Modeling the Photo-Absorption Properties of Noble Metal Nanoclusters: a Challenge for Density-Functional Theory

Modeling the emergence of the plasmon resonance in noble metal nanoclusters is still a challenge to tackle for theoretical chemistry. The systems are indeed too small to neglect quantum-size effects but too large to be easily assessed with quantum mechanics. We test here a robust answer to this still open question: the simplified variant to time-dependent density-functional theory (TDDFT). This electronic structure-based method cumulates the advantage to be applied to extended systems, like the ones under investigation, in computing thousands of excitations on a sufficiently large energy range to cover the emergence of plasmon-like states. By employing this approach under a semilocal exchange-correlation approximation such as PBE, we show that the modeled photo-absorption spectra can lead to a misinterpretation of the absorbing bands, or in other words, can provide the good answer for the wrong reason because of the too low energy gap predicted between $d$ and $s$ valence orbitals. However, we demonstrate that a global or range-separated hybrid exchange-correlation approximation such as PBE0 or RSX-PBE0, the latter being parameterized herein for sTDA, is a robust answer to the problem. We notice however that both approaches are not able to solve in the same time the energy positioning and intensity emergence of a plasmon band, PBE0 being more accurate to model the former property while RSX-PBE0 being preferred to predict the latter.