Performances of the Lamb Model to Describe the Vibrations of Gold Quantum-Sized Clusters

摘要

Lamb modes describe the vibrations of an object as a whole from the stellar scale to the nanometer one. Lamb description has been built from the linear elasticity theory and considers a homogeneous elastic sphere. Our work tries to determine the minimum scale where this description remains valid by studying the vibration of quantum-sized gold clusters (Au-6, Au-9, and Au-25) stabilized by organic molecules. First, our work shows that experimental frequencies of small-functionalized gold clusters obtained by low-frequency Raman spectroscopy can be interpreted with density functional theory calculations. Moreover, the Lamb model broadly succeeds in predicting these Raman acoustic modes only if a correction considering the mass of the surrounding ligands is added. Ligands affect vibrational modes of the core by their mass but also by their covalent bond with the core. The unexpected consequence of this electronic stabilization by the ligands is the sustainability of the Lamb description for clusters as small as six atoms. Finally, the limit of the Lamb model can be reached out at low temperature where the vibration mode spectrum presents a substructuration that the Lamb description, developed for a homogeneous sphere, is unable to predict.