Time-dependent H2 formation and protonation
  Methods: The microscopic equations of H2-formation and protonation are
integrated numerically over time in such a manner that the overall structures
evolve self-consistently under benign conditions. Results: The equilibrium H2
formation timescale in an H I cloud with N(H) ~ 4x10^{20}/cm^2 is 1-3 x 10^7
yr, nearly independent of the assumed density or H2 formation rate constant on
grains, etc. Attempts to speed up the evolution of the H2-fraction would
require densities well beyond the range usually considered typical of diffuse
gas. The calculations suggest that, under benign, quiescent conditions,
formation of H2 is favored in larger regions having moderate density,
consistent with the rather high mean kinetic temperatures measured in H2, 70-80
K. Formation of H3+ is essentially complete when H2-formation equilibrates but
the final abundance of H3+ appears more nearly at the very last instant.
Chemistry in a weakly-molecular gas has particular properties so that the
abundance patterns change appreciably as gas becomes more fully molecular,
either in model sequences or with time in a single model. One manifestation of
this is that the predicted abundance of H3+ is much more weakly dependent on
the cosmic-ray ionization rate when n(H2)/n(H) < 0.05. In general, high
abundances of H3+ do not enhance the abundances of other species (e.g. HCO+)
but late-time OH formation proceeds most vigourously in more diffuse regions
having modest density, extinction and H2 fraction and somewhat higher
fractional ionization, suggesting that atypically high OH/H2 abundance ratios
might be found optically in diffuse clouds having modest extinction.
