The computational characterization of the single molecule magnet (SMM) [Fe4(AcS(CH2)5C(CH2O)3)2(dpm)6] (Fe4C5) with Ac = CH3CO and Hdpm = dipivaloylmethane, grafted on the Au(111) surface (Fe4C5@Au(111)) is presented. For the first time, ab initio molecular dynamics (AIMD) calculations have been used to study the evolution of the structural properties of a SMM once adsorbed on a metallic substrate. Important structural rearrangements induced by the grafting process can be observed thanks to the AIMD approach. This allows us to elucidate some possible mechanisms that govern the SMM's magnetism on a surface, which wouldn't be revealed by the standard static approach. The sampling of the SMM@Au(111)'s configurational space at finite temperature, together with magneto-structural correlations, makes it possible to study the fluctuation amplitude of magnetic properties, thus revealing that a single minimum of the free energy surface (FES) is populated at 200 K. Starting from the finite temperature scenario, the potential energy surface (PES) was sampled by means of thermal annealing calculations showing that multiple local minima could be populated at 0 K. Both isotropic exchange coupling constants and zero field splitting (ZFS) parameters are calculated for the identified Fe4C5@Au(111) local minima, thereby allowing an in-depth characterization of the Fe4C5 magnetic properties from the isolated to the grafted scenario. The cutting-edge computational protocol used here shows that the experimentally observed retention of a spin S = 5 ground state upon grafting results from balancing the major modifications on spin Hamiltonian (SH) parameters. The electronic effects of the metal on the magnetic properties of Fe4C5 have been also discussed.