  We revise the rates of reactions CH + S -> CS + H and C_2 + S -> CS + C,
important CS formation routes in dark and diffuse warm gas. 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 have calculated the
full potential energy surfaces 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 to apply a statistic adiabatic method to determine the
rate constants. This study of the CH + S reaction shows that its rate is nearly
independent on the temperature in a range of 10-500 K with an almost constant
value of 5.5 10^{-11} cm^3/s at temperatures above 100~K. This is a factor \sim
2-3 lower than the value obtained with the capture model. The rate of the
reaction C_2 + S depends on the temperature taking values close to 2.0 10^{-10}
cm^3/s at low temperatures and increasing to 5. 10^{-10} cm^3/s for
temperatures higher than 200~K. Our modeling provides a rate higher than the
one currently used by factor of \sim 2. These reactions were selected for
involving open-shell species with many degenerate electronic states, and the
results obtained in the present detailed calculations provide values which
differ a factor of \sim 2-3 from the simpler classical capture method. We have
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, but it is not possible to fit all sulphur-bearing
molecules better than a factor of 10 at the same chemical time.
