Strong-field effects in the photo-induced dissociation of the hydrogen molecule on a silver nanoshell

Abstract

Plasmonic catalysis is a rapidly growing field of research, both from experimental and computational perspectives. Experimental observations demonstrate an enhanced dissociation rate for molecules in the presence of plasmonic nanoparticles under low-intensity visible light. The hot-carrier transfer from the nanoparticle to the molecule is often claimed as the mechanism for dissociation. However, the charge transfer time scale is on the order of a few femtoseconds and cannot be resolved experimentally. In this situation, ab initio non-adiabatic calculations can provide a solution. Such simulations, however, have their own limitations related to the computational cost. To accelerate plasmonic catalysis simulations, many researchers resort to applying high-intensity external fields to nanoparticle-molecule systems. Here, we show why such an approach can be problematic and emphasize the importance of considering strong-field effects when interpreting the results of time-dependent density functional theory simulations of plasmonic catalysis. By studying the hydrogen molecule dissociation on the surface of a silver nanoshell and analyzing the electron transfer at different field frequencies and high intensities, we demonstrate that the molecule dissociates due to multiphoton absorption and subsequent ionization.

Fig. 1. (a) Atomic structure of the relaxed Ag^L1₅₅ nanoshell with H₂ (interatomic distance of 0.75 Å) at a distance of 3 Å from the nanoshell facet. (b) Absorption spectrum of Ag^L1₅₅ + H₂. (c) Time-dependent field strength of the external field pulse with a Gaussian envelope (σ = 5 fs, t₀ = 18 fs) with ℏω₀ = ℏω_p = 3.15 eV. The maximum field strength E₀ = 1.94 V Å⁻¹ (0.038 a.u.) corresponds to the maximum intensity I_max = 1 × 10¹⁴ W cm⁻².

Fig. 2. H–H bond length as a function of time for the three chosen field frequencies. Field intensity is (a) I_max = 2 × 10¹³ W cm⁻² and (b) I_max = 1 × 10¹⁴ W cm⁻². The maximum of the external field arrives at 18 fs.

Fig. 3. Time evolution of the Mulliken (lines) and Bader (symbols) population change [ΔNe = N_e(t) − N_e(t = 0)] on (a and c) Ag^L1₅₅ and (b and d) H₂ for the three studied field frequencies. Field intensity is (a and b) I_max = 2 × 10¹³ W cm⁻² and (c and d) I_max = 1 × 10¹⁴ W cm⁻².

Fig. 4. Time evolution of the Ag^L1₅₅ + H₂ orbital populations induced by an external field with intensity (left panels, (a–c)) I_max = 2 × 10¹³ W cm⁻² and (right panels, (d–f)) I_max = 1 × 10¹⁴ W cm⁻². For each I_max, the field frequency is (a and d) ℏω₀ = 2 eV, (b and e) ℏω₀ = 3.15 eV, and (c and f) ℏω₀ = 4.1 eV. Orbital populations are calculated every 0.2 fs as sums of the squares of the projections of the time-dependent occupied MOs on the initially unoccupied orbitals. Only populations with maximum values >0.1 are plotted.

Fig. 5. Time-dependent electric dipole moment for (a) I_max = 2 × 10¹³ W cm⁻² and (b) I_max = 1 × 10¹⁴ W cm⁻².

Fig. 6. Comparison of the H–H bond length with (solid lines) and without (dashed lines) augmented basis. Field intensity is (a) I_max = 2 × 10¹³ W cm⁻² and (b) I_max = 1 × 10¹⁴ W cm⁻².

Fig. 7. Time evolution of the Mulliken (lines) and Bader (symbols) population change [ΔN_e = N_e(t) − N_e(t = 0)] on (a) Ag^L1₅₅, (b) ghost atoms, and (c) H₂ for I_max = 2 × 10¹³ W cm⁻², and on (d) Ag^L1₅₅, (e) ghost atoms, and (f) H₂ for I_max = 1 × 10¹⁴ W cm⁻².