humlíček, 1979) for every individual line under the
conditions given in Table 5. We assume H/He broadening governed by background
atmospheres composed of 85% H2 and 15% He–typical Jovian-like atmosphere
conditions. The spectral sampling resolution is optimized as a function of
temperature, pressure, and spectral subdivisions in such a way as to fully
resolve the individual lines.

##  4 Results: Absorption Cross-Section

In this section, we present a brief discussion on the line-list source for
each absorber, as well as illustrative examples of the pre-computed ACS data.
Then, we compare our generated ACS data with the currently available
database’s.

###  4.1 H2O

Partridge & Schwenke (1997) used high-level ab initio approach to computing
the potential energy surface and dipole moment function of water. They then
empirically adjusted their water line list (hereafter, $PS97$) by comparing
their line position with available laboratory spectra. About a decade later,
the ExoMol team (Barber et al., 2006) computed the $BT2$ water line list,
which includes $\sim$twice as many transitions with a somewhat lower total
angular quantum number $J$ but over a wider spectral range, extending deeper
into the blue-optical. However, the comparison of both line lists with
laboratory H2O measurements showed that the $PS97$ ACSs are more accurate in
predicting line positions than $BT2$ at wavelengths longer than 1 $\micron$
(Alberti et al., 2015; Melin & Sanders, 2016). It is for this reason that the
$PS97$ list has been used in several works (e.g., Freedman et al. (2014);
Marley & Robinson (2015)), despite more modern line lists. Meanwhile,
HITEMP—the high-temperature arm of the CfA HITRAN database—was created, using
a trimmed version of the $BT2$ line list, but with rigorous validation and
adjustments against laboratory data (Rothman et al., 2010). Recently, ExoMol
improved the $BT2$ line list by refining the potential energy surfaces, and
extending the wavelength range down to 0.25 $\micron$ (40,000 cm-1), referred
to as the $POKAZATEL$ (Polyansky et al., 2018) line list. Table 6 summarizes
these line lists and their key differences, and Fig. 3 compares the resultant
cross-sections for a representative pressure/temperature. Besides the spectral
range, there are extensive differences in their line positions, line shifts
with pressure, and the number of lines, clearly apparent in different spectral
regions such as the 2.420–2.424 $\micron$ band (K band)–subject to numerous
high-resolution observations (e.g., Birkby et al. (2013)). Brogi & Line (2019)
showed that these differences matter in constructing high-resolution
spectroscopy cross-correlation functions potentially leading to bias in the
interpretation of the atmospheric composition. Recently, Gandhi et al. (2020)
compared the water $POKAZATEL$ data with the laboratory HITEMP data, also in
the context of high-resolution cross-correlation spectroscopy, showing very
good agreement up to temperatures of $\sim$1200 K.

In our ACS database, we used the $POKAZATEL$ H2O line list over the full
spectral range of 0.25–100 $\micron$ at the temperature and pressure
conditions given in Table 5. Figure 4 shows a subset of our ACSs as a function
of temperature.

More recently, Conway et al. (2020) have published their H2O line list
calculated from experimental spectroscopic data, which includes $\sim$106
transitions and it is limited up to $J_{max}$=20. Their line lists have shown
a significant improvement in the line position for the ultraviolet spectral
region. Note that the current ground-based telescopes with very high
resolution are mostly detecting in the near-IR region; however, future
telescopes in the UV-Vis regions are required to have accurate line positions
for high-resolution cross-correlation modeling of observational data.

###  4.2 TiO

Several spectroscopic measurements have been carried out to determine the
spectroscopic parameters such as electronic dipole moments, hyperfine spectral
properties, and rotational and vibrational constants for the TiO electronic
ground state101010In diatomic spectroscopy, in general, the electronic ground
state is represented by $X$ and the higher electronic states are labeled by
$A$, $B$, and so on. In addition, the electronic multiplicity (2S+1) and the
total orbital angular momentum ($\Lambda$) are used to represent the
electronic state. For example, $X^{3}\Delta$ is the ground state of TiO with a
multiplicity of 3 and orbital angular momentum of $\Delta$, which is
equivalent to $\Lambda$=2. Hence, $C^{3}\Delta-X^{3}\Delta$ is showing the
electronic transition between the TiO state $C$ and $X$, with the same total
orbital and spin angular momentums. Chapter 9 by Bernath (2005) provided
detailed information on this topic., $X^{3}\Delta$, as well as the low-lying
excited states such as $B^{3}\Pi$, $C^{3}\Delta$, and $D^{3}\Pi$ (Steimle &
Virgo, 2003; Amiot et al., 1995; Balfour et al., 1993). In addition, several
laboratory measurements have been done to determine the line position and
strength between the following TiO electronic states:
($C^{3}\Delta-X^{3}\Delta$) (Hodges & Bernath, 2018),
($c^{1}\Phi-a^{1}\Delta$) (Bittner & Bernath, 2018), ($b^{1}\Pi-a^{1}\Delta$)
(Ram et al., 1996; Bittner & Bernath, 2018), ($A^{3}\Pi-X^{3}\Delta$) (Ram et
al., 1999), ($f^{1}\Delta-a^{1}\Delta$) (Brandes & Galehouse, 1985), and
($c^{1}\Phi-a^{1}\Delta$) (Bittner & Bernath, 2018).

Kurucz (1992) collected the available laboratory spectroscopic data for all
TiO transitions to make the first comprehensive laboratory TiO line list
(hereafter TiO-$Kurucz92$). Concurrently, Plez et al. (1992) used a
theoretical spectroscopic method to calculate the transition dipole moments to
generate TiO opacities. A few years later, they used more accurate dipole
moments from Langhoff (1997) as well as the available spectroscopic measured
data to improve line positions and intensities of the TiO nine low-lying
electronic states (Plez, 1998).

Schwenke (1998) independently used ab initio methods that included the spin-
orbit and rotation-orbit coupling to compute potential energy surfaces for 13
electronic states. These surfaces were used as a Rydberg–Klein–Rees (RKR)
potential to extract rovibrational energy levels. Schwenke (1998) also adopted
the transition moments from Langhoff (1997) to determine the intensities for
each rovibrational transition in order to compute a complete line list
(intensities and positions) for 45$\times$106 lines. Allard et al. (2000)
compared these two ($Plez92$ and $Schwenke98$) TiO line lists in the context
of M- and Brown-dwarf atmospheres, finding that the $Schwenke98$ data could
better model the thermal emission from cool substellar atmospheres.

Hoeijmakers et al. (2015) used $Schwenke98$ and $Plez92$ line lists to
detect/identify TiO in the HD 209458b atmosphere via high-resolution cross-
correlation spectroscopy (R$\approx$100,000) finding that the line positions
in both lists are not sufficient to extract an accurate signal. These mounting
inadequacies in line positions and intensities motivated the need for a
better, more comprehensive, TiO line list. ExoMol used a high-quantum level of
basis set computation methods with spin-orbit coupling to generate all
rovibronic (rotation-vibration-electronic) transitions between the 13 low-
lying electronic states, covering a spectral range of 0.33–100 $\micron$
(called $TOTO$, McKemmish et al. (2019a)). In our ACS database we used this
$TOTO$ line list111111 exomol.com/data/molecules/TiO/49Ti-16O/Toto/ from
0.3-100 $\micron$ over the conditions given in Table 5. Figure 5 summarizes a
subset of these ACSs and Figure 6 and 7 compare to past line lists using
identical computational setups.

More recently, Bernath (2020a) have recorded the TiO spectra in the
visible–near-infrared regions (476–1176 nm) at 2300 K, and compared the
measured intensity and line position with the TOTO data. In addition, Nugroho
et al. (2020) applied high-resolution cross-correlation spectroscopy method
using the TiO $Plez1998$ (updated version) and $TOTO$ line lists, but they
could not detect TiO signature in KELT-20b atmosphere. Note that even though
both Nugroho et al. (2020) and our study have used the same TiO-$TOTO$ line
list, our generated ACS data are different from their data because of the
following reasons. First, their resolution is 100 points/wavenumber, however,
our resolution is at least 1 times finer than them for several pressure-
temperature points. Second, Their line wing cut-off is 100 cm-1 which is
different from ours. Besides, our pre-generated ACS data covers a wider
temperature and pressure range with larger grid points than the current pre-
generated ACSs.

###  4.3 VO

Numerous laboratory works have focused on determining the spectroscopic
constants of the ground-state ($X^{4}\Sigma^{-}$) and low-lying excited
states, including the $A-X$ ($\sim$1.1 $\micron$ (Cheung et al., 1982)), $B-X$
( $\sim$0.74 $\micron$ (Huang et al., 1992)), and $C-X$ ($\sim$0.43–0.58
$\micron$ (Hopkins et al., 2009)) systems as well as quartet–quartet
transitions (e.g., ${}^{4}\Delta-^{4}\Pi$ and ${}^{4}\Delta-^{4}\Phi$,
$\sim$0.85 and 1.05 $\micron$ (Merer et al., 1987)) and doublet–doublet
transitions (e.g., ${}^{2}\Delta-^{2}\Delta$ and ${}^{2}\Phi-^{2}\Delta$,
$\sim$0.45 and 1.4 $\micron$ (Ram et al., 2002; Ram & Bernath, 2005).
Complimenting the experiments, several theoretical ab initio works on VO have
been undertaken to assign all rovibronic transitions to improve the
atmospheric modeling of ultra-hot atmospheres (e.g., (Miliordos & Mavridis,
2007)). Hübner et al. (2015) computed potential energy surfaces of the
electronic ground and excited states and their corresponding spectroscopic
constants (equilibrium radius, dissociation energies). McKemmish et al. (2016)
(hereafter, $VOMYT$) improved upon these previous ab initio results by
including spin-orbit and spin-spin couplings as well as by leveraging
available spectroscopic data to modify the potential energy surface to improve
line positions and intensities, resulting in a robust VO line list with
2.77$\times$108 transitions. We used this $VOMYT$ line list121212
exomol.com/data/molecules/VO/51V-16O/VOMYT/ to generate our VO cross-sections
given the parameters in Table 5. A sample of these cross-sections is shown for
multiple temperatures and pressures in Fig. 8. In addition, Fig. 9 illustrates
the difference between the $VOMYT$ ACS data with the old ones computed from
the $Plez$ and $Schwenke$ line lists for the full UV-Vis-IR range. The reason
for these considerable differences is due to the calculated number of
transitions and the computed electronic states from each line list. For
example, Plez (1999) has accounted for 3.1 million lines, while $VOMYT$ has
277 million transitions, which explains why it has a higher ACS value. The
number of transitions in the $Schwenke$ line list is much smaller than $VOMYT$
as shown in the figure. Further details can be found in table 19 by McKemmish
et al. (2016).

