Results of a theoretical study on the properties of Ir4 clusters in the gas–phase and on oxide surfaces are presented. The work is based on density functional theory (DFT) within the generalized gradient approximation (GGA) and ultrasoft pseudopotentials. Properties of a small particle such as Ir4 cluster are entirely determined by its geometry. The already known result that the most stable form of Ir4 in the gas–phase is the square structure which is significantly more stable than the butterfly and tetrahedron is confirmed. This result is in contradiction with experiments which indicate that the oxide supported Ir4 adopts a tetrahedral configuration. It is shown in this thesis that the chemical environment has a strong influence on the relative stability of Ir4 clusters. On MgO(100) surface, the square isomer remains the most stable Ir4 structure, well separated in energy from the other two. Moreover, the tetrahedron is heavily distorted by the interaction with the surface oxygen. Presence of point defects (neutral and charged O vacancies) affects the energy ordering making tetrahedron and square very close in energy, but the structural distortion of the tetrahedron is even bigger and the predicted data do not correspond to experiments. On TiO2(110) the tetrahedron and square structures become degenerate and the butterfly becomes the least stable isomer. Moreover, structural distortions are very small, in agreement with experimental data. It is shown that the TiO2 surface influences the relative stability of the three isomers through a particularly strong electrostatic field. Interactions of Ir4 with H, C and O atoms as well as with CO molecules have been studied. Adsorption of a single C atom strongly influences the relative stability of the three isomers. Upon C adsorption, the butterfly becomes the most stable gas–phase isomer while on both surfaces the tetrahedron is the most probable structure. Adsorption of a single H or O atom does not produce the same effect. The interaction with CO molecules is also important given the experimental procedure used for producing supported Ir4 clusters. It is shown that on MgO(100), CO dissociation is as probable as the competing process CO desorption justifying the presence of carbon adatoms on Ir4 clusters which brings theoretical predictions in better agreement with experimental data.