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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. 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