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

In this study we demonstrate for the first time that the unified Monte Carlo approach can be applied to model gas-grain chemistry in large reaction networks. Specifically, we build a time-dependent gas-grain chemical model of the interstellar medium, involving about 6000 gas-phase and 200 grain surface reactions. This model is used to test the validity of the standard and modified rate equation methods in models of dense and translucent molecular clouds and to specify under which conditions the use of the stochastic approach is desirable. 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 model differ from those in the deterministic models by more than an order of magnitude, at least, when tunneling is accounted for and/or diffusion energies are 3x lower than the binding energies. In this case, surface reactions, involving light species, proceed faster than accretion of the same species. In contrast, in the model without tunneling and with high binding energies, when the typical timescale of a surface recombination is greater than the timescale of accretion onto the grain, we obtain almost perfect agreement between results of Monte Carlo and deterministic calculations in the same temperature range. At lower temperatures ($\sim10$ K) gaseous and, in particular, surface abundances of most important molecules are not much affected by stochastic processes.