In the field of nanotechnology, the ultimate goal is to produce nanostructures with specially tailored properties that contrast with those in the bulk. Actinide dioxide nanomaterials play an increasingly important role in the design of novel nuclear fuels, as they are expected to improve both efficiency and safety. Modeling these nanoparticles is, however, still a challenge because the number of stable structures increases exponentially with the number of atoms. This challenge is greater for a two-component system such as a metal oxide where the metal center can co-exist in various oxidation states depending on the local structure. Hence a relativistic quantum-level of theory is a must to search for the global and local-minima structures of actinide oxide particles.