The interaction of Rh-6 clusters with the nitrous oxide (N2O) molecule was studied by means of density functional theory (DFT) calculations through the zero-order-regular approximation (ZORA), which includes relativistic effects explicitly. The purpose of this work is to characterize the N2O reduction to N-2 and O by Rhs clusters. The identified low-lying and degenerate states of Rh-6, octahedron with multiplicities of I and 7, and a triangular prism with a septet, present many active sites of reduction. The initial steps of the N2O + Rh-6 reaction were studied through different adsorption modes, each one having different multiplicities. The Rh Rh bonds define the active sites to produce N2O dissociation. The most successful reaction pathway originates when the linear N=N-O molecule is approached parallel to the Rh Rh bonds, being this active site the most numerous in the systems. The N-O bond breaks in five addressed multiplicities, with 2 and 3 degenerate energy cases in the octahedron. Other approaches studied are: N2O pointing toward the triangular or square face bisectors or to the surface between two Rh Rh bonds. In these two cases, the N2O molecule moves toward one of the Rh Rh bonds dissociating over it. Overall, to reduce N2O, the prism structure presents a greater number of different active sites, but the octahedron has more edges, in which the oxide can break. For each calculation, many parameters were obtained and are included in the text: vibrational frequencies, distances between atoms, binding energies, total electronic charges, as well as optimized geometries. An important result of this work is the feature that Rh-6 is the smallest nanoparticle having several structures at the ground state, which greatly increases the number of active sites being able to reduce the nitrous oxide contaminant. (C) 2015 Elsevier B.V. All rights reserved.