Quantum mechanical origin of the plasmonic properties of noble metal nanoparticles

Abstract

Small silver and gold clusters (less than 2 nm) display a discrete absorption spectrum characteristic of molecular systems whereas larger particles display a strong, broad absorption band in the visible. The latter feature is due to the surface plasmon resonance, which is commonly explained by the collective dipolar motion of free electrons across the particle, creating charged surface states. The evolution between molecular properties and plasmon is investigated. Time-dependent density functional theory (TDDFT) calculations are performed to study the absorption spectrum of cluster-size silver and gold nanorods. The absorption spectrum of these silver nanorods exhibits high-intensity longitudinal and transverse modes (along the long and short axis of the nanorod respectively), similar to the plasmons observed experimentally for larger nanoparticles. These plasmon modes result from a constructive addition of the dipole moments of nearly degenerate single-particle excitations. The number of single-particle transitions involved increases with increasing system size, due to the growing density of states available. Gold nanorods exhibit a broader absorption spectrum than their silver counterpart due to enhanced relativistic effects, affecting the onset of the longitudinal plasmon mode. The high-energy, high-intensity beta-peak of acenes also results from a constructive addition of single-particle transitions and I show that it can be assigned to a plasmon. I also show that the plasmon modes of both acenes and metallic nanoparticles can be described with a simple configuration interaction (CI) interpretation. The evolution between molecular absorption spectrum and plasmon is also investigated by computing the density of states of spherical thiolate-protected gold clusters using a charge-perturbed particle-in-a-sphere model. The electronic structure obtained with this model gives good qualitative agreement with DFT calculations at a fraction of the cost. The progressive increase of the density of states with particle size observed is in accordance with the appearance of a plasmon peak. The optical properties of nanoparticles can be tuned by varying their composition. Therefore, the optical behavior of the bimetallic Au[subscript](25-n)Ag[subscript]n(SH)[subscript]18[superscript]- cluster for different values of n using TDDFT is analyzed. A large blue shift of the HOMO-LUMO absorption peak is observed with increasing silver content, in accordance with experimental results.