Incorporation of stochastic chemistry on dust grains in the PDR code
  using moment equations
  Unlike gas-phase reactions, chemical reactions taking place on interstellar
dust grain surfaces cannot always be modeled by rate equations. Due to the
small grain sizes and low flux,these reactions may exhibit large fluctuations
and thus require stochastic methods such as the moment equations.
  We evaluate the formation rates of H2, HD and D2 molecules on dust grain
surfaces and their abundances in the gas phase under interstellar conditions.
We incorporate the moment equations into the Meudon PDR code and compare the
results with those obtained from the rate equations. We find that within the
experimental constraints on the energy barriers for diffusion and desorption
and for the density of adsorption sites on the grain surface, H2, HD and D2
molecules can be formed efficiently on dust grains.
  Under a broad range of conditions, the moment equation results coincide with
those obtained from the rate equations. However, in a range of relatively high
grain temperatures, there are significant deviations. In this range, the rate
equations fail while the moment equations provide accurate results. The
incorporation of the moment equations into the PDR code can be extended to
other reactions taking place on grain surfaces.
