•Rhn+N2O reaction study must consider the geometry of the reactants and spin.•N2O reduction mechanism catalysed by Rhn clusters ends up breaking the N2O bond.•The N2O activation never occurs through the NN bond rupture.•Most of Rh clusters capture N2O and there are some spin states that also activate it.•The spin states transfer enough charge from Rh to N2O to break the N2O bond. This work presents many possible theoretical reaction pathways of N2O reduction to N2 and O on Rhn 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 Rh2 quintet ground state, N2O is also chemisorbed and dissociation occurs for the next two excited states (triplet and septet). In the Rh3 case, there are N2O adsorption and dissociation for Rh3 quartet ground state and for most excited states. Several dissociation cases take place when N2O is parallel to the plane and parallel to a Rh3 bond. On the Rh4, however, there are two optimal geometries: tetrahedral and square; for both cases there are N2O adsorption and dissociation.