Influence of surface and bulk water ice on the reactivity of a water-forming reaction

On the surface of icy dust grains in the dense regions of the interstellar medium a rich chemistry can take place. Due to the low temperature, reactions that proceed via a barrier can only take place through tunneling. The reaction H + H$_2$O$_2$ $\rightarrow$ H$_2$O + OH is such a case with a gas-phase barrier of $\sim$26.5 kJ/mol. Still the reaction is known to be involved in water formation on interstellar grains. Here, we investigate the influence of a water ice surface and of bulk ice on the reaction rate constant. Rate constants are calculated using instanton theory down to 74 K. The ice is taken into account via multiscale modeling, describing the reactants and the direct surrounding at the quantum mechanical level with density functional theory (DFT), while the rest of the ice is modeled on the molecular mechanical level with a force field. We find that H$_2$O$_2$ binding energies cannot be captured by a single value, but rather depend on the number of hydrogen bonds with surface molecules. In highly amorphous surroundings the binding site can block the routes of attack and impede the reaction. Furthermore, the activation energies do not correlate with the binding energies of the same sites. The unimolecular rate constants related to the Langmuir-Hinshelwood mechanism increase as the activation energy decreases. Thus, we provide a lower limit for the rate constant and argue that rate constants can have values up to two order of magnitude larger than this limit.