Dependence of Plasmon Energies on the Acoustic Normal Modes of Ag_n (n = 20, 84, and 120) Clusters

The vibrational and optical properties of Ag₂₀, Ag₈₄, and Ag₁₂₀ closed-shell clusters are investigated through a combination of continuum mechanics and density functional theory approaches. The acoustic vibrational frequencies associated with these tetrahedral silver clusters are found to be in close correspondence for the two theories, demonstrating the ability of finite-element calculations to reproduce first-principles computational results, even down to few-atom structures. TDDFT calculations of the absorption spectra of these clusters indicate a strong plasmon-like mode both for equilibrium structures of the clusters and for structures where the acoustic breathing mode is excited by amounts that are accessible to ultrafast experiments. The plasmon-like mode energy is found to vary linearly with the acoustic mode displacement (for small displacements), with a slope that increases with increasing cluster size. For larger clusters, the TDDFT slope is larger than the FDTD slope, which indicates that there are systematic errors in the continuum theory result for small particles. We also examine the ground and plasmon excited potential energy curves and show that the displacement in equilibrium geometry between these curves is too small to give breathing mode excitation that is consistent with observations based on vertical excitation alone. This suggests that breathing mode excitation arises during internal conversion after the initial photoexcitation.