The interactions of Os4, Os5, and Os5C clusters with various sites of a MgO(001) support were investigated theoretically with the aid of a scalar-relativistic density functional cluster model method. Adsorption geometries of C4v clusters centered above a magnesium cation and the Os atoms oriented either to the nearest surface oxygen anions (A) or between them (B) were considered. The influence of surface Vs and Vs2- defects on the adsorption of the clusters was also investigated. The calculated base Os−Os distances in supported Os5 and Os5C square-pyramidal clusters are at most 0.1 A longer (2.5−2.6 A) than the values calculated for the corresponding free osmium clusters but about 0.4 A (or more) shorter than the values determined by EXAFS spectroscopy for MgO-powder-supported clusters formed by decarbonylation of [Os5C(CO)14]2- and shown to retain the Os5C frame. The experimental Os−Os distances characterizing the supported clusters are close to the experimental and calculated bond lengths for coordinati...