###  4.4 FeH

FeH (iron monohydride) is a diatomic radical with a high-multiplicity ground
state ($X^{4}\Delta$), resulting in a complex electronic spectrum (see page 71
in Veillard (2012)). Several laboratory spectroscopic measurements have been
performed since the 1970s to record and analyze the FeH
$F^{4}\Delta-X^{4}\Delta$ 0–0 band (known as Wing-Ford band) (McCormack &
Oconnor, 1976) as well as to characterize the infrared FeH spectra (Phillips
et al., 1987a). Later, Dulick et al. (2003) used an ab initio quantum mechanic
approach to calculate a new line list for several vibrational bands in the
$F^{4}\Delta-X^{4}\Delta$ system, including the electronic transmission dipole
moment and spectroscopic constants (e.g., rotation and vibration constants).
Following their theoretical work, Wende, S. et al. (2010) used high-resolution
spectroscopy to record the Wing-Ford spectral lines in 989.8–1076.6 nm. In the
same year, Hargreaves et al. (2010) used the above laboratory data to
investigate the $E^{4}\Pi-A^{4}\Pi$ ($\sim$1.58 $\micron$) rovibrational
spectra. Note that the band strength of the $E-A$ system calculated from this
work has been problematic in several astrophysical spectral observations,
further discussed in §4.4.1, and so we did not include this $E-A$ band in
generating our FeH opacities. More recently, (Bernath, 2020b) synthesized
these works into the MoLLIST line database. We used the FeH line list by
Dulick et al. (2003)131313 exomol.com/data/molecules/FeH/56Fe-1H/MoLLIST/;
Note that the reference given in the ExoMol website is mistakenly to the
recent work by Wende, S. et al. (2010), but the provided line lists there are
from Dulick et al. (2003). to compute our cross-sections over the properties
given in Table 5. Fig. 10 (left) illustrates a few pressure points from our
grid and Fig. 10 (right) shows the results of including the Hargreaves et al.
(2010) $E-A$ band.

####  4.4.1 Comments on FeH Line Lists

The history of the FeH line lists is complex and deserves an expanded
discussion. Much of the uncertainty involves the $E^{4}\Pi-A^{4}\Pi$
electronic transition near 1.58 $\micron$ (6300 cm-1, Fig. 10 (right panel).
Hargreaves et al. (2010) obtained the positions and intensities within this
band using a spectrum previously recorded with a Fourier Transform
Spectrometer at Kitt Peak National Observatory from an emission spectrum
produced by a King-type furnace as the source (Phillips et al., 1987b). A
calibration step was necessary to convert the measured emission intensities,
without an absolute intensity scale, into line strengths at a given
temperature, resulting in their line list for this $E-A$ transition.

However, there are several potential sources of uncertainty in this measured
intensities-to-line strengths conversion. First, the temperature of the tube
furnace was determined to be closer to 2200 K based on the relative line
intensities (instead of the 2673 K as recorded by Phillips et al. (1987b)).
The actual final calibration connecting the lab data to intensities was done
using lines that had been individually identified by Balfour et al. (2004).
The spread in the intensities (see Figure 1 in Hargreaves et al. (2010) paper)
is quite large and a linear regression was used to obtain a conversion factor
for the intensities. Hargreaves et al. (2010) mentioned in the paper that
points used to calibrate the laboratory intensities contained considerable
scatter, and the change in the assumed temperature may play a role in the
intensity problem. In addition, An average lower state energy (2250 cm-1) is
used for all unassigned lines (96$\%$ of the lines provided), which would
contribute to the uncertainty at temperatures away from 2200 K as the line
list from this work was provided at 2200 K. Two points to note: the ratio of
the partition function $Q$(2673K)/$Q$(2200K) = 1.64 and the change in the
factor needed to convert emission intensities to absorption values (see Eq. 6
in Hargreaves et al. (2010)) is approximately a factor of 2 when considering
the ratio of the two temperatures. These caveats may play a role in
astrophysical data-model comparisons, suggesting that this FeH band, in
particular, deserves further theoretical and laboratory attention.

###  4.5 TiH

Several spectroscopic works have been performed to record and assign the TiH
spectral systems including the ${}^{4}\Gamma-X^{4}\Phi$ system (530 nm Steimle
et al. (1991); Launila & Lindgren (1996)) and the vibrational
${}^{4}\Phi-X^{4}\Phi$ system (938 nm (Andersson et al., 2003; Linton et al.,
2012)) system. Burrows et al. (2005) re-investigate the previous TiH
spectroscopy data in order to derive new spectroscopic constants to produce a
line list, called MoLLIST. We employed this line-list141414
exomol.com/data/molecules/TiH/48Ti-1H/MoLLIST/ to generate pre-computed ACS
data over the parameters given in Table 5. Cross-sections for select pressures
are shown in Fig. 11 (left).

###  4.6 CrH

An emission spectrum of the $A^{6}\Sigma^{+}-X^{6}\Sigma^{+}$ (0.74–1
$\micron$) system was first recorded by (Ram et al., 1993), later expanded
upon by (Bauschlicher et al., 2001) who fit more bands (i.e., 1–0, 1–1, and
2–0) in the region of 0.67–1.11 $\micron$. Recently, Bernath (2020b) combined
them all these line-lists into the MoLLIST database. We used MoLLIST
reformatted by the ExoMol group151515
exomol.com/data/molecules/CrH/52Cr-1H/MoLLIST/ to generate ACS data for the
available spectral range (i.e., 0.7–1.6 $\micron$). Fig. 11 (right) shows our
cross-sections as a function of pressure.

###  4.7 CaH

The infrared and electronic transitions of the ground state $X^{2}\Sigma^{+}$,
excited states ($A^{2}\Pi$, $B^{2}\Sigma^{+}$, and $E^{2}\Sigma$, 0.45–1 and
2–14 $\micron$ respectively) have been characterized using high-resolution
Fourier transform spectroscopy (Ram et al., 2011; Shayesteh et al., 2013). The
Einstein-A-coefficients have also been calculated for these band systems (Li
et al., 2012; Alavi & Shayesteh, 2017a; Yadin et al., 2012). Additional ab
initio investigations determined the transition dipole moments of the ground
state $X^{2}\Sigma^{+}$, excited states (i.e., $A^{2}\Pi$, $B^{2}\Sigma^{+}$,
and $E^{2}\Sigma$) (Shayesteh et al., 2017; Weck et al., 2003) covering
wavelengths from 1–2 and 14–100 $\micron$. Our cross-sections employs the
laboratory-based lists synthesized by Bernath (2020b) 161616
exomol.com/data/molecules/CaH/40Ca-1H/MoLLIST over the 0.45–1 and 2–14
$\micron$ regions. For the remaining spectral range, i.e. 1–2 and 14–100
$\micron$, we used the ab initio line list from Yadin et al. (2012)171717
exomol.com/data/molecules/CaH/40Ca-1H/Yadin/. Figure 12 (right) summarizes our
cross-sections at 2000K over a range of pressures.

###  4.8 MgH

The spectroscopy of the ground state and low-lying excited electronic states
of MgH has been the subject of numerous investigations. Balfour & Cartwright
(1975a, b) and later Shayesteh & Bernath (2011) have measured the rovibronic
transitions of the $A-X$ and $B^{\prime}-X$ systems in order to extract line
positions, dissociation energies, rotational constants, and their potential
energy surfaces. Employing the latest potential energy surface’s, Yadin et al.
(2012) calculate all infrared transitions for the MgH ground electronic state
for 1.2–100 $\micron$. In addition, GharibNezhad et al. (2013) used high-
resolution spectroscopic data to produce a line list from 0.35–1.2 $\micron$.
We compute our cross-section using the Yadin et al. (2012)
181818exomol.com/data/molecules/MgH/24Mg-1H/Yueqi/ line list from 1.2–100
$\micron$ and the GharibNezhad et al. (2013)191919
exomol.com/data/molecules/MgH/24Mg-1H/MoLLIST from 0.35–1.2 $\micron$. Figure
12(left) illustrates a slice on our cross-section grid for 2000K over a
representative range in pressures.

###  4.9 SiO

Since the 1970s, SiO has been the subject of several spectroscopic studies
over the UV-Vis to the IR using data recorded from both hot gas cells as well
as the sunspots (Barrow & Stone, 1975; Campbell et al., 1995; Sonnabend et
al., 2006). Furthermore, the SiO potential energy surfaces, Einstein A
coefficients, and other spectroscopic constants have been theoretically
studied using ab inito method (Langhoff & Bauschlicher, 1993; Langhoff &
Arnold, 1979). Later, as a part of the ExoMol initiative, Barton et al. (2013)
improved the potential energy surface of the ground state and dipole moment
function. In our calculation, we used the Barton et al. (2013) line list202020
exomol.com/data/molecules/SiO/28Si-16O/EBJT/ to calculate cross-sections over
1.67–100 $\micron$ for the temperature and pressure range’s reported in Table
5. Figure 13(right) shows a slice on our ACS grid for 2000 K over a
representative range in pressures.

