  Continuous-time, random-walk Monte Carlo simulations of H2 formation on
grains have been performed for surfaces that are stochastically heated by
photons. We have assumed diffuse cloud conditions and used a variety of grains
of varying roughness and size based on olivine. The simulations were performed
at different optical depths. We confirmed that small grains (r <= 0.02 micron)
have low modal temperatures with strong fluctuations, which have a large effect
on the efficiency of the formation of molecular hydrogen. The grain size
distribution highly favours small grains and therefore H2 formation on these
particles makes a large contribution to the overall formation rate for all but
the roughest surfaces. We find that at A_V=0 only the roughest surfaces can
produce the required amount of molecular hydrogen, but by A_V=1, smoother
surfaces are possible alternatives. Use of a larger value for the evaporation
energy of atomic hydrogen, but one still consistent with experiment, allows
smoother surfaces to produce more H2.
