Density functional theory is used to investigate the structures of cationic rhodium cluster oxides, Rh(6)O(m) (+) (m=1,4). On the monoxide and dioxide, the oxygen atoms occupy bridge sites, while on trioxide and tetroxide clusters, high-coordination sites are favored. A range of spin multiplicities are investigated for each cluster, with high spin multiplicities found to be less favored for the oxides compared with the naked metal clusters. The dissociation of nitric oxide on low-energy isomers of Rh(6)O(4) (+) is investigated and found to be unfavorable compared to molecular adsorption due to a combination of thermodynamic and kinetic factors. These calculations are consistent with, and help to account for, the experimentally observed reactivity of rhodium and rhodium oxide clusters with nitric oxide [M. S. Ford et al., Phys. Chem. Chem. Phys. 7, 975 (2005)].