###  4.10 AlH

Different rovibronic lines of AlH have been measured in the lab using high-
resolution spectroscopy, including the $A^{1}\Pi-X^{1}\Sigma^{+}$ band at
400–550 nm (Szajna & Zachwieja, 2009; Ram & Bernath, 1996), the
$C^{1}\Sigma^{+}-X^{1}\Sigma^{+}$ band at 220–240 nm (Szajna & Zachwieja,
2010). In addition, the AlH dissociation energy and the low-lying electronic
states have been characterized using ab initio approach’s Matos et al. (1987).
Recently, Yurchenko et al. (2018) employed these spectroscopic constants of
the ground state and the first low-lying excited state, and experimental
potential energy curves to calculated all rovibrational transitions between
the energy levels. We employed their line list, named
$WYLLoT$212121exomol.com/data/molecules/AlH/27Al-1H/AlHambra/,222222Although
in the paper by Yurchenko et al. (2018), it was named as WYLLoT line list, the
ExoMol website provided the AlH line list files with “AlHambra” name., to
generate our ACSs from 0.4–100 $\micron$ for the temperature and pressure
ranges in Table 5. Figure 13 (right) represents a subset of our ACSs as a
function of pressure.

###  4.11 Comparison to Other Absorption Cross-Section Databases

There are other cross-section databases, some publicly available such as
(Villanueva et al., 2018; Chubb et al., 2020), and some are not (Sharp &
Burrows, 2007; Freedman et al., 2008, 2014; Goyal et al., 2018). We build on
these past works by implementing the latest line lists, primarily drawn from
the ExoMol, and provide an up-front description of our sources of pressure
broadening and how we approach the problem when no data is available (see §3).
Table 7 summarizes the known differences between our database and past
absorption cross-section database’s. In summary, our database resolution is
sufficiently large to be applicable for interpretation of $HST$ and $JWST$
observed data as well as high-resolution cross-correlations’. In addition, we
used a constant number for the wing cut-off to avoid overestimation of the
opacity continuum. The temperature, pressure, and wavelength ranges are also
wider and have more grids (1460 T-P points) than other available pre-generated
databases in order to fully model the (Ultra)Hot-Jupiters and M-L dwarf
atmospheres.

##  5 Impact of Opacities on highly-irradiated exoplanet atmospheres

We assess the impact of the newly generated ACSs on the atmospheres and
spectra of M dwarfs and hot Jupiters–specifically, the influence of metal
hydrides and oxides from EXOPLINES vs. Freedman2014 (Freedman et al., 2014)
(see the list of the Freedman2014’s line lists at Table 2 by Lupu et al.
(2014)). First, we simulate a representative Ultra-Hot Jupiter atmosphere
(Tirr= $\sim$2000 K, $\log g$=3, Tstar=6500 K, solar composition) with a
1D-self-consistent radiative-convective thermochemical equilibrium model, Sc-
CHIMERA232323The core radiative transfer, CHIMERA, found at
https://github.com/mrline/CHIMERA, previously described in Piskorz et al.
(2018); Arcangeli et al. (2018); Gharib-Nezhad & Line (2019). We compute the
planetary emission and transmission spectrum from 0.3–5.0 $\mu$m. Major
opacity sources included in these models are H2O, TiO, VO, FeH, CO, CO2, CH4,
NH3, H2S, HCN, C2H2, PH3, CaH, MgH, CrH, SiO, AlH, Na, K, H2–H2, H2–He, Fe,
Mg, Ca, H- bound/free-free continuum, and H2/He Rayleigh scattering within the
correlated-K resort-rebin framework (Amundsen et al., 2016).

We illustrate the effects of TiO, VO, H2O individually, and as combined with
other metal hydrides (FeH, CaH, MgH, CrH, SiO, and AlH, with sources listed in
Table 4). Figure 14 shows both transmission (left) and emission (right)
spectra for an Ultra Hot Jupiter, varying only the choice of line list.
Focusing first on the transmission spectrum, we report significant differences
in the spectral shape below 1.0$\mu$m; however, in the near-infrared, the
residual differences are well below 50 ppm242424$HST$ WFC3 (1.1–1.4 µm)
precision of 15–50 ppm are routinely achieved (Line et al., 2016; Kreidberg et
al., 2014). Comparable or better precision are anticipated with $JWST$ (Bean
et al., 2018) . Between 0.3–1.0 $\mu$m, we find that major differences are due
to the choice of TiO line list (TOTO vs. Schwenke, Freedman et al. (2014)),
leading up to 320 ppm in residuals. Differences arising purely from the choice
of metal hydride line lists (FeH, MgH, and CaH from MoLLIST), are around 75
ppm for the transmission spectrum, notably over wavelengths covered by the
HST/WFC3 bandpass (1.4–2.0 $\mu$m). We also investigated the influence of H2O
line list choice on the transmission spectra, where we find residual
differences fall under 10 ppm when comparing Schwenke (Freedman et al., 2014)
to $POKAZATEL$.

For the thermal emission spectrum; similarly, TiO line list choice leads to
significant differences in the spectral shape, especially from 1.0–5.0 $\mu$m,
with up to 80 ppm differences. Metal hydrides and H2O lead to residual
differences around 10 ppm, also consistent with the transmission spectrum (see
Figure 14). Moreover, the total differences between all old ACS data (e.g.,
TiO-Schwenke, VO-Plez, MgH-Weck, CaH-Weck, FeH-old) against the EXOPLINES ACS
data (TiO-TOTO, VO-VOMYT, MgH-MoLLIST, CaH-MoLLIST, FeH-MoLLIST), are
dominated by TiO and metal hydride line list differences, altogether leading
up to the same level of residuals.

We also illustrated the impact of these new ACSs data on the Temperature-
Pressure (TP-) profile of this candidate WASP-121b atmosphere in Fig. 15. This
figure shows that the new TiO-TOTO ACS data change the TP profile by $\sim$60
K between 1mbar and 1 bar. The impact of all new molecular ACSs (TiO, VO,
etc.) is $\sim$130 K between 1 mbar to 1 bar. These differences in the TP-
profile lead to change in the atmospheric chemical composition, emission, and
transmission synthetic spectra.

More recently, Piette et al. (2020) showed that incorporating the different
TiO opacities (i.e., TOTO, Plez, and Schwenke) biases the synthetic emission
and transmission spectra of ultra-hot Jupiters (R$\sim$104) up to $\sim$1000
ppm in the visible and 100 ppm in the near-IR spectral region. In another
instance for high-resolution ground-based spectroscopy, Herman et al. (2020)
used TiO-Plez ACS to identify the potential presence of TiO optical lines in
WASP-33b. Implications of these works strongly vouch for the critical vetting
of line lists used to compute appropriate ACS, especially concerning oxygen-
bearing molecules such as H2O and TiO to robustly determine bulk chemical
properties (such as C/O ratio) of sub-stellar atmospheres (Molaverdikhani et
al., 2019), as well as improving the atmospheric circulation models of hot
Jupiters (Kataria et al., 2016).

##  6 Impact of Opacities on M-dwarf atmospheres

M-dwarf atmospheric spectra are also subject to differences arising from
various line lists. To quantify these differences, using the same self-
consistent modeling framework described above, we simulate a dust-free
$T_{\mathrm{eff}}$ = 3000 K, $\log g$=5, solar composition atmosphere. In an
upcoming paper by Iyer et al. (In Prep), we will discuss our M-dwarf model in
great detail. Consistent with the hot Jupiter case, TiO line-list differences
have the largest influence on the spectral shape and the temperature profile.
We find that the TiO-$TOTO$ (EXOPLINES) line-list alone, when compared to the
$Schwenke/Allard$ (Figure 16, left) produces spectral differences of up to
125$\%$, primarily between 0.3–1.0 $\mu$m. Alternatively, the effect of VO
opacity ($Plez$ (Freedman et al., 2014) vs $VOMYT$ (EXOPLINES)) and H2O
(Schwenke (Freedman et al., 2014) vs $POKAZATEL$ (EXOPLINES)) do not
contribute to any notable differences at lower resolutions (R=100), however,
we see up to a 30$\%$ difference due to the effect of metal hydrides below
1$\mu$m, and up to 12$\%$ over the near-IR (1.4–2.0 $\mu$m) bandpasses. TiO
attributes to the largest variation in the temperature profile as well; (see
Figure 16, right), with up to 50 K in differences between 1 mbar to 0.1 bar,
and up to 20 K difference deeper than 100 bars, because of a subtle shift in
the adiabat. Furthermore, the absorption cross-sections from the hydrides
(calculated from MoLLIST) lead to thermal profile differences of up to 10 and
20 K respectively, from 1 mbar to 0.1 bar and down to 100 bars. Undoubtedly,
this level of bias—in both hot Jupiters and M-dwarfs—arising purely from
generational differences of line lists would lead to improper atmospheric
inferences. McKemmish et al. (2019b) also have recently investigated the
impact of (Plez, 1998), (Schwenke, 1998), and TOTO TiO line lists on M-dwarf
flux, which showed large differences in their synthetic flux.

