Surface plasmons in quantum-sized noble-metal clusters: TDDFT quantum calculations and the classical picture of charge oscillations

Abstract

The localized surface-plasmon resonance of metal nanoparticles corresponds to a classical charge oscillation of the quasi-free conduction electrons. In the case of noble-metal nanoparticles, interband transitions from the d electrons influence the spectra strongly. In addition, the inhomogeneity of the nanoparticles at the atomistic level becomes important for small sizes. Using the time-evolution formulation of time-dependent density-functional theory, we show that in spherical 147-atom silver clusters, the localized surface-plasmon resonance corresponds indeed to a collective charge oscillation resembling the schematic picture, while the dynamics in a comparable gold cluster shows multiple modes which correspond to the spectra without strong resonance. Short nanorods show the same difference between Au and Ag. However, nanorods of high aspect ratio develop a silver-like charge oscillation. Monatomic silver chains behave similarly to the nanorods and show a clear transverse charge oscillation mode. The role of the d electrons in the screening of the localized surface-plasmon resonance is demonstrated.

Optical response of silver clusters and their hollow shells from linear-response TDDFT

“…From this point of view, the Sternheimer approach and wave-packet propagation approach have an advantage versus iterative TDDFT: former approaches only need the xc potential, and do not involve the TDDFT kernel. Fortunately, local and semi-local functionals correctly capture trends of the plasmonic response in nano-particles as was well documented in the past [73], and are still widely used [82].…”

Kohn–Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory: An Efficient Tool for Analyzing Plasmonic Excitations

“…Time-dependent density-functional theory (TDDFT) 1 built on top of Kohn-Sham (KS) density-functional theory (DFT) 2,3 is a powerful tool in computational physics and chemistry for accessing the optical properties of matter. 4,5 Starting from seminal works on jellium nanoparticles, [6][7][8] TDDFT has become a standard tool for modeling plasmonic response from a quantummechanical perspective, 9,10 and proven to be useful for calculating the response of individual nanoparticles, [11][12][13][14][15][16][17][18][19][20][21] and their compounds [22][23][24][25][26][27][28][29][30][31][32] as well as other plasmonic materials. [33][34][35][36] Additionally, a number of models and concepts have been developed for quantifying and understanding plasmonic character within the TDDFT framework.…”

Localized Surface Plasmon Resonance in Free Silver Nanoclusters Agn, n = 20–147

“…36 Recently, a few TDDFT studies have been performed on Ag n clusters with n ∼ 8 − 300 atoms. 22,24,[37][38][39][40][41][42][43][44][45] However, while most studies used a local or semi-local formulation for the exchange and correlation functional, one of us have shown that the use of a hybrid functional is required 3 to correctly describe the excitations of d-type electrons which present charge-transfer and Rydberg characters. 46,47 Such excitations cannot be described within TDDFT with a local or semi-local density functional in the adiabatic approximation used in standard calculations.…”