Optical spectra of silver clusters and nanoparticles of all sizes from the TDDFT+U method

TL;DR

This paper demonstrates that the TDDFT+U method accurately predicts optical spectra of silver clusters and nanoparticles across all sizes, effectively capturing quantum effects and plasmon resonances, thus enabling better theoretical understanding and design.

Contribution

The study introduces the use of the DFT+U method within RT-TDDFT to accurately model optical spectra of silver clusters from few atoms to nanoparticles, showing high agreement with experiments across all sizes.

Findings

Accurate spectra for silver clusters from 4 to 923 atoms.

Both discrete and broad plasmon resonances are captured.

The U parameter is transferable across different sizes.

Abstract

The localized surface-plasmon resonances (LSPRs) of coinage-metal clusters and nanoparticles provide the basis for a great number of applications, the conception and necessary optimization of which require precise theoretical description and understanding. However, for the size range from clusters of a few atoms through nanoparticles of a few nanometers, where quantum effects and atomistic structure play a significant role, none of the methods employed to date has been able to provide high-quality spectra for all sizes. The main problem is the description of the filled shells of d electrons which influence the optical response decisively. In the present work we show that the DFT+U method, employed with real-time time-dependent density-functional theory calculations (RT-TDDFT), provides spectra in good agreement with experiment for silver clusters ranging from 4 to 923 atoms, the latter representing a nanoparticle with a diameter of 3 nm. Both the electron-hole-type discrete spectra of the smallest clusters and the broad plasmon resonances of the larger sizes are obtained. All calculations have been carried out using the same value of the effective U parameter that has been found to provide good results in bulk silver. The agreement with experiment for all sizes shows that the U parameter is surprisingly transferable. Our results open the pathway for TDDFT calculations of many practically relevant systems including clusters coupled to bio-molecules or to other nano-objects.