  We present a multi-scale analysis of molecular hydrogen in a Milky Way-like
simulated galaxy. Our census covers the gas content of the entire disc, to
radial profiles and the Kennicutt-Schmidt relation, to a study of its molecular
clouds, and finally down to a cell-by-cell analysis of the gas phases. Where
observations are available we find agreement. A significant fraction of the H2
gas is in low-density regions mixed with atomic hydrogen and would therefore be
difficult to observe. We use the molecular addition to ramses-rt, an adaptive
mesh refinement grid code with the hydrodynamics coupled to moment-based
radiative transfer. Three resolutions of the same galaxy detail the effects it
has on H2 formation, with grid cells sized 97, 24, and 6.1 pc. Only the highest
resolution yields gas densities high enough to host significant H2 fractions,
and resolution is therefore key to simulating H2. Apart our pieces of galactic
analysis are disparate, but assembled they provide a cohesive portrait of H2 in
the interstellar medium. H2 chemistry on the atomic scale is sufficient to
generate its dynamics throughout an entire galaxy.
