Vibrational and thermodynamic properties of transition-metal nanoclusters

The knowledge of the vibrational spectrum of a cluster, which is the fingerprint of its structure, is necessary for the development of thermodynamics of clusters (melting, heat capacity, solid-solid structural transitions) and for the understanding of experimental vibrational spectra. In summary, the full vibrational spectrum of Ni$_N$ and Cu$_N$ nanoclusters with $N$ from $2$ to $150$ atoms has been determined using the analytical expression of the embedded-atom method (EAM) for the {\em force-constant tensor} for the first time. In the determination of the spectra we have employed the global-minimum structures obtained in our previous unbiased EAM studies (see e.g. Physical Review B, 2004; 2006). Furthermore, using those spectra and the superposition approximation, the thermodynamic properties of the clusters have been calculated quantum mechanically, including their heat capacity and solid-solid transition temperatures for several structural changes in the Ni and Cu clusters. Both the vibrational spectrum and the thermodynamic functions show strong cluster-size effects. We emphasized that our approach is general. It is based only on the (common) EAM form of the total energy and applicable to many other many-body potentials.