The reduction of NO x is crucial for reducing air pollution from vehicle exhaust. In the presence of Rh-based catalysts, the dissociation of NO and the formation of N 2 O and N 2 constitute the important elementary steps of NO x reduction. The present study used density functional theory (DFT) to investigate the catalytic performances of the Rh(111) surface and Rh 55 and Rh 147 clusters toward these elementary reactions. The NO dissociation reaction was found to have minimum activation barriers (E a ) of 0.63, 0.68, and 1.25 eV on Rh 55 , Rh 147 , and Rh(111), respectively. Therefore, it is the fastest on small Rh clusters. In contrast, the N 2 formation reaction is relatively inefficient on small clusters, with corresponding E a values of 2.14, 1.79, and 1.71 eV. Because of the stronger binding of N atoms to the Rh clusters than to the Rh surface, N 2 formation through the recombination of N atoms has a higher E a value on Rh clusters. The calculated reaction rate constants confirmed that small Rh clusters are less reactive for N 2 formation than Rh(111), especially at low temperatures. Our results also suggest that N 2 O formation is largely endothermic and, thus, thermodynamically unfavored.