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

TL;DR

This study uses ab initio methods to analyze how silver clusters transition from molecular to nanoscale behavior, revealing size-dependent changes in electronic structure and plasmonic properties around 140 atoms.

Contribution

It compares two ab initio approaches for small clusters and identifies the size at which silver clusters exhibit plasmonic behavior, bridging molecular and nanoparticle regimes.

Findings

Agreement between methods for small clusters

Transition from molecular to nanoparticle behavior at 140 atoms

Emergence of plasmon resonance in larger clusters

Abstract

Electronic and optical properties of silver clusters were calculated using two different \textit{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 $\sim 1.7$\,nm). Above this cluster size the step-like electronic structure, evident as several features in the imaginary part of the polarizability of all clusters smaller than Ag$_\mathrm{147}$, gives way to a dominant plasmon peak localized at wavelengths 350\,nm$\le\lambda\le$ 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.