A hybrid moment equation approach to gas-grain chemical modeling
  [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. 
Fujun Du and Berengere Parise
astro-ph.GA physics.chem-ph