##  7 Current Challenges with Opacities

Several spectroscopic parameters are critical for computing absorption cross
sections and their subsequent effect in the modeling of observations (e.g.,
Fortney et al., 2019). Some challenges arise simply due to lack of laboratory
data, and some are because of the computational shortcuts used to improve the
speed of these often lengthy calculations. Therefore, it is crucial to
consider these all differences between the Voigt profiles, broadening
treatment, wing cut-off and other details in order to evaluate and cross-check
different opacity databases generated by either CPU-based computing codes such
as ExoCross and HAPI252525https://github.com/hitranonline/hapi, or GPU-based
codes such as Radis262626https://radis.readthedocs.io/en/latest/ and
Helios-K272727https://helios-k.readthedocs.io/en/latest/(Yurchenko et al.,
2018; Kochanov et al., 2016; van den Bekerom & Pannier, 2021; Grimm et al.,
2021). We briefly discuss the current pressing challenges in producing
accurate cross-sections:

  * $\blacksquare$

The Lack of Pressure Broadening Data—As discussed in §3, the pressure-
broadening coefficients, $\gamma_{\mathrm{L}}$ and $n_{T}$, are critical to
the proper computation of the Lorentz line widths and wings, which dictates
the “off line” continuum. For an absorber, these coefficients depend on the
broadening gas, quantum $J$ number, molecular symmetry282828Spectroscopic
parameters such as pressure-broadening and molecular angular momentums
(simply, quantum numbers) depend on the molecular geometry and the symmetry
between different energy states. For example, CH4 is a tetrahedral molecule
and has $A_{1},A_{1},F_{1},F_{2}$ and $E$ symmetries, which can be found from
character tables. For further details, check Table 3 by Rothman et al. (2005)
and the discussion in chapter 3 by Bernath (2005). Several examples of
broadening data can also be found in chapters 4 and 5 by Buldyreva et al.
(2011). , temperature, and also the specific interactions with the broadening
gas (e.g., the complexity in the line profile of Na and K atoms studied by
Allard et al. (2019, 2016)). The current state of broadening data for many
molecules important in exoplanet/substellar atmospheres is concerning. In most
cases for many absorbers $\gamma_{\mathrm{L}}$ measurements are limited to
below 500 K (e.g., see review by Hartmann et al. (2018)). Most data are only
applicable to “Earth-like” conditions through “air-broadening” or reducing
solar-system giant-like atmospheres through H2/He broadening. Regarding the
metal hydrides and oxides in question, as far as our best knowledge, there is
no laboratory/theoretical broadening data available..

  * $\blacksquare$

Compositional dependency of absorption cross sections: One of the key findings
of the Kepler Mission is that a majority of exoplanets fall within this “warm
mini-Neptune” regime (Rp $\sim$2–4REarth T$<$1000 K) (Batalha, 2014). The bulk
composition of these exoplanets is not hydrogen-dominant, and therefore,
incorporating the pre-generated H2/He-broadened opacities to model their
atmospheres may cause errors and biases in interpreting their observational
emission and transmission spectra. For example, (Gharib-Nezhad & Line, 2019)
have shown that using the H2/He-broadened of water opacity for modeling a
candidate super-Earth steam atmosphere could lead up to 80 ppm (part-per-
million) difference in transmission and 250 ppm in the emission spectra, which
are detectable by both $HST$ and the future $JWST$ telescopes. As a result,
there is uncertainty and inaccuracy in atmospheric modeling observables such
as composition, which could lead to a misinterpretation of observational data.

  * $\blacksquare$

Line Profile—The Voigt profile is the most common line shape applied in
opacity computations. This profile is based on the ideal gas assumption where
no interactions between broadening (e.g., the bath gas/background) molecules
exist. However, these interactions do occur, and hence, this effect should be
taken into account with more advanced line profiles such as the speed-
dependent Voigt profile (Pickett, 1980; Buldyreva et al., 2011). These
broadener gas interactions have been explored at both low and high pressures
(Ngo et al., 2012; Grigoriev et al., 1999). Table 1 by Ngo et al. (2013)
illuminates some of these differences.

  * $\blacksquare$

Voigt Profile Algorithm—The specific algorithm and inherent approximations
used to compute the Voigt profile can result in non-negligible uncertainties.
The Voigt algorithm by Humlíček (1979) is the most widely used due to the
balance between accuracy and computational efficiency. However, it has been
shown (Zaghloul, 2015; Schreier, 2018a) that this algorithm is not always
accurate over the pressure, temperature, and wavelength regions. Other
algorithms exist, but need to be continually assessed for accuracy in
different situations (Schreier, 2018b).

  * $\blacksquare$

Line Wing Cut-Off—This dictates the frequency extent to which the Lorentz line
wings are computed from the line core–typically employed to reduce the
computational burden. Choosing too short of a wing cut-off, particularly for
high pressures ($>$10 bar), can result in large errors in the opacity
continuum depending upon the number of transitions. Hartmann et al. (2002)
proposed an empirical correction factor for the wing cut-off to fully model
the 3.3 $\micron$ band of CH4, however, this study is only limited to room
temperature and the broadener is H2 molecule. Further investigations are
required to understand the accurate wing cut-off for different line profiles.

  * $\blacksquare$

Intensity Cut-Off—This effectively limits the number of lines over which to
compute the line strengths and profiles, and subsequent cross sections. Line
intensities are typically given as the line strength at a particular reference
temperature, usually 296K. Choosing a cut will remove the weaker lines that
can present as stronger lines at higher temperatures, resulting in a critical
loss in overall opacity. The cutoff choice is particularly influential with
line lists that contain billions of transitions, which can result in the
exclusion of a substantial portion of the weaker transitions, resulting in an
altered “pseudo-continuum” shape. Figure 17 illustrates the impact of line-
strength cut-off on the $POKAZATEL$ H2O cross-sections at 2000 K, 10-3 bar
over the short wavelengths (0.25 - 0.5 $\micron$ ).

  * $\blacksquare$

Pressure-shift— As a result of collision by the broadening gas, the line-
center blue/red shifts by $\sim$0.001-0.005 cm-1/bar, depending on the
broadener, temperature, and quantum number $J$. At high pressures, lines
extensively overlap due to their large line-width, but the line center will
shift as well. To the best of our knowledge, this concept has not been applied
in generating ACSs for the majority of absorbers (including the current
study).

  * $\blacksquare$

Partition function— The strength of each individual line for different
temperatures is scaled directly by the partition function, usually treated as
a separate data source in opacity calculations. Partition function value for a
given temperature is calculated from all the energy levels that have been
obtained from spectroscopy measurements or through $abinitio$ calculations
(e.g., see equations by Barklem & Collet (2016) and Yurchenko et al. (2018)).
Hence, incompleteness or inaccuracy in the measured/computed energy levels
results in errors in the partition function, and consequently in the computed
line strengths, and resulting cross-sections. For example, the water partition
function and its associated uncertainty have been studied by Vidler & Tennyson
(2000). In addition, Sousa-Silva et al. (2014) have assessed the potential
errors and challenges associated with calculating the PH3 and NH3 partition
function values.

##  8 Summary and Conclusions

The major objective of this investigation is to provide a comprehensive pre-
computed absorption cross-section database relevant to the spectral modeling
of atmospheres of irradiated hot Jupiters and substellar objects. To this end,
we present a public database of pre-computed molecular absorption cross-
sections for all the isotopologues of MgH, AlH, CaH, TiH, CrH, FeH, SiO, TiO,
VO, and H2O. The pressure and temperature range of the grid span 10-6–3000 bar
and 75–4000 K, respectively (except H2O which is 500–4000 K) and their
spectral coverage vary depending on the availability of the line list data,
typically covering 0.25–330 $\mu$m where possible.

We applied detailed care when determining the pressure broadening
coefficients. Where available, we started from the published values estimated
for the H2/He broadening, or otherwise used a $J$-dependent collision theory.
We described the history of the line lists of various species, and when
possible compared the influence of available line lists on the absorption-
cross sections. Finally, we determined the impact of line list choice (hence
cross-sections) on the temperature structure and emergent spectra of a hot
Jupiter and M-dwarf using a 1D self-consistent radiative-convective model.
From the latter experiment we found that:

  * $\blacksquare$

The TiO-$TOTO$ line list compared to the TiO-Schwenke line-list (and
subsequent cross-sections) had the most significant influence on the thermal
structures of the hot Jupiter ($\sim$60K differences) and a generic 3000 K
M-dwarf (50 K differences). The resultant hot Jupiter spectra (R=100) differed
between the two line-list scenarios of up to $\sim$80 ppm in
emission/secondary eclipse and $\sim$320 ppm (near 0.3–1 $\micron$) in
transmission. The M-dwarf emergent spectra differed up to 125$\%$ over the
wavelengths most influenced by TiO (0.3–1.0 $\micron$).

  * $\blacksquare$

Considering the large differences in the number of transitions in the various
H2O line lists (see Table 6 and Fig. 3), the resulting differences in the
emergent spectra and temperature structure were are negligible at these
resolutions (R=100). However, at high resolution (R$>$50,000) these
differences in line positions and intensities are more apparent and have been
previously shown to influence molecular abundance determinations of transiting
hot Jupiter’s using cross-correlation spectroscopy Brogi & Line (2019); Gandhi
et al. (2020).

  * $\blacksquare$

The metal hydride (FeH, MgH, and CaH) cross-sections derived from the MoLLIST
line-lists compared to past line lists (MgH-Weck, CaH-Weck) also result in
notable differences in atmospheric observables, with up to an 80 K difference
in the hot Jupiter temperature structure and 10 K in the M-dwarf. Differences
in the hot Jupiter emission/transmission spectra approach $\sim$50 ppm (around
1.4–2 $\micron$). In the M-dwarf spectra, up to 45$\%$ change in flux occurs
near 1.0 $\micron$ and 12$\%$ between 1.4–2.0 $\micron$.

