Optical spectra of silver clusters and nanoparticles from 4 to 923 atoms from the TDDFT+U method

Mohit Chaudhary & Hans-Christian Weissker

Nature Communications 15, 9225 (2024).

https://www.nature.com/articles/s41467-024-53428-6

Many of the applications of metal clusters and nanoparticles make use of the localized surface-plasmon resonances. To use the full potential of these systems, their properties need to be understood precisely ; accurate, predictive calculations are necessary, which today are mostly attempted using Time-Dependent Density-Functional Theory (TDDFT). In the noble metals, the presence of the filled shell of d electrons complicates these calculations, because these electrons are notoriously badly described in the customary “simple” approximations of TDDFT. In the present work, we use the Hubbard U correction within the TDDFT+U method to obtain precise spectra of a large size range of systems, ranging from 4-atom clusters to 3-nm nanoparticles (923 atoms). The U parameter has been found to be surprisingly transferable; the value found to perform well for the bulk metal produced good results for all sizes. The computational cost of this approach is not much higher than for a “normal” TDDFT calculation. It will open the pathway for precise, predictive calculations of systems of practical relevance, including the coupling of clusters between each other or with bio-molecules.