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

Abstract

Absorption spectra of silver nanoclusters, Ag n with n = 20−147, are investigated in the framework of the time-dependent density functional theory (TDDFT) with the use of a range-separated hybrid density functional. Our calculated spectra reproduce well the experimental data. The plasmon-like band energy is situated at about 4 eV for all clusters in gas phase. A description of the plasmonic behavior is given using analyses and tools derived from ab initio quantum calculations. The plasmon band originates from multiple peaks gathered in a relatively small range of energy. High intensive peaks near the center of the band present a strong plasmonic character which has been characterized in terms of transition density, hole-electron excitation, transition contribution map (TCM), and generalized plasmonicity index (GPI).

Oxidation-Induced Surface Plasmon Band Fragmentation in Silver Clusters

“…19,[33][34][35] For silver clusters, the description of excited states in TDDFT within the adiabatic approximation requires a correction of the self-interaction error (SIE) and a correct asymptotic behaviour. The best results 36 have been obtained with range separated hybrid functionals (RSHs). Those functionals significantly reduce the SIE problems and improve the asymptotic behaviour at long range thanks to the inclusion of Hartree-Fock exchange.…”

Comprehensive Microscopic Theory for Coupling of Longitudinal--Transverse Fields and Individual--Collective Excitations

“…When one prepares the |µ of Ĥ0 , including the Coulomb interaction at equilibrium, the nanostructure optical responses, e.g., the plasmon-polariton and SPE spectra, are obtained within a theoretical framework for the prepared eigenstates. Recently, the first-principles calculation for a nanostructure or a nanoscale cluster of atoms was developed 15,26,27,29,31,32,46 , where the electronic states with the electron-electron interaction (the L component of the EM field) are evaluated precisely. In those previous studies, however, the T field was not self-consistently considered.…”

“…In the present work, we focus on the fact that the coupling between plasmons and SPEs via the T field, as well as the treatment of the microscopic nonlocal response involving the T field, has been missed in the previous frameworks, which is particularly related with the latter case in the above discussion. Recent ab initio calculations successfully implemented coherent coupling or hybridization between plasmon-like and single-particle-like excitations [26][27][28][29][30][31][32] . In those studies, the Coulomb interaction corresponding to part of the induced L field was considered.…”

Effects of ligands on (de-)enhancement of plasmonic excitations of silver, gold and bimetallic nanoclusters: TD-DFT+TB calculations

“…An accurate description of plasmons including the detailed quantum nature of excitations is challenging. In particular variants of time-dependent density functional theory are used to calculate absorption spectra of (bare) gold and silver nanoparticles, [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and detailed discussions of the efficiency and limitations of these approaches are available in literature. [53][54][55][56][57] Among these, the traditional ''Casida-type'' TD-DFT formalism is used extensively for small ligand-protected clusters and has a computational cost depending on, and increasing rapidly with, the number of exited-states that need to be determined.…”