Energetics of free pure metallic nanoclusters with different motifs by equivalent crystal theory

Abstract

The energy of metallic Ni, Cu, Pd, Ag, Pt, and Au nanoparticles up to 5000 atoms are studied by equivalent crystal theory ECT, a quantum approximate method QAM that describes the ground state structure and the surface properties of metals and semiconductors at zero temperature. ECT relies on the universal binding energy relation to predict with precision and speed the energy of a crystal in a specific configuration. For each pure metallic nanoparticle of each chosen motif icosahedron, octahedron, and decahedron, the energy variation with the number of atoms Nat is studied. Crossover and minimum energy values are calculated and/or estimated and compared with the results obtained by molecular dynamics MD. Our results confirm the qualitative behavior i.e., icosahedron shapes are less energetic for small sizes, decahedron for medium sizes, and octahedron for bigger sizes predicted by MD, but the calculated crossover and minimum energy values are, in general, larger for all metals and geometries examined. Also, we studied the trends in relaxation between layers and the behavior of the average radius Rav of each relaxed nanoparticle as Nat was increased. For each motif, the most stable structures i.e., with the best truncation follow a simple law of Rav in terms of Nat. This simple law is unchanged for the four different motifs and can be extended for all six metals after a simple parametrization is performed.