by François Lique & Benjamin Desrousseaux & Amélie Godard Palluet & Marie Gueguen & Sándor Demes & Michał Żółtowski & Paul Pirlot Jankowiak & Alexandre Faure & Guillaume Raffy, on

## Presentation of the workshop

From the 13th to the 16th of June 2022, the workshop on Collisional excitation of (reactive) astrophysical molecules and its applications was taking place in Saint-Florent (Corsica). It was organized by F. Lique.

Astronomers, experimentalists and theoreticians were gathered to discuss the state-to-state chemistry and its effect on astrophysical modeling.

During this workshop, B. Desrousseaux, M. Gueguen, S. Demes, A. Faure and G. Raffy presented their work.

The workshop was also the opportunity to P. Pirlot Jankowiak, A. Godard Palluet and M. Żółtowski to give a talk during the young researcher session.

## Centre d'Études Sous Marines (CESM) - Saint Florent, Corsica

The CESM is an associative sailing and diving club created in 1949.

This non-profit organization is offering sailing and diving activities to vacationers for over 60 years.

Since 2011, the center lends its premises to workshops about physical and chemical processes in the interstellar medium organised by François Lique and Carole Le Guen.

## Tracking uncertainties, from the laboratory to the observations - __M. Gueguen__

In this talk, the collisional excitation of N^{+} by He and by H_{2} is presented.

I provide exact quantum scattering calculations for He + N^{+}, and collisional rates based on a spherically averaged interaction potential for H_{2} + N^{+}.

On the basis of these results, I discuss the role of idealizations and approximations in advancing astrochemical models, especially with respect to the traditional use of He as a model for H_{2} when dynamic calculations are not computationally accessible for the latter.

## Hyperfine excitation of C_{2}H and its isotopologues in the interstellar medium - __P. Pirlot Jankowiak__, P. J. Dagdigian and F. Lique

Since the discovery of the ethynyl CCH radical in the interstellar medium [1], it has been detected in a wide range of astrophysical environments. It is one of the most abundant hydrocarbon in space and together with its detected isotopologues (CCD, ^{13}CCH and C^{13}CH), they are useful tracers of physical conditions. Indeed, as abundances strongly depend on the formation pathways, the measurment for the ratio [CCD]/[CCH] may constrain the age of molecular clouds in astrophysical models [2]. However, hyperfine resolved ^{13}C-based spectra show a higher intensity in favor of C^{13}CH lines than ^{13}CCH ones [3, 4] whereas their formation path is supposed to be the same. It is then of high interest to investigate this apparent different abundance of the two isotopologues.

An accurate interpretation of these observations requires to determine precise rate coefficients. Such quantities are necessary for non local thermodynamic equilibrium modeling which takes into account competition between radiative and collisional processes.

Non zero nuclear spins from ^{13}C, D and H atoms lead to a resolved hyperfine structure for these species.

Such complex energetic structure is a real theoretical challenge as exact scattering calculations are not feasible in a reasonable time. Then, it is necessary to develop numerical and methodological tools in order to determine accurate collisional data for astrophysical applications. In this study, I present the calculations of new accurate collisional data for all the CCH isotopologues.

Scattering calculations have been performed using a recoupling technique in order to determine accurate hyperfine resolved rate coefficients of CCH and its isotopologues in collision with H_{2}. These data were derived for a large range of temperature and are expected to improve abundance ratio calculations and better understand the evolution of the isotopic fraction in astrochemical models.

[1] K. D. Tucker, M. L. Kutner, and P. Thaddeus, The Astrophysical Journal 193, 115 (1974).

[2] S. P. Trevino-Morales, P. Pilleri, A. Fuente, C. Kramer, E. Roueff , M. Gonzalez-Garcia, J. Cernicharo, M. Gerin, J. R. Goicoechea, J. Pety, O. Berné, V. Ossenkopf, D. Ginard Pariente, S. Garcia-Burillo, J. R. Rizzo, and S. Viti, A&A 569 (2014).

[3] S. Cuadrado, J. R. Goicoechea, P. Pilleri, J. Cernicharo, A. Fuente, and C. Joblin, A&A 575 (2015).

[4] N. Sakai, O. Saruwatari, T. Sakai, S. Takano, and S. Yamamoto, A&A 512 (2010).

[5] A. Spieldiedel, N. Feautrier, F. Najar, D. Ben Abdallah, F. Dayou, M. L. Senent, and F. Lique, Mon. Not. R. Astronom. Soc. 421, 1891 (2012).

[6] F. Dumouchel, F. Lique, A. Spieldiedel, and N. Feautrier, Mon. Not. R. Astronom. Soc. 471, 1849 (2017).

[7] P. J. Dagdigian, Mon. Not. R. Astronom. Soc. 479, 3227 (2018).

