Free energy surface of two- and three-dimensional transitions of Au 12 nanoclusters obtained byab initiometadynamics

The description of the conformational space generated by metal nanoparticles is a fundamental issue for the study of their physicochemical properties. In this investigation, an exhaustive exploration and a unified view of the conformational space of a gold nanocluster is provided using a Au 12 cluster as an example. Such system is characterized by coexisting planar/quasiplanar and tridimensional conformations separated by high-energy barriers. The conformational space of Au 12 has been explored by means of Born-Oppenheimer ab initio metadynamics, i.e., a molecular dynamics simulation coupled with a history dependent potential to accelerate events that might occur on a long time scale compared to the time step used in the simulations (rare events). The sampled conformations have complex, in general not intuitive topologies that we have classified as planar/quasiplanar or tridimensional, belonging to different regions of the free energy surface. Three conformational free energy basins were identified, one for the planar/quasiplanar and two for the tridimensional structures. At thermodynamic equilibrium, the planar/quasi-planar and tridimensional conformations were found to coexist, to be fluxional and to be separated by high-free-energy barriers. The comparison between the free energy and the potential energy revealed the relevance of the entropic contribution in the equilibrium distribution of the conformations of the cluster.