Modeling the emergence of the plasmon resonance in noble metal nanoclusters is still a challenge to overcome for theoretical chemistry. The systems are indeed too small to neglect quantum-size effects but too large to be easily addressed with quantum mechanics. We test here a robust answer to this still open question: the simplified variant to time-dependent density-functional theory (TDDFT). Applied to extended systems, this electronic structure-based method succeeds in computing a sufficient number of excitations to cover the emergence of plasmon-like states. By employing it under a semilocal exchange-correlation approximation such as PBE, we show that the most intense absorption band, which could be wrongly assigned to the plasmon band, has a strong interband character. We suspect the too low energy gap between (n–1)d and ns valence orbitals as the origin of the d-contamination of the excitations. We demonstrate however that a global or range-separated hybrid exchange-correlation approximation such as PBE0 or RSX-PBE0 is a robust answer to the problem. We notice that both approximations are not able to solve at the same time the energy positioning and intensity of the plasmon band, PBE0 being more accurate for energy positioning and RSX-PBE0 for intensity. All in all, we warn the user that a random choice of the exchange-correlation approximation opens the door to getting the correct answer for the wrong reason.

Modeling the emergence of the plasmon resonance in noble metal nanoclusters is still a challenge to overcome for theoretical chemistry. The systems are indeed too small to neglect quantum-size effects but too large to be easily addressed with quantum mechanics. We test here a robust answer to this still open question: the simplified variant to time-dependent density-functional theory (TDDFT). Applied to extended systems, this electronic structure-based method succeeds to compute a sufficient number of excitations to cover the emergence of plasmon-like states. By employing it under a semilocal exchange-correlation approximation such as PBE, we show that the most intense absorption band, that could be wrongly assigned to the plasmon band, has a strong interband character. We suspect the too low energy gap between $(n-1)d$ and $ns$ valence orbitals as the origin of the $d$-contamination of the excitations. We demonstrate however that a global or range-separated hybrid exchange-correlation approximation such as PBE0 or RSX-PBE0 is a robust answer to the problem. We notice that both approximations are not able to solve at the same time the energy positioning and intensity of the plasmon band, PBE0 being more accurate for energy positioning and RSX-PBE0 for intensity. All in all, we warn the user that a random choice of the exchange-correlation approximation opens the door to getting the correct answer for the wrong reason.

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.