# Kohn-Sham decomposition in real-time time-dependent density-functional theory: An efficient tool for analyzing plasmonic excitations

## TL;DR

This paper introduces an efficient Kohn-Sham decomposition method for RT-TDDFT, enabling detailed analysis of plasmonic excitations in molecules and nanoparticles, bridging a gap with linear-response approaches.

## Contribution

It develops a novel analysis technique for Kohn-Sham electron-hole decomposition in RT-TDDFT, validated against Casida's method and applied to large silver nanoparticles.

## Key findings

- Small nanoparticles show split plasmon resonances due to single-electron transitions.
- Large nanoparticles form a distinct plasmon resonance.
- The method is computationally efficient and accurate.

## Abstract

The real-time-propagation formulation of time-dependent density-functional theory (RT-TDDFT) is an efficient method for modeling the optical response of molecules and nanoparticles. Compared to the widely adopted linear-response TDDFT approaches based on, e.g., the Casida equations, RT-TDDFT appears, however, lacking efficient analysis methods. This applies in particular to a decomposition of the response in the basis of the underlying single-electron states. In this work, we overcome this limitation by developing an analysis method for obtaining the Kohn-Sham electron-hole decomposition in RT-TDDFT. We demonstrate the equivalence between the developed method and the Casida approach by a benchmark on small benzene derivatives. Then, we use the method for analyzing the plasmonic response of icosahedral silver nanoparticles up to Ag$_{561}$. Based on the analysis, we conclude that in small nanoparticles individual single-electron transitions can split the plasmon into multiple resonances due to strong single-electron-plasmon coupling whereas in larger nanoparticles a distinct plasmon resonance is formed.