  We present P-GADGET3-K, an updated version of GADGET3, that incorporates the
chemistry package KROME. P-GADGET3-K follows the hydrodynamical and chemical
evolution of cosmic structures, incorporating the chemistry and cooling of
H$_2$ and metal cooling in non-equilibrium. We performed different runs of the
same ICs to assess the impact of various physical parameters and prescriptions,
namely gas metallicity, molecular hydrogen formation on dust, star formation
recipes including or not H$_2$ dependence, and the effects of numerical
resolution. We find that the characteristics of the simulated systems, both
globally and at kpc-scales, are in good agreement with several observable
properties of molecular gas in star-forming galaxies. The surface density
profiles of SFR and H$_2$ are found to vary with the clumping factor and
resolution. In agreement with previous results, the chemical enrichment of the
gas component is found to be a key ingredient to model the formation and
distribution of H$_2$ as a function of gas density and temperature. A SF
algorithm that takes into account the H$_2$ fraction together with a treatment
for the local stellar radiation field improves the agreement with observed
H$_2$ abundances over a wide range of gas densities and with the molecular
Kennicutt-Schmidt law, implying a more realistic modelling of the star
formation process.
