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OH radicals play a key role as an intermediate in the water formationchemistry of the interstellar medium. For example the reaction of OH radicalswith H$_2$ molecules is among the final steps in the astrochemical reactionnetwork starting from O, O$_2$, and O$_3$. Experimentally it was shown thateven at 10 K this reaction occurs on ice surfaces. As the reaction has a highactivation energy only atom tunneling can explain such experimental findings.  In this study we calculated reaction rate constants for the title reaction ona water-ice I$_h$ surface. To our knowledge, low-temperature rate constants ona surface are not available in the literature. All surface calculations weredone using a QM/MM framework (BHLYP/TIP3P) after a thorough benchmark ofdifferent density functionals and basis sets to highly accurate correlationmethods. Reaction rate constants are obtained using instanton theory whichtakes atom tunneling into account inherently, with constants down to 110 K forthe Eley-Rideal mechanism and down to 60 K for the Langmuir-Hinshelwoodmechanism. We found that the reaction is nearly temperature independent below80 K. We give kinetic isotope effects for all possible deuteration patterns forboth reaction mechanisms. For the implementation in astrochemical networks, wealso give fit parameters to a modified Arrhenius equation. Finally, severaldifferent binding sites and binding energies of OH radicals on the I$_h$surface are discussed and the corresponding rate constants are compared to thegas-phase case.

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