Silicon monosulfide is an important silicon bearing molecule detected in circumstellar envelopes and star forming regions. Its formation and destruction routes are not well understood, partially due to the lack of a detailed knowledge on the involved reactions and their rate coefficients. In this work we have calculated and modeled the potential energy surface (PES) of the HSiS system employing highly accurate multireference electronic structure methods. After obtaining an accurate analytic representation of the PES, which includes long-range energy terms in a realistic way via the DMBE method, we have calculated rate coefficients for the Si+SH$rightarrow$SiS+H reaction over the temperature range of 25-1000K. This reaction is predicted to be fast, with a rate coefficient of $sim 1times 10^{-10}rm cm^3, s^{-1}$ at 200K, which substantially increases for lower temperatures (the temperature dependence can be described by a modified Arrhenius equation with $alpha=0.770times 10^{-10}rm cm^3,s^{-1}$, $beta=-0.756$ and $gamma=9.873, rm K$). An astrochemical gas-grain model of a shock region similar to L1157-B1 shows that the inclusion of the Si+SH reaction increases the SiS gas-phase abundance relative to ce{H2} from $5times 10^{-10}$ to $1.4times 10^{-8}$, which perfectly matches the observed abundance of $sim 2times 10^{-8}$.
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