With the upcoming higher fidelity characterization of extra-solar planets and
their hosts (e.g., M-dwarfs), accurate absorption cross section ingredients
(line lists, broadening) are becoming increasingly critical to the success of
properly estimating their atmospheric properties. We encourage the community
to continue to invest resources in line list validation and vetting, ab initio
and laboratory measurements of key broadening coefficients, and production and
curation of vetted absorption cross-section databases.

##  9 Supplementary data

The pre-generated absorption cross-sections (ACS) data from this study are
uploaded in ZENODO https://zenodo.org/record/4458189. Our full isotopologue-
weighted binary database is approximately 0.5 Tb which includes 10 molecular
sets of 1460 ACS temperature-pressure data with the size of $\sim$44GB per
molecule. The un-weighted individual isotopologues ACS binary data are consist
of 22 sets of molecular ACS data with 1460 temperature-pressure points for
each and the total size of $\sim$1 TB. The database will available in multiple
formats to suit various needs. First, we will post a 5 Gb resampled version of
the database on Zenodo, due to their file size limitations. The Zenodo
database will be in the same format as the (Freedman et al., 2014) database
currently used by PICASO (Batalha et al., 2019; Batalha & Rooney,
2020)292929Zenodo Opacities (Freedman et al., 2014). Second, the full
unsampled database (MySQL format) will be available via an FTP-like portal.
Last, we will also launch a web portal so that users can visualize and plot
subsets of the data without needing to download it all.

##  10 Acknowledgements

EGN would like to thank Drs. J. Fortney, R. Lupu, I. Gordon, and R. Hargreaves
for their useful comments and discussions during this study. EGN and ARI
acknowledge Research Computing at Arizona State University for providing HPC
resources that have contributed to the research results reported within this
paper. EGN, MRL, and RF acknowledge support from HST-AR-15796. MRL and ARI
acknowledge support from NASA grant NNX17AB56G. NEB and RF acknowledge support
from 19-NUP2019-0011. We also acknowledge the ExoMol team for their continued
production of large line lists and pertinent data critical to high-temperature
atmospheric modeling. EGN’s research was supported by an appointment to the
NASA Postdoctoral Program at the NASA Ames Research Center, administered by
Universities Space Research Association under contract with NASA. Finally, we
thank the anonymous reviewers for their thoughtful comments.

##  11 Software

We used the publicly available $ExoCross$ code (Yurchenko et al., 2018)
developed by the ExoMol group to generate the cross sections, and the CHIMERA
radiative transfer and retrieval tool to produce the simulated
emission/transmission spectra.

##  Appendix A Appendices

###  A.1 Calculating the Lorentz coefficient ($\gamma_{\mathrm{L}}$) based on
collision theory

The interaction between a given absorber with other atoms or molecules (i.e.,
perturbers) induces an extra width in the recorded spectral lines. In order to
understand and calculate the line width, this interaction may be treated in
two ways. The first approach is the classical approximation method in which
the collision between the absorber and broadener occurs through a straight
trajectory. The second method, however, uses quantum mechanical theory to
describe the motion of perturbers. Limitations in both methods have been
discussed in detail by Baranger (1958). In this study, we used Anderson theory
which deals simultaneously with the motion of perturbers and the transition
between energy levels with classical and quantum mechanics (Anderson, 1949).
The total energy in the system is then solved through perturbation theory, and
the collisional half-with of the spectral line can be represented by Eq. A1
(see Eq. 28 by Anderson (1949)):

$\Delta\nu_{\nicefrac{{1}}{{2}}}=\frac{1}{2\pi}n_{b}\bar{v}_{th}\sigma_{col}$
(A1)

where $n_{b}$ is the number density of perturbers, $\bar{v}_{th}$ is the mean
relative velocity of the gas (=$\sqrt{8k_{B}T/\mu\pi}$), and $\sigma_{col}$ is
the collision cross-section in $\AA^{2}$ unit. Using the gas kinetic theory,
HWHM linewidth $\Delta\nu_{1/2}$ (in Hz/Pa) may be written as:

$\Delta\nu_{\nicefrac{{1}}{{2}}}=\left(\frac{8k_{B}T}{\mu\pi}\right)^{1/2}\frac{1}{2k_{B}\pi}\
T^{-1/2}\ \sigma_{col}\ p_{b}$ (A2)

where $k_{\mathrm{B}}$ is a Boltzmann constant and $\mu$ is the reduced mass
of the colliding pair in atomic mass unit
($\mu=M_{absorber}M_{broadener}/(M_{absorber}+M_{broadener})$), and
$p_{\mathrm{b}}$ is the partial pressure of the broadening gas. Comparing Eq.
A2 to Eq. 2 shows that $\Delta\nu_{\nicefrac{{1}}{{2}}}$ is equivalent to
Lorentz HWHM ($\Gamma_{\mathrm{L}}$) (see Eq. 36c and its related discussion
by Baranger (1958)). By converting the unit of Eq. A2 to cm-1/atm and cm-1/bar
, the Lorentz coefficient $\gamma_{\mathrm{L}}$ can be written as:

$\gamma_{\mathrm{L}}[cm^{-1}/atm]=0.0567\ (T\mu)^{-1/2}\ \sigma_{col}$ (A3)

or,

$\gamma_{\mathrm{L}}[cm^{-1}/bar]=0.0574\ (T\mu)^{-1/2}\ \sigma_{col}$ (A4)

in which, the temperature dependence of the $\gamma_{\mathrm{L}}(T)$ is:

$\gamma_{\mathrm{L}}(T)=\gamma_{\mathrm{L}}(T_{0})\left(\nicefrac{{T}}{{T_{0}}}\right)^{-1/2}$
(A5)

Note that this equation can only provide a rough estimate of the pressure-
broadening coefficients because the accuracy of the results relies on the
collision cross section and also kinetic theory to provide the temperature-
dependence coefficient of -1/2.

Table 1: Available calculated/estimated Lorentz coefficient,
$\gamma_{\mathrm{L,b}}$[cm-1/atm] from the literature (for Eq. 2).

Absorber | Broadener | $\gamma_{\rm{L,b}}(J=0)^{\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}{*}}$ | $\gamma_{\rm{L,b}}$ | Reference
---|---|---|---|---
H2O |  H2 | 0.09 | laboratory data | Ba17
H2O |  He | 0.02 | laboratory data | Ba17
TiO, VO |  H2 | 0.1 |  0.1 - 0.002$J_{\rm lower}$∗∗ | Sh07
TiO, VO |  He | 0.06 |  0.06 - 0.0012$J_{\rm lower}$ |
FeH, TiH, CrH |  H2 | 0.075 |  0.075 - 0.001$J_{\rm lower}$ | Du03,Bu02,Bu05
FeH, TiH, CrH |  He | 0.045 |  0.045 - 0.0006$J_{\rm lower}$ |

∗$\gamma_{\mathrm{L,b}}$ is reported for $J$=0 and 296 K. For H2O, we adopted
the $J$-dependency proposed in the cited studies. The $J$-dependency of other
molecules is discussed in §3.3.

∗∗Note, this equation was mistakenly proposed to provide a FWHM of
$\gamma_{\rm{L}}$ by Sharp & Burrows (2007), but in fact, it is for
calculating the HWHM value.

References: Ba17: The H2O Lorentz coefficients were collected by the ExoMol
group http://exomol.com/data/molecules/H2O/, and was discussed by Barton et
al. (2017); Bu05: (Burrows et al., 2005); Bu03: (Burrows et al., 2002); Du03:
(Dulick et al., 2003); Sh07: Sharp & Burrows (2007).

Table 2: Collision cross-section used to calculate the Lorentz pressure-
broadening coefficient, $\gamma_{\mathrm{L,b}}$[cm-1/atm]

Absorber | Broadener | $\mu$ | $\sigma_{col}$ | $\gamma_{\mathrm{L,b}}$ | Reference
---|---|---|---|---|---
24Mg1H |  H2 | 1.85 | NA | 0.08 |  =$\gamma_{\mathrm{L}}$(CaH–H2)
24Mg1H |  He | 3.45 | NA | 0.05 |  =$\gamma_{\mathrm{L}}$(CaH–He)
40Ca1H |  H2 | 1.91 | NA | 0.08 |  =1.6$\gamma_{\mathrm{L}}$(CaH–He)
40Ca1H |  He | 3.64 |  $\sim$27 | 0.05 | [1]
27Al1H |  H2 | 1.87 | NA | 0.08 |  =$\gamma_{\mathrm{L}}$(CO–H2)
27Al1H |  He | 3.50 | NA | 0.05 |  =$\gamma_{\mathrm{L}}$(CO–He)
28Si16O |  H2 | 1.91 |  $\sim$20 | 0.05 | [2]
28Si16O |  He | 3.67 |  $\sim$10 | 0.02 | [3]

Notes:

1\. The reported $\sigma_{\mathrm{col}}$ [$\AA^{2}$] is the excitation
collision cross section (for $J=0\rightarrow 1$ in most cases) for collision
kinetic energy calculated for 296 K ($E_{kin}=(4k_{B}T/\pi)$ $\approx
5.2\times 10^{-21}$Joule=262 cm-1 = 0.032 eV).

2\. The calculated $\gamma_{\mathrm{L,b}}$ is used to calculate HWHM Lorentz
width, $\Gamma_{\mathrm{L,b}}$ in Eq. 2.

3\. $\gamma_{\mathrm{L,b}}$ is reported at temperature 296 K for $J$=0. §3.3
discusses its $J$-dependency.

