Ab initio insights into plasmonic and strong-field contributions to H$_2$ dissociation on silver nanoshells

Modeling plasmonic catalysis by applying femtosecond laser pulses of high intensity ($10^{13}-10^{15}$ W cm$^{-2}$), although justified by the time-dependent density functional theory (TDDFT) time-scale limitations, can lead to a dissociation mechanism that is completely unrelated to the plasmon excitation created under low-intensity continuous light in experiments (on the order of 1 W cm$^{-2}$). In this study, we examine the dissociation of H$2$ on a large octahedral Ag nanoshell under varying field intensity, frequency, and duration, and we explore the possibility of identifying optimal modeling conditions accessible with current TDDFT simulations. We show that using this large nanoshell that consists in the outer layer of the Ag${231}$ cluster, it is still possible to disentangle the role of the plasmon from strong-field effects at applied field intensities as high as $(2-8) \times 10^{13}$ W cm$^{-2}$. In particular, although strong-field effects are always present at these intensities, we find that the excited plasmon dominates the dissociation process at the lowest applied intensity of $2 \times 10^{13}$ W cm$^{-2}$. Furthermore, at the highest intensity, at which strong-field effects become dominant, the plasmon contributes to accelerating the dissociation of the molecule. Overall, our simulations pave the way to bridge the intensity gap between TDDFT modeling and experiments in plasmonic catalysis.

💡 Research Summary

Plasmonic catalysis exploits the localized surface plasmon resonance (LSPR) of metallic nanoparticles to accelerate chemical reactions under light illumination. In experiments, the illumination intensity is typically on the order of 1 W cm⁻² and continuous, whereas real‑time time‑dependent density‑functional theory (TDDFT) combined with Ehrenfest dynamics (ED) can only treat femtosecond laser pulses with intensities of 10¹³–10¹⁵ W cm⁻² because of computational cost. This mismatch raises a critical question: do the high‑intensity pulses used in simulations trigger the same dissociation mechanism as the low‑intensity continuous light used experimentally? Strong‑field (non‑linear) effects such as multiphoton absorption and ionization can dominate at high intensities, potentially masking the genuine plasmon‑driven chemistry.

The authors address this issue by moving from the previously studied tiny Ag₅₅ nanoshell to a much larger octahedral Ag₍₂₃₁₎ cluster and, more specifically, to its outer layer (146 Ag atoms), denoted Ag L1 231. A hydrogen molecule is adsorbed at one vertex of the shell, a location where the electric field of the dipolar plasmon is strongly enhanced. Geometry optimization with DFT‑PBE (CP2K, GPW, DZVP basis, GTH pseudopotentials) yields an adsorption distance of 2.275 Å, an H–H bond length of 0.763 Å, an adsorption energy of –0.17 eV, and an ionization potential of 4.6 eV for the combined system.

The linear optical response is obtained via real‑time TDDFT using a weak δ‑kick. The absorption spectrum shows a pronounced plasmon peak at 2.48 eV and a weaker high‑energy tail (4–7 eV) associated with d‑sp interband transitions, in good agreement with experimental plasmon energies for Ag octahedra (2.75–3.0 eV).

To probe the interplay of plasmonic and strong‑field effects, the authors apply four Gaussian laser pulses (pulse‑1 to pulse‑4) with peak intensities ranging from 2 × 10¹³ to 8 × 10¹³ W cm⁻², durations (σ) of 5–15 fs, and central frequencies either resonant with the plasmon (2.48 eV) or far off‑resonant (8 eV). The electric field is polarized along the vertex‑to‑center (z) axis.

Key observations:

1. Linear‑vs‑non‑linear response – At the lowest intensity (2 × 10¹³ W cm⁻², pulse‑1), the resonant pulse generates a dipole moment with a markedly larger amplitude than the off‑resonant pulse, and the induced dipole persists long after the pulse, indicating a predominantly linear plasmonic response. The rapid decay of the dipole in the plotted data reflects the strong‑field component, yet induced‑density visualizations reveal a collective electron displacement characteristic of a genuine plasmon excitation, whereas the off‑resonant case shows only localized single‑ and multi‑pair excitations.

2. Impact on H₂ bond – Time evolution of the H–H distance shows that under resonant excitation the bond stretches dramatically within ~150 fs, reaching >1.5 Å, a clear precursor to dissociation. Under off‑resonant excitation at the same intensity the bond length remains close to its equilibrium value, oscillating only weakly. This demonstrates that hot electrons generated by the plasmon efficiently weaken the H–H bond, while a comparable strong field without plasmonic enhancement does not.

3. Strong‑field dominance at higher intensity – When the intensity is increased to 8 × 10¹³ W cm⁻² (pulse‑4), multiphoton absorption leads to partial ionization of both the Ag shell and the H₂ molecule. The dipole response becomes less dependent on resonance, indicating that non‑linear electron dynamics dominate. Nevertheless, even in this regime the resonant pulse still produces a slightly larger dipole and a faster bond elongation than the off‑resonant pulse, showing that the plasmon continues to assist the dissociation even when strong‑field effects are prominent.

4. Pulse duration effects – Longer pulses (σ = 10 fs, 15 fs) reduce the efficiency of energy transfer from the plasmon to the molecule, because the field spends more time in the non‑linear regime where the collective oscillation is damped. Consequently, the bond‑stretching rate diminishes, highlighting the importance of short, intense pulses to preserve plasmonic character.

Overall, the study identifies an intensity window (≈2 × 10¹³ W cm⁻²) where the plasmonic contribution dominates H₂ dissociation on the Ag nanoshell, and a higher‑intensity window (≈8 × 10¹³ W cm⁻²) where strong‑field effects become dominant but the plasmon still provides an acceleration factor. By using a larger nanoparticle, the authors demonstrate that the linear plasmonic regime can be accessed at lower field strengths than previously possible with small clusters, thereby enabling a clearer separation of plasmonic and strong‑field mechanisms within the computational limits of TDDFT‑ED.

The implications are twofold: (i) the results provide a concrete guideline for choosing laser parameters in future TDDFT studies aimed at mimicking experimental plasmonic catalysis, and (ii) they suggest that experimental designs employing larger plasmonic nanostructures could achieve plasmon‑driven chemistry at lower intensities, narrowing the gap between theory and practice. This work thus paves the way for more realistic first‑principles modeling of plasmonic catalysis and for the rational design of nanostructures that maximize plasmonic enhancement while minimizing unwanted strong‑field side effects.