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 C 2 + 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 C 2 +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 cm 3 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 C 2 + S → CS + C does depend on the temperature, and takes values close to 2.0 × 10 −10 cm 3 s −1 at low temperatures, which increase to ~ 5.0 × 10 −10 cm 3 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.< Réduire