The interaction of H 2 molecules with a Cu(100) metallic surface has been investigated by DFT approaches using a (H 2) nCu 13 cluster model. Nine exchange-correlation functionals, belonging to the generalized gradient approximations (GGA), meta GGA (mGGA), hybrid Kohn-Sham/Hartree-Fock models, either based on GGAs or mGGAs, range-separated hybrids, and double-hybrid families, have been tested on the chemisorption and physisorption processes involving one or two H 2 layers. The addition of an empirical correction for dispersion has also been tested for some of these functionals. The calculated energies and structural parameters were compared to sophisticated multi reference configuration interaction including Davidson's correction for quadruple excitations (MRCI + Q). Our results show that among the nine considered exchange-correlation functionals, none can accurately reproduce all processes involved in the successive layers adsorption. Although an hybrid based on a mGGA such as M06-2X can quantitatively describe both the physisorption step and dissociation barriers involved in the adsorption of the first H 2, it fails to reproduce its chemisorption. On the other hand, significant discrepancies with the reference post-HF data are obtained for the description of the second layer interaction, no matter which functional is considered, outlining the need of improvement and/or development of exchange-correlation functionals suitable for complex systems such as H 2/H 2Cu.