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The spin-density functional theory (DFT) and DFT+$U$ with Hubbard $U$ termaccounting for on-site Coulomb interactions were applied to investigatestructure, stability, and electronic properties of different terminations ofthe Fe$_3$O$_4$(111) surface. All terminations of the ferrimagneticFe$_3$O$_4$(111) surface exhibit very large (up to 90%) relaxations of thefirst four interlayer distances, decreasing with the oxide layer depth. Ourcalculations predict the iron terminated surface to be most stable in a widerange of the accessible values of the oxygen chemical potential. The adsorptionof Au and Pd on two stable Fe- and O-terminated surfaces is studied. Ourresults show that Pd binds stronger than Au both to the Fe- and O-terminatedsurface. DFT+$U$ gives stronger bonding than DFT. The bonding of bothadsorbates to the O-terminated magnetite surface is by 1.5-2.5 eV stronger thanto the Fe-terminated surface.

Surface properties of the clean and Au/Pd covered Fe$_3$O$_4$(111): a DFT and DFT+$U$ study