## Collisional excitation of CCS by He: new potential energy surface and scattering calculations - __A. Godard Palluet__ and F. Lique

The physical conditions in space are derived from the spectra captured by telescopes. The spectral analysis requires to know the population of molecular energy levels. However, the local thermodynamic equilibrium conditions are rarely fulfilled in astrophysical media. Hence, the population of energy levels and the intensity of spectral lines are determined with a radiative transfer model that takes both radiative and collisional processes into account. Radiative transitions are characterized by Einstein’s coefficients, for which analytical formula exist, and collisional transitions are characterized by rate coefficients. The later are system-specific, and their determination in laboratory are extremely difficult. Therefore, radiative transfer model relies almost exclusively on theoretical estimates [1]. They are preferentially obtained from scattering calculations performed on a potential energy surface (PES) which describe the electronic interaction between the two colliders.

The CCS(^{3}Σ^{-}) radical and its isotopologues have been detected in several dark molecular clouds, including TMC-1 and also in the circumstellar enveloppe IRC+10216. However, their rate coefficients do not exist in the literature and astrophysicists use rates from OCS to infer the one of CCS isotopologues [2]. However, the CCS radical presents a large fine structure splitting, which makes the estimation of the rate coefficients incorrect and the line modelisation difficult [3]. Therefore, the CCS rate coefficients must be accurately determined.

During this presentation, the PES used for the close-coupling scattering calculations will be presented. It was obtained with the gold standard UCCSD(T) method and an aVQZ basis set with additional mid-bond functions. The first accurate fine state-to-state rate coefficients for the 5 - 50 K temperature range of the ^{12}C^{12}C^{32}S isotopologue will be presented. These rates were also computed for the ^{13}C^{12}C^{32}S, ^{12}C^{13}C^{32}S and ^{12}C^{12}C^{34}S isotopologues, including the hyperfine structure for ^{13}C-based isotopologues. The isotopic effect on the fine and hyperfine structure resolved rate coefficients will be discussed.

[1] J. Loreau, F. Lique and A. Faure, ApJ., 853 L5 (2018)

[2] H. Suzuki, S. Yamamoto, M. Ohishi, N. Kaifu, S. Ishikawa, Y. Hirahara, S. Takano, ApJ., 392 551 (1992).

[3] S. Saito, K. Kawaguchi, S. Yamamoto, M. Ohishi, H. Suzuki, N. Kaifu, ApJ., 317 L115 (1987).

[4] J. Cernicharo, M. Guélin, H. Hein, C. Kahane, A&A, 181 L9 (1987).

[5] M. Ikeda, Y. Sekimoto, S. Yamamoto, J. Mol. Spectrosc., 185 21 (1997).

## Collisional energy transfer in the CO-CO system - __M. Żółtowski__, J. Loreau and F. Lique

Accurate determination of the physical conditions in comets can be inferred from the modeling of molecular spectra. However, the full exploitation of molecular spectra requires to go beyond the local thermodynamic equilibrium (LTE) approach and hence requires radiative and collisions properties of the molecular species.

Among the cometary molecules, CO is of key importance, and is even the dominant species in cometary at large heliocentric distances. Here, we present new scattering calculations for the rotational excitation in CO-CO collisional system using non-reactive quantum scattering code MOLSCAT.

Calculations were performed using coupled-channel methods within the coupled states approximation, using the four dimensional potential energy surface calculated of Vissers et al. Collisional rate coefficients are provided for rotational levels up to j ≤ 10 and for temperatures up to 150 K.

The new results are compared to the previous ones from literature and significant differences are found, especially for the dominant transitions. The impact of these new data of the astrophysical modeling is also discussed.

## Hibridon 5 - __G. Raffy__, B. Desrousseaux, F. Lique

Hibridon© is a program package to solve the close-coupled equations which occur in the quantum treatment of inelastic atomic and molecular collisions. Gas-phase scattering, photodissociation, collisions of atoms and/or molecules with flat surfaces, and bound states of weakly-bound complexes can be treated.

Currently, Hibridon© is officially distributed in its 4.3.7 version, with last modifications from September 2006. We are currently working on the 5th version of the software, integrating some changes to the code:

Use git to manage the source code (stored on github)

- Gather all user’s custom modifications of the Hibridon© code and merge them to obtain an up-to-date starting point

- Add Automatic testing of the Hibridon© installation and continuous integration (CI)

- Replace the previous custom build system with cmake to make Hibridon© easy to install on various platforms

- Replace the previous custom fortran preprocessing system with the more standard fpp

- Add dynamic memory allocation

## Statistical approaches of inelastic and reactive collisions - __B. Desrousseaux__, M. Konings, J. Loreau and F. Lique

Observational spectra are our main source of knowledge about interstellar environments. In such low density environments, the frequency of collisions is not large enough to maintain a local thermodynamical equilibrium (LTE) [1]. It is then necessary to take into account both radiative and collisional processes in order to properly interpret molecular spectra. It is then crucial to obtain state-to-state rate coefficients describing the collisional (de)excitation of interstellar species with the main collisional partners (H_{2}, H, He).

