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[Context] The stochasticity of grain chemistry requires special care inmodeling. Previously methods based on the modified rate equation, the masterequation, the moment equation, and Monte Carlo simulations have been used.[Aims] We attempt to develop a systematic and efficient way to model thegas-grain chemistry with a large reaction network as accurately as possible.[Methods] We present a hybrid moment equation approach which is a general andautomatic method where the generating function is used to generate the momentequations. For large reaction networks, the moment equation is cut off at thesecond order, and a switch scheme is used when the average population ofcertain species reaches 1. For small networks, the third order moments can alsobe utilized to achieve a higher accuracy. [Results] For physical conditions inwhich the surface reactions are important, our method provides a majorimprovement over the rate equation approach, when benchmarked against therigorous Monte Carlo results. For either very low or very high temperatures, orlarge grain radii, results from the rate equation are similar to those from ournew approach. Our method is faster than the Monte Carlo approach, but slowerthan the rate equation approach. [Conclusions] The hybrid moment equationapproach with a cutoff and switch scheme is applicable to large gas-grainnetworks, and is accurate enough to be used for astrochemistry studies. Thelayered structure of the grain mantle could also be incorporated into thisapproach, although a full implementation of the grain micro-physics appears tobe difficult.

A hybrid moment equation approach to gas-grain chemical modeling