  Investigating how formamide forms in the interstellar medium is a hot topic
in astrochemistry, which can contribute to our understanding of the origin of
life on Earth. We have constructed a QM/MM model to simulate the hydrogenation
of isocyanic acid on amorphous solid water surfaces to form formamide. The
binding energy of HNCO on the ASW surface varies significantly between
different binding sites, we found values between $\sim$0 and 100 kJ mol$^{-1}$.
The barrier for the hydrogenation reaction is almost independent of the binding
energy, though. We calculated tunneling rate constants of H + HNCO
$\rightarrow$ NH$_2$CO at temperatures down to 103 K combining QM/MM with
instanton theory. Tunneling dominates the reaction at such low temperatures.
The tunneling reaction is hardly accelerated by the amorphous solid water
surface compared to the gas phase for this system, even though the activation
energy of the surface reaction is lower than the one of the gas-phase reaction.
Both the height and width of the barrier affect the tunneling rate in practice.
Strong kinetic isotope effects were observed by comparing to rate constants of
D + HNCO $\rightarrow$ NHDCO. At 103 K we found a KIE of 231 on the surface and
146 in the gas phase. Furthermore, we investigated the gas-phase reaction
NH$_2$ + H$_2$CO $\rightarrow$ NH$_2$CHO + H and found it unlikely to occur at
cryogenic temperatures. The data of our tunneling rate constants are expected
to significantly influence astrochemical models.
