Ab initio calculations of optical properties of silver clusters: cross-over from molecular to nanoscale behavior

Abstract

Abstract. Electronic and optical properties of silver clusters were calculated using two different ab initio approaches: (1) based on all-electron full-potential linearized-augmented plane-wave method and (2) local basis function pseudopotential approach. Agreement is found between the two methods for small and intermediate sized clusters for which the former method is limited due to its all-electron formulation. The latter, due to non-periodic boundary conditions, is the more natural approach to simulate small clusters. The effect of cluster size is then explored using the local basis function approach. We find that as the cluster size increases, the electronic structure undergoes a transition from molecular behavior to nanoparticle behavior at a cluster size of 140 atoms (diameter ∼1.7 nm). Above this cluster size the steplike electronic structure, evident as several features in the imaginary part of the polarizability of all clusters smaller than Ag147, gives way to a dominant plasmon peak localized at wavelengths 350 nm ≤ λ ≤ 600 nm. It is, thus, at this length-scale that the conduction electrons' collective oscillations that are responsible for plasmonic resonances begin to dominate the opto-electronic properties of silver nanoclusters.

Thermoplasmonic Response of Semiconductor Nanoparticles: A Comparison with Metals

“…In reality, however, the system boundaries are not always smooth and one needs to additionally account for the effect of the surface roughness as well [22] . In even smaller nanoclusters (radii∼1-5 nm), the number of charge carriers for both metallic and semiconducting systems becomes really small and the discreteness of the band-structure needs to be taken into account to model dielectric permittivity and plasmonic response [23,24,25,26] . However, to understand and isolate the differences in the thermoplasmonic response of semiconducting and metallic nanoparticles, we limit ourselves to the temperature dependent response of ideal spherically smooth particles whose behavior can be modeled using the Mie theory [8,27] .…”

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.…”

The collective excitations and static dipole polarizability in small nanoparticles

“… the average diameter of the colloidal particle is D ≥ 1 nm due to the limited resolution of the electron microscopy. As can be seen, ћω in is increasing when the size of the noble metal cluster decreases . Substituting the value D = 0.73 nm (see Table .)…”

“…As can be seen, ћω in (11) is increasing when the size of the noble metal cluster decreases. 32,33 Substituting the value D = 0.73 nm (see Table 1.) into (11), one finds ћω = 4.00 eV.…”