Calculation of the free energy barrier in the freezing of nanoclusters by atomistic simulations

Small metal nanoclusters exhibit various structural modifications, for example, for fcc metals, cuboctahedra, decahedra, and icosahedra. In many experiments, high-resolution electron microscopy, under typical cluster-growth condition, routinely detected metal clusters of icosahedral or decahedral structures that are not energetically the most stable. This implies that the structure and formation of nanoclusters produced from the liquid state or gas phase are governed by kinetics rather than by energetics and the free energy barrier of initial structural formation plays an important role in determining the preferential structure among the different structural isomers. In order to understand the kinetics, we investigated the free energy barrier for the freezing of Au nanoclusters using the umbrella sampling technique combined with constrained molecular dynamics simulation. The analysis showed that there is a surprisingly low transition barrier for the formation of an icosahedral structure from the liquid cluster at moderate undercooling, which explains well why the icosahedral cluster structure is formed frequently in experiments in spite of its energetic metastbaility.