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.
