[Context] The stochasticity of grain chemistry requires special care in
modeling. Previously methods based on the modified rate equation, the master
equation, the moment equation, and Monte Carlo simulations have been used.
[Aims] We attempt to develop a systematic and efficient way to model the
gas-grain chemistry with a large reaction network as accurately as possible.
[Methods] We present a hybrid moment equation approach which is a general and
automatic method where the generating function is used to generate the moment
equations. For large reaction networks, the moment equation is cut off at the
second order, and a switch scheme is used when the average population of
certain species reaches 1. For small networks, the third order moments can also
be utilized to achieve a higher accuracy. [Results] For physical conditions in
which the surface reactions are important, our method provides a major
improvement over the rate equation approach, when benchmarked against the
rigorous Monte Carlo results. For either very low or very high temperatures, or
large grain radii, results from the rate equation are similar to those from our
new approach. Our method is faster than the Monte Carlo approach, but slower
than the rate equation approach. [Conclusions] The hybrid moment equation
approach with a cutoff and switch scheme is applicable to large gas-grain
networks, and is accurate enough to be used for astrochemistry studies. The
layered structure of the grain mantle could also be incorporated into this
approach, although a full implementation of the grain micro-physics appears to
be difficult.Comment: 11 pages, 4 figures. Accepted for publication in Astronomy and
Astrophysic
