Atom Tunneling in the Water Formation Reaction H$_2$ + OH $\rightarrow$ H$_2$O + H on an Ice Surface

OH radicals play a key role as an intermediate in the water formation chemistry of the interstellar medium. For example the reaction of OH radicals with H$_2$ molecules is among the final steps in the astrochemical reaction network starting from O, O$_2$, and O$_3$. Experimentally it was shown that even at 10 K this reaction occurs on ice surfaces. As the reaction has a high activation energy only atom tunneling can explain such experimental findings. In this study we calculated reaction rate constants for the title reaction on a water-ice I$_h$ surface. To our knowledge, low-temperature rate constants on a surface are not available in the literature. All surface calculations were done using a QM/MM framework (BHLYP/TIP3P) after a thorough benchmark of different density functionals and basis sets to highly accurate correlation methods. Reaction rate constants are obtained using instanton theory which takes atom tunneling into account inherently, with constants down to 110 K for the Eley-Rideal mechanism and down to 60 K for the Langmuir-Hinshelwood mechanism. We found that the reaction is nearly temperature independent below 80 K. We give kinetic isotope effects for all possible deuteration patterns for both reaction mechanisms. For the implementation in astrochemical networks, we also give fit parameters to a modified Arrhenius equation. Finally, several different binding sites and binding energies of OH radicals on the I$_h$ surface are discussed and the corresponding rate constants are compared to the gas-phase case.