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In this study we demonstrate for the first time that the unified Monte Carloapproach can be applied to model gas-grain chemistry in large reactionnetworks. Specifically, we build a time-dependent gas-grain chemical model ofthe interstellar medium, involving about 6000 gas-phase and 200 grain surfacereactions. This model is used to test the validity of the standard and modifiedrate equation methods in models of dense and translucent molecular clouds andto specify under which conditions the use of the stochastic approach isdesirable.  We found that at temperatures 25--30 K gas-phase abundances of H$_2$O,NH$_3$, CO and many other gas-phase and surface species in the stochastic modeldiffer from those in the deterministic models by more than an order ofmagnitude, at least, when tunneling is accounted for and/or diffusion energiesare 3x lower than the binding energies. In this case, surface reactions,involving light species, proceed faster than accretion of the same species. Incontrast, in the model without tunneling and with high binding energies, whenthe typical timescale of a surface recombination is greater than the timescaleof accretion onto the grain, we obtain almost perfect agreement between resultsof Monte Carlo and deterministic calculations in the same temperature range. Atlower temperatures ($\sim10$ K) gaseous and, in particular, surface abundancesof most important molecules are not much affected by stochastic processes.

A Unified Monte Carlo Treatment of Gas-Grain Chemistry for Large Reaction Networks. I. Testing Validity of Rate Equations in Molecular Clouds