Quantum time-independent close-coupling calculations is the method of choice to obtain accurate enough collisional rate coefficients at typically low interstellar temperatures (< 100 K). However, in the case of reactive systems, i.e. open-shell molecules and ions that can undergo a reaction with the most dominant interstellar species H or H_{2}, this method is impractical due to its memory and CPU requirements. As a result, the astrophysical community lack of appropriate collisional data for many detected reactive molecules of key importance in astrochemistry (NH, OH^{+}, CH^{+}, HCl^{+}, H2O^{+}, …), preventing a proper determination of their abundance.

We present a new approach based on the statistical adiabatic channel model [2, 3] (SACM) to compute collisional rate coefficients in the case of reactive molecules. This efficient approach allows the determination of the rate coefficients with an accuracy meeting the needs of astrophysical applications while overcoming the memory and CPU limitations of the close-coupling method. In particular, this new approach was successfully validated on light triatomic collisional systems for which full quantum time-independent close-coupling results were available such as CH^{+} – H and SH^{+} – H. The present statistical approach should be considered as a useful alternative to prohibitive close-coupling calculations in order to provide the astrophysical community with accurate collisional data.

[1] E. Roueff and F. Lique, “Molecular Excitation in the Interstellar Medium: Recent Advances in Collisional, Radiative, and Chemical Processes”, Chemical Reviews 113, 8906–8938 (2013).

[2] M. Quack and J. Troe, “Complex Formation in Reactive and Inelastic Scattering: Statistical Adiabatic Channel Model of Unimolecular Processes III”, Berichte der Bunsengesellschaft für physikalische Chemie 79, 170–183 (1975).

[3] M. Quack and J. Troe, “Specific Rate Constants of Unimolecular Processes II. Adiabatic Channel Model.”, Berichte der Bunsengesellschaft für physikalische Chemie 78, 240–252 (1974).

## Collision of C_{5}H_{6} with He: the first precise modeling of the excitation of a cyclic molecule - __S. Demes__, C. Bop and F. Lique

We are aiming to study the rotational excitation of a large cyclic molecule - cyclopentadiene (C_{5}H_{6}) - for the first time in collision with helium. We have calculated a 3-dimensional rigid rotor potential energy surface on the CCSD(T)-F12/aVTZ level of theory. An analytical fit is performed then, resulting 96 radial functions, involving very high angular anisotropies (up to λ = 18). Due to its very small rotational constants, cyclopentadiene is characterized with an extremely dense rotational structure, possessing more than 40 rotational states with internal energies below 9 cm^{-1}. This makes the scattering calculations very challenging even at lower energies.

## New scattering code: SARAS - __B. Desrousseaux__ and F. Lique

As for now, full quantum time-independent close-coupling calculations is the method of choice to obtain accurate collisional rate coefficients at typically low interstellar temperatures (< 100 K). However, in the case of reactive systems, i.e. open-shell molecules and ions that can undergo a reaction with the most dominant interstellar species H or H2, this method is impractical due to its memory and CPU requirements. As a result, reliable collisional data is missing for many detected reactive molecules of key importance in astrochemistry (NH, OH^{+}, CH^{+}, HCl^{+}, H2O^{+}, …), preventing a proper determination of their abundance.

We intend to develop a new approach [2-5] based on the statistical adiabatic channel model (SACM) of Quack and Troe [6, 7] to compute collisional rate coefficients in the case of reactive molecules. This efficient approach would allow the determination of the rate coefficients with an accuracy meeting the needs of astrophysical applications while overcoming the memory and CPU limitations of the close-coupling method.

In order to efficiently apply this method, I am currently developping a new software: SARAS. The source code benefits from the object oriented features and modularity of the Fortran 2008 standard. It is made massively parallel using the Message Passing Interface (MPI) and thus fully profits from nowadays supercomputer architectures.

[1] Roueff, E. & Lique, F. Molecular Excitation in the Interstellar Medium: Recent Advances in Collisional, Radiative, and Chemical Processes. Chemical Reviews 113, 8906–8938 (2013).

[2] Loreau, J., Lique, F. & Faure, A. An efficient statistical method to compute molecular collisional rate coefficients. ApJ 853, L5 (2018).

[3] Loreau, J., Faure, A. & Lique, F. Scattering of CO with H2O: Statistical and classical alternatives to close-coupling calculations. J. Chem. Phys. 8 (2018).

[4] Desrousseaux, B., Konings, M., Loreau, J., Lique, F. HD-H+ collisions: statistical and quantum state-to-state studies. Physical Chemistry Chemical Physics 23-35 (2021).

[5] Konings, M., Desrousseaux, B., Lique, F., Loreau, J. Benchmarking an Improved Statistical Adiabatic Channel Model for Competing Inelastic and Reactive Processes. The Journal of Chemical Physics 155-10 (2021).

[6] Quack, M. & Troe, J. Complex Formation in Reactive and Inelastic Scattering: Statistical Adiabatic Channel Model of Unimolecular Processes III. Berichte der Bunsengesellschaft für physikalische Chemie 79, 170–183 (1975).

[7] Quack, M. & Troe, J. Specific Rate Constants of Unimolecular Processes II. Adiabatic Channel Model. Berichte der Bunsengesellschaft für physikalische Chemie 78, 240–252 (1974).