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We present P-GADGET3-K, an updated version of GADGET3, that incorporates thechemistry package KROME. P-GADGET3-K follows the hydrodynamical and chemicalevolution of cosmic structures, incorporating the chemistry and cooling ofH$_2$ and metal cooling in non-equilibrium. We performed different runs of thesame ICs to assess the impact of various physical parameters and prescriptions,namely gas metallicity, molecular hydrogen formation on dust, star formationrecipes including or not H$_2$ dependence, and the effects of numericalresolution. We find that the characteristics of the simulated systems, bothglobally and at kpc-scales, are in good agreement with several observableproperties of molecular gas in star-forming galaxies. The surface densityprofiles of SFR and H$_2$ are found to vary with the clumping factor andresolution. In agreement with previous results, the chemical enrichment of thegas component is found to be a key ingredient to model the formation anddistribution of H$_2$ as a function of gas density and temperature. A SFalgorithm that takes into account the H$_2$ fraction together with a treatmentfor the local stellar radiation field improves the agreement with observedH$_2$ abundances over a wide range of gas densities and with the molecularKennicutt-Schmidt law, implying a more realistic modelling of the starformation process.

Modelling H$_2$ and its effects on star formation using a joint implementation of GADGET-3 and KROME