Mechanical Vibrations of Atomically Defined Metal Clusters: From Nano- to Molecular-Size Oscillators

Acoustic vibrations of small nanoparticles are still ruled by continuum mechanics laws down to diameters of a few nanometers. The elastic behavior at lower sizes (<1-2 nm), where nanoparticles become molecular clusters made by few tens to few atoms, is still little explored. The question remains to which extent the transition from small continuous-mass solids to discrete-atom molecular clusters affects their specific low-frequency vibrational modes, whose period is classically expected to linearly scale with diameter. Here, we investigate experimentally by ultrafast time-resolved optical spectroscopy the acoustic response of atomically defined ligand-protected metal clusters Au _n(SR) _m with a number n of atoms ranging from 10 to 102 (0.5-1.5 nm diameter range). Two periods, corresponding to fundamental breathing- and quadrupolar-like acoustic modes, are detected, with the latter scaling linearly with cluster diameters and the former taking a constant value. Theoretical calculations based on density functional theory (DFT) predict in the case of bare clusters vibrational periods scaling with size down to diatomic molecules. For ligand-protected clusters, they show a pronounced effect of the ligand molecules on the breathing-like mode vibrational period at the origin of its constant value. This deviation from classical elasticity predictions results from mechanical mass-loading effects due to the protecting layer. This study shows that clusters characteristic vibrational frequencies are compatible with extrapolation of continuum mechanics model down to few atoms, which is in agreement with DFT computations.