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We compare deterministic and stochastic approaches to models of grain-surface chemistry
in molecular clouds in order to specify under which conditions the stochastic approach
is mandatory. We also study the validity of the modified rate approximation.
Two distinct cases are considered: (1) the surface mobility of all species is due to
thermal hopping, (2) the same but with temperature-independent quantum tunneling for
H and H2. The physical conditions in the core and the outer region of the TMC1 cloud are
adopted.
For the first time realistic time--dependent gas--grain Monte Carlo chemical model of
interstellar medium, involving about 5000 gas phase and 200 grain surface reactions,
has been developed. We found that at 10~K abundances of many important gaseous and in
particular surface molecules are not much affected by stochastic processes. However at
higher temperatures discrepancy between stochastic and deterministic models becomes
significant. At 30~K gas-phase abundances of H2O, NH3, and CO in the stochastic
model differ from those in the deterministic model by up to an order of magnitude. The
major result, which is only captured by a stochastic model, is a new catalytic formation
route of molecular hydrogen, potentially efficient on warm dust grains with T>20K.
We conclude that stochastic effects can have significant impact on chemical evolution
of molecular clouds and have to be properly taken into account in theoretical models
aimed at interpretation of results obtained with future observational facilities
like ALMA and eVLA.
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