4\. In the case of AlH–H2 and AlH–He systems, we used CO Lorentz coefficients
because they both have a very close dipole moment and reduced mass.

5\. In a case of MgH, CaH, and SiO molecules, we used this assumption of
$\gamma_{\mathrm{L,b}}$(He)=0.6$\gamma_{\mathrm{L,b}}$(H2).

Reference: [1](Akpinar & Akbalik, 2010), [2](Yang et al., 2018), [3](Dayou, F.
& Balança, C., 2006).

Table 3: Fitted coefficients of the Fourth-order Padé formula (see Eq. 4) to
provide $\gamma_{\mathrm{L}}$[cm-1/atm] for $J$ quantum numbers up to 500.

Absorber | Broadener |  a0 |  a1 |  a2 |  a3 |  b1 |  b2 |  b3 |  b4
---|---|---|---|---|---|---|---|---|---
AlH |  H2 | 7.6101e-02 | -4.3376e-02 | 1.9967e-02 | 2.4755e-03 | -5.6857e-01 | 2.7436e-01 | 3.6216e-02 | 1.5350e-05
AlH | He | 4.8630e-02 | 2.1731e+03 | -2.5351e+02 | 3.8607e+01 | 4.4644e+04 | -4.4438e+03 | 6.9659e+02 | 4.7331e+00
CaH, MgH |  H2 | 8.4022e-02 | -8.2171e+03 | 4.6171e+02 | -7.9708e+00 | -9.7733e+04 | -1.4141e+03 | 2.0290e+02 | -1.2797e+01
CaH, MgH | He | 5.0424e-02 | -1.1014e+02 | 2.2833e+01 | 2.8527e-01 | -2.4407e+03 | 5.5472e+02 | -3.4490e+01 | 6.5808e+00
CrH, FeH, TiH |  H2 | 7.0910e-02 | -6.5083e+04 | 2.5980e+03 | -3.3292e+01 | -9.0722e+05 | -4.3668e+03 | 6.1772e+02 | -2.4038e+01
CrH, FeH, TiH | He | 4.2546e-02 | -3.0981e+04 | 1.2367e+03 | -1.5848e+01 | -7.1977e+05 | -3.4645e+03 | 4.9008e+02 | -1.9071e+01
SiO |  H2 | 4.7273e-02 | -2.7597e+04 | 1.1016e+03 | -1.4117e+01 | -5.7703e+05 | -2.7774e+03 | 3.9289e+02 | -1.5289e+01
SiO | He | 2.8364e-02 | -6.7705e+03 | 2.7027e+02 | -3.4634e+00 | -2.3594e+05 | -1.1357e+03 | 1.6065e+02 | -6.2516e+00
TiO, VO |  H2 | 1.0000e-01 | -2.4549e+05 | 8.7760e+03 | -8.7104e+01 | -2.3874e+06 | 1.6350e+04 | 1.7569e+03 | -4.1520e+01
TiO, VO | He | 4.0000e-02 | -2.8682e+04 | 1.0254e+03 | -1.0177e+01 | -6.9735e+05 | 4.7758e+03 | 5.1317e+02 | -1.2128e+01

Notes:

1\. See §3.3 for a detailed discussion regarding the calculation of these
Fourth-order Padé coefficients.

2\. These coefficients were used to compute the pre-generated absorption
cross-sections in this study.

Table 4: Summary list of opacities: molecules, temperature, pressures, and
their line lists (see §3.5 $\&$ 4).

Absorber | Line list |  $\lambda$ [$\mu$m] | No. Lines | P [bar] | T [K] | PT points |  Icutoff |  Abundance($\%$) | Reference
---|---|---|---|---|---|---|---|---|---
26Al1H | WYLLoT | 0.4–330 |  3.6$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 0.00 | Yu18
27Al1H | WYLLoT | 0.4–330 |  3.6$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 100.00 | Yu18
27Al2H | WYLLoT | 0.4–330 |  3.6$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 0.00 | Yu18
40Ca1H | MoLLIST | 0.45-1, 2-14 |  1.9$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 96.93 | Al17,Li12
40Ca1H | Yadin | 1-2, 14-330 |  2.7$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 96.93 | Ya12
52Cr1H | MoLLIST | 0.7–1.6 |  1.4$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 83.78 | Bu02
56Fe1H | MoLLIST | 0.37–330 |  1.2$\times 10^{5}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 91.74 | We10
24Mg1H | MoLLIST | 0.35–1.2 |  3.1$\times 10^{4}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 78.99 | Gh13
24Mg1H | Yadin | 1.2–330 |  6.7$\times 10^{3}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 78.99 | Ya12
25Mg1H | Yadin | 1.2–330 |  6.7$\times 10^{3}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 10.00 | Ya12
26Mg1H | Yadin | 1.2–330 |  6.7$\times 10^{3}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 11.01 | Ya12
28Si16O | EBJT | 1.67–330 |  1.8$\times 10^{6}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 92.00 | Ba13
28Si17O | EBJT | 1.67–330 |  1.8$\times 10^{6}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 0.03 | Ba13
28Si18O | EBJT | 1.67–330 |  1.8$\times 10^{6}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 0.19 | Ba13
29Si16O | EBJT | 1.67–330 |  1.8$\times 10^{6}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 4.67 | Ba13
30Si16O | EBJT | 1.67–330 |  1.8$\times 10^{6}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 3.08 | Ba13
48Ti1H | MoLLIST | 0.4–2 |  2.0$\times 10^{5}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 73.71 | Bu05
46Ti16O | TOTO | 0.3–330 |  3.0$\times 10^{7}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 8.22 | Mc19
47Ti16O | TOTO | 0.3–330 |  3.0$\times 10^{7}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 7.42 | Mc19
48Ti16O | TOTO | 0.3–330 |  3.0$\times 10^{7}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 73.54 | Mc19
49Ti16O | TOTO | 0.3–330 |  3.0$\times 10^{7}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 5.40 | Mc19
50Ti16O | TOTO | 0.3–330 |  3.0$\times 10^{7}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 5.17 | Mc19
51V16O | VOMYT | 0.28–330 |  2.8$\times 10^{8}$ |  10-6–3000 | 75-4000 | 1460 |  10-50 | 99.5 | Mc16
1H${}_{2}^{16}$O | POKAZATEL | 0.25–100 |  1.1$\times 10^{9}$ |  10-6–300 | 500-4000 | 1460 |  10-34 | 99.75 | Po18

Notes:

1\. We used a single line list for some molecules such as TiO, SiO, and H2O.
For some molecules such as CaH and MgH, multiple line lists were used in order
to compute opacity data for the full spectral range. See §3.5 and §4 for more
details on the line lists.

2\. Species are weighted according to their solar/natural elemental abundances
provided by NIST database: www.nist.gov/pml/atomic-weights-and-isotopic-
compositions-relative-atomic-masses.

3\. For each species, absorption cross section data are provided in two ways:
separate for each isotopologues and weighted based on their natural abundance.

References: Al17=Alavi & Shayesteh (2017b), Bu02=Burrows et al. (2002)
Ba13=Barton et al. (2013), Bu05=Burrows et al. (2005), Gh13=GharibNezhad et
al. (2013), Li12=Li et al. (2012), Mc19=McKemmish et al. (2019b),
Mc16=(McKemmish et al., 2016), Po18=Polyansky et al. (2018), We10=Wende, S. et
al. (2010), Ya12=Yadin et al. (2012), Yu18=Yurchenko et al. (2018)

Table 5: Opacity computational details

Absorbers: |  |  |  |
---|---|---|---|---
|  H2O | TiO | VO | SiO | CaH |  |  |
| MgH | AlH | TiH | CrH | FeH |  |  |
Broadeners∗: 85% H2 + 15% He |  |
T[K] grid: (73 points)∗∗ |  |
| 75 | 100 | 110 | 120 | 130 | 140 | 150 | 160
| 170 | 180 | 190 | 200 | 210 | 220 | 230 | 240
| 250 | 260 | 270 | 275 | 280 | 290 | 300 | 310
| 320 | 330 | 340 | 350 | 375 | 400 | 425 | 450
| 475 | 500 | 525 | 550 | 575 | 600 | 650 | 700
| 750 | 800 | 850 | 900 | 950 | 1000 | 1100 | 1200
| 1300 | 1400 | 1500 | 1600 | 1700 | 1800 | 1900 | 2000
| 2100 | 2200 | 2300 | 2400 | 2500 | 2600 | 2700 | 2800
| 2900 | 3000 | 3100 | 3200 | 3300 | 3400 | 3500 | 3750
| 4000 |  |  |  |  |  |  |
P[bar] grid: (20 points) |  |
|  10-6 |  3$\times$10-6 |  10-5 |  3$\times$10-5 |  10-4 |  3$\times$10-4 |  |
|  10-3 |  3$\times$10-3 |  10-1 |  3$\times$10-1 |  10-2 |  3$\times$10-2 |  |
| 1 | 3 | 10 | 30 | 100 | 300 |  |
| 1000 | 3000 |  |  |  |  |  |
Wing cutoff:† |  |  |
|  P$>$200 bar: 150 cm-1 |
|  P$\leqslant$200 bar: 30 cm-1 |
Opacity code: ExoCross(Yurchenko et al., 2018) |  |
Voigt Algorithm: Humlíček (1979) |  |

∗These broadening mixture is a good choice for hydrogen-dominated atmospheres
such as (Ultra) hot-Jupiters and M dwarfs. For high metallicity atmospheres
such as super-Earths and mini-Neptunes, better choice of broadeners such as
H2O and CO2 is essential.

∗∗ For H2O molecule, absorption cross-sections are calculated for temperature
range 500–4000K.

