The catalytic conversion of nitrous oxide (N2O) is of crucial environmental relevance because this chemical compound is a greenhouse gas with an important contribution to climate change, even larger than CO2, depleting the ozone layer. Recently, reduction of N2O catalyzed by rhodium subnanoclusters has been the subject of intensive research, both experimental and theoretical, finding dependencies of reaction rate on the size and geometry and electronic structure of the cluster. In this work, the catalytic reduction mechanism of N2O by Rh6– and Rh6+ ionic clusters has been studied by means of density functional theory calculations within the zero-order-regular approximation (ZORA), which explicitly includes relativistic effects. The N2O + Rh6– and N2O + Rh6+ reaction pathways were approached starting from a comprehensive search of different stable adsorption modes; transition states were determined as well. We have obtained that the Rh6– anions present the lowest activation barriers without spin selectivit...