The atomic structure and electronic properties of gas-phase and MgO(100)-supported iridium tetramers are studied using density functional theory. At variance with experimental data, the most stable Ir4 isomer on MgO(100) is the square one, as in the gas phase, and the metastable tetrahedral isomer is highly distorted by interactions with the substrate. In the presence of a single carbon adatom, the most stable structure of Ir4 is tetrahedral for both environments and the structural distortion of the adsorbed cluster is reduced. On MgO(100), the binding energy of a C adatom to tetrahedral Ir4 is 1.6 eV larger than that to the square isomer, due to strong interactions between C-2p orbitals and a low-energy unoccupied molecular orbital of tetrahedral Ir4