†To compute the line-profile and include the effect of pressure-broadening,
Lorentz profile is used. The calculation of Lorentz profile for each
individual line can be extended to the full spectral range or be limited to a
few wavenumbers. This is one main challenge in computing opacities, and some
studies such as (Hartmann et al., 2002) and (Bézard et al., 2011) have shown
the non-Lorentzian behavior of the line profile. See §7 for more discussion.

Table 6: Comparing different H2O line lists.

Line Lists | Method |  $\lambda$[ $\micron$ ] | $J_{max}$ | No. Lines | Note | Ref.
---|---|---|---|---|---|---
PS97 | $ab\ initio$ | 0.4 – 100 | 55 |  $\sim$3$\times$108 |  more accurate than BT2 for $\lambda>$1 | [1]
BT2 | $ab\ initio$ | 0.33 – 100 | 50 |  $\sim$5$\times$108 | more transition than Ames1997, shorter wavelength | [2]
POKAZATEL | $ab\ initio$ | 0.25 – 100 | 72 |  $\sim$1$\times$109 |  higher intensity than BT2 at $\lambda<$1 $\micron$ | [3]
HITEMP |  lab/$ab\ initio$ | 0.33 – 100 | 50 |  $\sim$1$\times$108 |  included strong BT2 lines and experimental lines∗ | [4]

∗After rigorous assessment of the impact of the BT2 intensity at 296–4000K,
Rothman et al. (2010) have kept only 25$\%$ of the BT2 lines (see their Eq. 2
and their criteria for different wavenumber ranges and temperatures).

Ref.: [1] (Partridge & Schwenke, 1997), [2] (Barber et al., 2006), [3]
(Polyansky et al., 2018), [4] (Rothman et al., 2010)

Table 7: Summary of the current opacity databases for the molecules in our
investigation.

Abs. Cross Sec. | Linelist |  $\lambda$ [$\mu$m] | T[K] | P[bar] |  Points/cm-1 | P-T Pairs |  Wing cut-off [cm-1]
---|---|---|---|---|---|---|---
H2O |  |  |  |  |
EXOPLINES | POKAZATEL | 0.25–100 | 500–4000 |  10-6–300 | 50–120 | 486 | 100–300
Gandhi2020∗ | POKAZATEL | 0.95–5 | 400–1600 |  10-5–10 | 100 | 49 | Not reported
Malik2019∗∗ | BT2 | 0.5–20 | 50–2900 |  10-6–103 | 100 | 812 | 100
Goyal2018† | BT2 | 0.33–100 | 70–3000 |  10-9–103 | 1000 | 800 | 100
MacDonald2019‡ | POKAZATEL | 0.4–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Freedman2014†† | Schwenke | 0.5–100 | 75–4000 |  10-6–300 | 80-120 | 1060 | 25–250
Chubb2020‡‡ | POKAZATEL | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500
TiO |  |  |  |  |
EXOPLINES | TOTO | 0.3–100 | 75–4000 |  10-6–3000 | 2–285 | 1460 | 30,150
Malik2019 | Plez/Schwenke | 0.5–5 | 50–2900 |  10-6–103 | 100 | 812 | 100
Goyal2018 | Plez | 0.3–100 | 70–3000 |  10-9–103 | 1000 | 800 | 100
MacDonald2019 | TOTO | 0.4–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Freedman2014 | Schwenke/Allard | 0.32–100 | 75–4000 |  10-6–300 | 80-120 | 1060 | 25–250
Chubb2020 | TOTO | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500
VO |  |  |  |  |
EXOPLINES | VOMYT | 0.28–100 | 75–4000 |  10-6–3000 | 2–285 | 1460 | 30,150
Malik2019 | VOMYT | 0.5–20 | 50–2900 |  10-6–103 | 100 | 812 | 100
Goyal2018 | VOMYT | 0.3–100 | 70-3000 |  10-9–103 | 1000 | 800 | 100
MacDonald2019 | VOMYT | 0.4–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Freedman2014 | Plez | 0.8–100 | 75–4000 |  10-6–300 | 80-120 | 1060 | 25–250
Chubb2020 | VOMYT | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500
FeH |  |  |  |  |
EXOPLINES | Dulick | 0.37–100 | 75–4000 |  10-6–3000 | 2–285 | 1460 | 30,150
Goyal2018 | Wende2010 | 0.67–50 | 70–3000 |  10-9–103 | 1000 | 800 | 10
MacDonald2019 | Wende2010 | 0.4–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Freedman2014 | Dulick/Hargreaves | 0.37–100 | 75–4000 |  10-6–300 | 80–120 | 1060 | 25–250
Chubb2020 | Wende2010 | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500
MgH |  |  |  |  |
EXOPLINES | MoLLIST/Yadin | 0.35–100 | 75–4000 |  10-6–3000 | 2–285 | 1460 | 30,150
Malik2019 | Yadin | 1.2–20 | 50–2900 |  10-6–103 | 100 | 812 | 100
MacDonald2019 | MoLLIST/Yadin | 0.4–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Freedman2014 | Weck | 0.3–2.5 | 75–4000 |  10-6–300 | 80–120 | 1060 | 25–250
Chubb2020 | Wende2010 | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500
AlH |  |  |  |  |
EXOPLINES | WYLLoT | 0.4–100 | 75–4000 |  10-6–3000 | 2–285 | 1460 | 30,150
Malik2019 | WYLLoT | 0.4–20 | 50–2900 |  10-6–103 | 100 | 812 | 100
MacDonald2019 | WYLLoT | 0.4–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Chubb2020 | WYLLoT | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500
CaH |  |  |  |  |
EXOPLINES | MoLLIST/Yadin | 0.45-100 | 75–4000 |  10-6–3000 | 2–285 | 1460 | 30,150
Malik2019 | Yadin | 1–20 | 50–2900 |  10-6–103 | 100 | 812 | 100
MacDonald2019 | Yadin | 1–50 | 100–3500 |  10-6–102 | 100 | 162 | 30
Freedman2014 | Weck | 0.8–2.5 | 75–4000 |  10-6–300 | 80–120 | 1060 | 25–250
Chubb2020 | MoLLIST | 0.3–50 | 100–3400 |  10-5–100 | 2-75 | 594 | 10-500

∗Gandhi2020=Gandhi et al. (2020) ACSs data were generate to be used for
calculating cross-correlation function for high-resolution exoplanet
spectroscopy.

∗∗Malik2019=Malik et al. (2019) ACS data have been used to model the
irradiated exoplanets. The pressure grid used for the opacities goes from
$10^{-6}$ bar to $10^{3}$ bar with a logarithmic step size of 1/3 dex, that
makes 28 pressure points. The temperature grid goes from 50 K to 2900 K with a
linear step size of 50 K between 50 K and 700 K, a step size of 100 K between
700 K and 1500K, and a step size of 200 K between 1500 K and 2900 K. That is
29 temperature points in total. Opacities above 3000 K were extrapolate.

†Goyal2018=Goyal et al. (2018) ACS data have been used in ATMO code for
modeling forward exoplanet spectra.

‡MacDonald2019=MacDonald (2019) (see chapter 5) ACS data are a part of
POSIEDON database for atmospheric retrievals.

††Freedman2014=(Lupu et al., 2014; Freedman et al., 2008, 2014) were used in
Exo-Transmit and PICASO code (Kempton et al., 2017; Batalha et al., 2019) to
model transmission, emission, and reflected exoplanetary atmospheric spectra.

‡‡Chubb2020=Chubb et al. (2020): In this work, the resolving power is 15,000
and the wing cut-off is 500$\times\gamma_{\mathrm{Voigt}}$. In comparison, our
resolution is 2-20 times larger in order to fully and accurately could be
employed in modeling $JWST$\- and high-resolution cross-correlation technique.
Our wing cut-off is also a constant number of 30 and 150 cm-1 because the real
shape of Voigt profile is non-Lorentzian and using a very large number can
lead to an intensive overestimation of the opacity continuum.

Figure 1: Comparison of H2 and He-broadening Lorentz HWHM of CO and HCl
molecules using laboratory data. HCl-H2 system has much stronger
$J$-dependency than CO-H2, which could be due to their difference in their
dipole moments. In contrast, the $J$-dependency of He is lower in both cases.
The black lines are also showing the fitted data with 4th order Padé equation
(Eq. 4). Since this equation could go to negative values in some systems and a
very large number for $J$=0 (such as HCl-He case), we applied additional
limitation (see Eq. 5). We used Eq. 4 to calculate the $J$-dependency of AlH,
MgH, CaH, SiO, TiH, FeH, and CrH (see Fig. 2). Data of CO and HCl systems in
this plot is collected from (Devi et al., 2004; Régalia-Jarlot et al., 2005;
Mantz et al., 2005; Toth et al., 1970; Li et al., 2018; Babrov et al., 1960)
(see §3.3 for more details.).

Figure 2: Example of used Lorentz coefficients for AlH, TiH, SiO, and MgH. The
AlH Lorentz coefficients are assumed to be equal to CO, because they both have
the same dipole moments. For other absorbers, the Lorentz coefficient are
decreasing sharply up to $J$=40 similar to HCl because they all have high
dipole moments. 4th order Padé equation (Eq. 4 including the constrains
introduced in (Eq. 5) is used and the coefficients are reported in Table 3 in
order to reproduce these broadening data (see §3.3 for more details.).

