Context :

Aims : To demonstrate the time-approach to equilibrium of H _ { 2 } -formation and protonation in models of diffuse or H I interstellar gas clouds previously published by the author .

Methods : The microscopic equations of H _ { 2 } -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 H _ { 2 } formation timescale in an H I cloud with N ( H ) \approx 4 \times 10 ^ { 20 } ~ { } ~ { } { cm } ^ { -2 } is 1 - 3 \times 10 ^ { 7 } yr , nearly independent of the assumed density or H _ { 2 } formation rate on grains , etc .
Attempts to speed up the evolution of the H _ { 2 } -fraction would require densities well beyond the range usually considered typical of diffuse gas .
The calculations suggest that , under benign , quiescent conditions , H _ { 2 } in the diffuse ISM formation of H _ { 2 } is favored in larger regions having moderate density , consistent with the rather high mean kinetic temperatures measured in H _ { 2 } , 70-80 K .

Formation of H _ { 3 } ^ { + } is essentially complete when H _ { 2 } -formation equilibrates but the final abundance of H _ { 3 } ^ { + } 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 H _ { 3 } ^ { + } is much more weakly dependent on the cosmic-ray ionization rate when n ( H _ { 2 } ) /n ( H ) \la 0.05 .
In general , high abundances of H _ { 3 } ^ { + } 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 H _ { 2 } fraction and somewhat higher fractional ionization , suggesting that atypically high OH/H _ { 2 } abundance ratios might be found optically in diffuse clouds having modest extinction .

Conclusions :