  We study the metallicity dependence of the H/H2 and C+/C/CO distributions in
a self-regulated interstellar medium (ISM) across a broad range of
metallicities (0.1 < $Z/Z_\odot$ < 3). To this end, we conduct high-resolution
(particle mass of 1 $M_\odot$) hydrodynamical simulations coupled with a
time-dependent H2 chemistry network. The results are then post-processed with
an accurate chemistry network to model the associated C+/C/CO abundances, based
on the time-dependent ("non-equilibrium") H2 abundances. We find that the
time-averaged star formation rate and the ISM structure are insensitive to
metallicity. The column densities relevant for molecular shielding are
correlated with the volume densities in gravitationally unstable gas. As
metallicity decreases, H2 progressively deviates from steady state
("equilibrium") and shows shallow abundance profiles until they sharply
truncate at the photodissociation fronts. In contrast, the CO profile is sharp
and controlled by photodissociation as CO quickly reaches steady state. We
construct effective one-dimensional cloud models that successfully capture the
time-averaged chemical distributions in simulations. At low metallicities, the
steady-state model significantly overestimates the abundance of H2 in the
diffuse medium. The overestimated H2, however, has little impact on CO.
Consequently, the mass fraction of CO-dark H2 gas is significantly lower than
what a fully steady-state model predicts. The mass ratios of H2/C+ and H2/C
both show a weaker dependence on Z than H2/CO, which potentially indicates that
C+ and C could be alternative tracers for H2 at low Z in terms of mass budget.
The time-dependent effect may explain the observed relationship between column
densities of H2 and CO in Galactic clouds without resorting to non-thermal
chemical reactions. Our chemistry code for post-processing is publicly
available.
