This work presents many possible theoretical reaction pathways of N2O reduction to N-2 and O on Rh-n nanoparticles (n = 1-4) using density functional theory (DFT) method and the zero order regular approximation (ZORA), which explicitly considers the scalar relativistic corrections. The Rh spin multiplicity is an essential condition to dissociate N2O, because can promote or inhibit the electron back donation from the metal. Rh activates N2O by exothermic and spontaneous reactions. For each case presented, the optimized geometry adsorption site, reaction energy, spin multiplicity and Voronoi charges are calculated. On a single Rh atom in the ground and low-lying excited states, the N2O is captured only. On the Rh-2 quintet ground state, N2O is also chemisorbed and dissociation occurs for the next two excited states (triplet and septet). In the Rh-3 case, there are N2O adsorption and dissociation for Rh-3 quartet ground state and for most excited states. Several dissociation cases take place when N2O is parallel to the plane and parallel to a Rh-3 bond. On the Rh-4, however, there are two optimal geometries: tetrahedral and square; for both cases there are N2O adsorption and dissociation. (C) 2013 Elsevier B.V. All rights reserved.