Modern observations of the interstellar medium ( ISM ) in galaxies detect a variety of atomic and molecular species .
The goal is to connect these observations to the astrochemical properties of the ISM .
3D hydro-chemical simulations attempt this but due to extreme computational cost , they have to rely on simplified chemical networks and are bound to individual case studies .
We present an alternative approach which models the ISM at larger scales by an ensemble of pre-calculated 1D thermo-chemical photodissociation region ( PDR ) calculations that determine the abundance and excitation of atomic and molecular species .
We adopt lognormal distributions of column density ( A _ { V } -PDFs ) for which each column density is linked to a volume density as derived by hydrodynamical simulations .
We consider two lognormal A _ { V } -PDFs : a diffuse , low density medium with average visual extinction of \overline { { A } _ { V } } = 0.75 { mag } and dispersion of \sigma = 0.5 and a denser giant molecular cloud with \overline { { A } _ { V } } = 4 { mag } and \sigma = 0.8 .
We treat the UV radiation field , cosmic-ray ionization rate and metallicity as free parameters .
We find that the low density medium remains fully H i - and C ii -dominated under all explored conditions .
The denser cloud remains almost always molecular ( i.e .
H _ { 2 } -dominated ) while its carbon phase ( CO , C i and C ii ) is sensitive to the above free parameters , implying that existing methods of tracing H _ { 2 } -rich gas may require adjustments depending on environment .
Our numerical framework can be used to estimate the PDR properties of large ISM regions and quantify trends with different environmental parameters as it is fast , covers wide parameter space , and is flexible for extensions .