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Aims. A method to determine effective rate coefficients for H 2  formation on grain surfaces is proposed based on the continuous-time, random-walk Monte Carlo simulation. Methods. Our Monte Carlo simulation is used to calculate the efficiency of molecular hydrogen formation via recombination of H atoms on flat and rough surfaces of olivine and amorphous carbon under a variety of diffuse cloud conditions. The results are then fitted to two types of rate laws to determine effective rate coefficients for use in rate equation treatments. These rate coefficients can be utilized in pure gas-phase models, where the rate of molecular formation is associated with a grain collision rate for H atoms multiplied by an efficiency factor, and in gas-grain models, where the actual diffusion of H atoms on a grain surface is considered. Results. The effective rate coefficients are tabulated as a function of incoming atomic hydrogen flux and surface temperature, over temperature ranges for which the surfaces show a reasonable efficiency of molecular hydrogen formation. For the flat surfaces studied, corrections to the standard rate treatment do not exceed a factor of three.

Effective rate coefficients for molecular hydrogen formation in diffuse interstellar clouds