Figure 3: Comparison of different H2O ACS for 0.1 bar and 1000K, including
POKAZATEL, BT2, and PS97. Note, that $POKAZATEL$ and $BT2$ line lists are from
ExoMol group, however, $POKAZATEL$ is the most recent version. In addition,
the Schwenke ACS is generated by Freedman et al. (2014) using Partridge &
Schwenke (1997) water line list (named $PS97$). Their expanded comparisons for
2.4 $\micron$ (bottom) shows some differences in their line positions,
intensities. Additionally, there are some extra lines from POKAZATEL that are
not exist in others. Although they are weak, but they can change the opacity
continuum, and so their inclusion is important in particularly windows
spectral regions (see 7 for more discussion). These differences result from
the implemented quantum mechanic level of complexity, and they could bias the
interpretation of medium-to-high-resolution observed data.

Figure 4: Example of H2O $POKAZATEL$ ACS spectra for 0.1 bar and multiple
temperatures. For the same pressure, ACS with higher temperature have broader
Doppler linewidth, and this will results in larger opacity in the line core
comparing to the wings.

Figure 5: Example of the pre-generated TiO-$TOTO$ ACS data: at a constant
pressure, Doppler effect is the main source of line-width, particularly at low
wavelengths (right). In contrast, at constant temperature, the higher pressure
shows the most broadening as a result of collisional effect (left). Note that
Lorentz width is dependent on the temperature as well. We used (McKemmish et
al., 2019b) line list to generated these ACS data.

Figure 6: Compare TiO absorption cross-sections generated from TOTO and Kurucz
line list for 1 bar and 3000 K. Note that there are noticeable differences in
the whole spectral range between both cases. 2.5–9 $\mu m$ region is showing
the highest inconsistency between two spectra. Overall, the TiO $TOTO$-ACS is
showing a larger value than the Kurucz data, which might be due to its large
number of transitions as well as the modified electronic states which results
in shift in some spectral bands.

Figure 7: Compare TiO absorption cross-sections generated from the $TOTO$ and
$Schwenke$ line list for 1 bar and 1500 K. There are noticeable differences in
the whole spectral range between both cases. The highest inconsistency is at
spectral regions $\sim$4–5 and 6.5–8.5 $\micron$, that results in a dramatic
bias in modeling low and high resolution synthetic emission or transmission
spectra. One possible explanation would be the difference between the number
of rotational levels that have been accounted by both $TOTO$ and $Schwenke$
linelist.

Figure 8: Example of our pre-generated VO-VOMYT absorption cross-sections: at
a constant pressure, Doppler effect is the main reason of controlling the
line-width, particularly at low wavelengths (right). In contrast, at constant
temperature, the higher pressure shows the most broadening as a result of
collisional effect (left). These pre-generated ACSs are from (McKemmish et
al., 2016) line list data, which consists of the 13 low-lying electronic state
and have $\sim$227 million lines.

Figure 9: Comparison of different VO absorption cross-sections generated from
different line lists: $Schwenke$, $VOMYT$, and $Plez$ at 2000 K and 1 bar.
$VOMYT$ line list (McKemmish et al., 2016) includes the 13 low-lying states
and $\sim$227 million transitions, and hence the intensity of its spectra
(red) is higher than other line lists (except $Plez$ around 10000 cm-1 which
resulted from A–X transitions). In contrast, $Plez$ line list (Plez,
1999)(green) has only the A–X, B–X, and C–X bands with no infrared
transitions, and so it is only showing data at 5000-25000 cm-1(0.4–2 $\micron$
). The central message of this figure is to show the difference between VO-ACS
data from different line lists is remarkable, and naive implementation of VO
ACS data could result in false conclusions and misinterpretation of the
observational exoplanet/brown-dwarf spectra.

Figure 10: (left) An example of our FeH ACS spectra generated from Dulick et
al. (2003) linelist for multiple pressures and 2000 K. (right) Comparison of
the FeH absorption cross-sections generated with (orange) and without (blue)
including the $E-A$ band. The discrepancies in these ACS data are due to the
lack of sufficient accuracy in the $E-A$ band.

Figure 11:  Example of our pre-generated TiH (left) and CrH (right) absorption
cross-sections data at 2000 K, and multiple pressures. The TiH line list have
been generated using a combination of ab initio data as well as spectroscopic
measurements for 0.4–2.1 $\micron$ (A–X and B–X systems) by Burrows et al.
(2005). The CrH line lists are also used from Burrows et al. (2002) for
0.65–1.65 $\micron$ (A–X system). These linelists are limited to these
wavelength range, and future laboratory/ab-initio studies are needed to extend
these spectra to higher wavelengths (e.g., for CrH at 1.38 $\micron$ gap).

Figure 12: Example of our pre-generated MgH (left) and CaH (right) absorption
cross-sections data at 2000 K, and multiple pressures. The generated MgH is a
combination of the laboratory line list from GharibNezhad et al. (2013) for
0.35–1.2$\micron$($A-X$ and $B-X$ transitions) as well as theoretical infrared
line lists from Yadin et al. (2012). The CaH includes laboratory measured line
lists from Alavi & Shayesteh (2017b); Li et al. (2012) for 0.45–1.0 ($A-X$ and
$B-X$), 0.7–11 (rovibrational transitions) by Shayesteh et al. (2004), and the
$\micron$ ($E-X$) transitions $\sim$0.48 $\micron$ by Li et al. (2012). CaH is
also consists of theoretical line list generated by (Yadin et al., 2012) for
rovibrational transitions. See Table 4 for further details.

Figure 13: Example of our pre-generated AlH (left) and SiO (right) absorption
cross-sections data at a 2000 K and multiple pressures. The AlH line list
(named WYLLoT) is obtained from experimentally-calculated electronic states of
$X$ and $A$ by Yurchenko et al. (2018) and so consists of A–X and X–X
transitions. On the other hand, the SiO line list in our study has been
computed using the available recorded SiO from both laboratory and sunspot
spectra as well as the computed dipole moments by Barton et al.
(2013).According to Barton et al. (2013), the SiO lines above 10000 cm-1 are
very weak and so any lines between 10000–65000 cm-1 was filtered in their
study.

Figure 14: Impact of pre-generated opacities in the transmission and emission
spectrum of a representative Ultra-Hot Jupiter. Transmission (Left) and
Emission (Right) spectra calculated using opacities from all old ACSs (red)
compared to all EXOPLINES ACSs (blue). Choice of linelists for TiO (TOTO vs
Schwenke, in orange), VO (Plez vs VOMYT, in green), H2O (Schwenke vs
POKAZATEL, in cyan), and metal hydrides (in lime, see Table 7 references)
along with combination differences of metal oxides (TiO and VO, in purple) as
well as H2O(magenta) showing notable residuals relative to all old ACS data
(red) of up to 300 ppm, primarily in the optical bandpass, between 0.3-1.0
$\mu$m at $JWST$ fiducial resolution at R=100 for transmission (Bottom Left)
and up to 80 ppm in the infrared between 1.0-5.0 $\mu$m for thermal emission
(Bottom Right), despite no significant shape differences amongst the spectra.
In both cases, TiO produces the largest residual differences. Therefore,
significant bias may arise with the choice of linelist in model atmospheres,
especially when characterizing ultra hot Jupiter atmospheres with $JWST$.

Figure 15: The impact of pre-generated opacities in the atmospheric structure
of a representative Ultra-Hot Jupiter.(Left) Thermal structure calculated
using pre-generated opacities from all old ACS (red) (Freedman et al. (2008),
See Table 7), compared to EXOPLINES (blue). (Right) Independent effects of TiO
(TOTO), VO (VOMYT), H2O (POKAZATEL), metal hydrides (FeH/MgH/CaH/CrH-MoLLIST,
and AlH-WYLLoT) (orange, green, cyan and lime respectively) as well as
combination differences of all EXOPLINES ACS (blue) show variation in the
thermal profile of up to 130 K for the same planet. The largest variations in
the thermal profile are purely due to ACS differences of metal hydrides and
oxides that are dominant in highly irradiated planet atmospheres.

Figure 16: Impact of pre-generated opacities in characterizing a fiducial
M-dwarf atmosphere, with Teff of 3000 K, $\log\mathrm{(g)}$ of 5 cm.s-2, solar
M/H, and C/O of 0.5. (Left) Model spectrum of the fiducial M-dwarf (showing
top-of-atmosphere (TOA) flux) varying opacities calculated from all old ACS
(red) compared to all EXOPLINES ACS (blue). Spectrum (R=100, covering
0.3-5$\mu$m) calculated with TiO TOTO linelist (orange) attributes to largest
residual differences in the spectral shape, with up to 125$\%$ in the optical
bandpass below 1$\mu$m, followed by 30$\%$ in residual differences caused
purely due to the effect of metal hydride opacities (MoLLIST, lime) below
1$\mu$m, and up to 12$\%$ between 1.4-2.0$\mu$m. H2O (POKAZTEL, cyan) and VO
(VOMYT, green) alone do not induce noteworthy differences within the spectra.
(Right) Atmospheric structure of fiducial M-dwarf, with respective residuals
in the thermal profile. Consistent with the spectral differences, TiO linelist
contributes to significant deviations within the T-P profile with up to 50 K
above 0.1 bar in pressure, and up to 20 K down to 100 bars. The effect of both
metal oxides (TiO and VO, purple), combined with H2O (magenta) and along with
all new opacities (EXOPLINES, blue) cause deviations in atmospheric structure
of up to a maximum of 60 K.

Figure 17: The impact of intensity cut-off on generating the H2O $POKAZATEL$
ACS data. Following Maxwell-Boltzmann distribution, the population of energy
levels with high $J$ quantum number increases with temperature. As a result,
weak lines become stronger at high temperatures, and so insufficient intensity
cut-off value results in accurate ACS. For instance, the choice of 10-30
(black) for intensity cut-off eliminate more lines in generating ACS data
comparing to 10-31 cm-1/(molecule cm-2) (cyan). The reported cut-off values
refer to 296 K.

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