Vibrations of Au-13 and FeAu12 nanoparticles and the limits of the Debye temperature concept

We present first-principles calculations of the vibrational density of states (VDOS), the specific heat and the mean-squared displacement of the five lowest-energy isomers of Au-13 and of two low-energy FeAu12 nanoparticles. We find that the vibrational contributions to the Helmholtz energy do not affect the energy ordering of the isomers. As expected, for nanoparticles the vibrational density of states differs dramatically from the function proposed by the Debye model. We demonstrate that, for the nanoclusters we studied, the alternative calculations of the \u27Debye temperature\u27 yield significantly inconsistent results. We conclude that T-D obtained from a particular thermodynamic property is neither applicable for deriving conclusions about other thermodynamic properties nor correlated with atomic bond strengths. Instead, in order to describe the temperature dependence of a nanoparticle\u27s mean-squared displacement and its specific-heat capacity, what is necessary is its discrete phonon spectrum