We present extensive pseudopotential density functional theory calculations dedicated to analyze the stability and dissociation behavior of NO molecules adsorbed on small nonmagnetic Rh-n(+/-) clusters. Following the experimental work of Anderson et al. (J. Phys. Chem. A 2006, 110, 10992), we consider rhodium structures of different sizes (n = 3, 4, 6, and 13) and charge states onto which we attach NO species in both molecular and dissociative configurations. The relative stability between different Rh-n(+/-) isomers depends on the ionization state of the clusters as well as on the presence of NO adsorbates on the surface. Various adsorbed configurations for the NO molecules are found when switching from cationic to neutral to anionic rhodium clusters. In particular adsorbed phases in which the NO molecule is attached with its N-O bond parallel to the plane of square or triangular facets are characterized by elongated nitrogen-oxygen interatomic distances, a fact that plays a fundamental role in the dissociation behavior of the adsorbate. We use the nudged elastic band method to analyze possible reaction pathways and transition states that could be present in our (R-h + NO)(+/-) systems. We found (as in surface studies) that the dissociation of the N-O bond is more easily obtained on square facets than on triangular atomic environments, a fact that indirectly reveals the structure of Rh clusters present in the gas phase experiments. The energy barriers that need to be overcome to achieve the breaking of the N-O bond depend on the charge state of the systems, a result that could be used to tune the catalytic activity of these types of materials.