  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 $\sim 1\times 10^{-10}\rm cm^3\, s^{-1}$ at 200K, which
substantially increases for lower temperatures (the temperature dependence can
be described by a modified Arrhenius equation with $\alpha=0.770\times
10^{-10}\rm cm^3\,s^{-1}$, $\beta=-0.756$ 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 $5\times 10^{-10}$ to $1.4\times 10^{-8}$, which
perfectly matches the observed abundance of $\sim 2\times 10^{-8}$.
