Vibrational Properties of Metal Nanoparticles: Atomistic Simulation and Comparison with Time-Resolved Investigation

Knowledge of the vibrational spectrum of metal clusters and nanoparticles is of fundamental interest since it is a signature of their morphology, and it can be used to determine their mechanical, thermodynamical, and other physical properties. It is expected that such a vibrational spectrum depends on the material, size, and shape of clusters and nanoparticles. In this work, we report the vibrational spectra and density of states of Au, Pt, and Ag nanoparticles in the size range of 0.5–4 nm (13–2057 atoms), with icosahedral, Marks decahedral, and FCC morphologies. The vibrational spectra were calculated through atomistic simulations (molecular dynamics and a normal-mode analysis) using the many-body Gupta potential. A discussion on the dependence of the vibrational spectrum on the material, size, and shape of the nanoparticle is presented. Linear relations with the nanoparticle diameter were obtained for the periods of two characteristic oscillations: the quasi-breathing and the lowest frequency (acoustic gap) modes. These linear behaviors are consistent with the calculation of the periods corresponding to the breathing and acoustic gap modes of an isotropic, homogeneous metallic nanosphere, performed with continuous elastic theory using bulk properties. Additionally, experimental results on the period corresponding to isotropic volume oscillations of Au nanoparticles measured by time-resolved pump–probe spectroscopy are presented, indicating a linear variation with the mean diameter in the size range of 2–4 nm. These, and similar results previously obtained for Pt nanoparticles with size between 1.3 and 3 nm, are in good agreement with the calculated quasi-breathing mode periods of the metal nanoparticles, independently of their morphologies. On the other hand, the calculated period of the mode with the highest (cutoff) frequency displays weak size and shape dependencies up to ∼4 nm, for all nanoparticles under study. In contrast with the behavior of other physicochemical properties, the clear consistency between experiments with atomistic and continuous media approaches resulting from this work indicates the existence of simple relations with size and weak dependence with the material and shape, for vibrational properties of metal nanoparticles.