Gas phase Elemental abundances in Molecular cloudS (GEMS). VIII. Unlocking the CS chemistry: The CH + S → CS + H and C2 + S → CS + C reactions

Context. Carbon monosulphide (CS) is among the few sulphur-bearing species that have been widely observed in all environments, including in the most extreme, such as diffuse clouds. Moreover, CS has been widely used as a tracer of the gas density in the interstellar medium in our Galaxy and external galaxies. Therefore, a complete understanding of its chemistry in all environments is of paramount importance for the study of interstellar matter.
Aims: Our group is revising the rates of the main formation and destruction mechanisms of CS. In particular, we focus on those involving open-shell species for which the classical capture model might not be sufficiently accurate. In this paper, we revise the rates of reactions CH + S → CS + H and C₂ + S → CS + C. These reactions are important CS formation routes in some environments such as dark and diffuse warm gas.
Methods: We performed ab initio calculations to characterize the main features of all the electronic states correlating to the open shell reactants. For CH+S, we calculated the full potential energy surfaces (PESs) for the lowest doublet states and the reaction rate constant with a quasi-classical method. For C₂+S, the reaction can only take place through the three lower triplet states, which all present deep insertion wells. A detailed study of the long-range interactions for these triplet states allowed us to apply a statistic adiabatic method to determine the rate constants.
Results: Our detailed theoretical study of the CH + S → CS + H reaction shows that its rate is nearly independent of the temperature in a range of 10-500 K, with an almost constant value of 5.5 × 10⁻¹¹ cm³ s⁻¹ at temperatures above 100 K. This is a factor of about 2-3 lower than the value obtained with the capture model. The rate of the reaction C₂ + S → CS + C does depend on the temperature, and takes values close to 2.0 × 10⁻¹⁰ cm³ s⁻¹ at low temperatures, which increase to ~ 5.0 × 10⁻¹⁰ cm³ s⁻¹ for temperatures higher than 200 K. In this case, our detailed modeling - taking into account the electronic and spin states - provides a rate that is higher than the one currently used by factor of approximately 2.
Conclusions: These reactions were selected based on their inclusion of open-shell species with many degenerate electronic states, and, unexpectedly, the results obtained in the present detailed calculations provide values that differ by a factor of about 2-3 from the simpler classical capture method. We updated the sulphur network with these new rates and compare our results in the prototypical case of TMC1 (CP). We find a reasonable agreement between model predictions and observations with a sulphur depletion factor of 20 relative to the sulphur cosmic abundance. However, it is not possible to fit the abundances of all sulphur-bearing molecules better than a factor of 10 at the same chemical time.