Nuclear-Electronic Quantum Dynamics in a Plasmonic Nanocavity

Abstract

Plasmonic nanocavities are a promising platform for strong light-matter coupling and enhanced spectroscopies at the single-molecule level. These nanoscale environments are challenging to model due to their strongly multimodal character and short cavity lifetimes. Herein, we study the effects of these environments using real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) coupled to multiple classical cavity modes in a manner that includes cavity loss. In RT-NEO-TDDFT, the quantum mechanical densities of all electrons and specified nuclei, typically protons, are propagated in real time. We show that a cavity with many modes at different frequencies can be used to probe and modify the nuclear-electronic quantum dynamics of chemical systems. Ultrafast excited-state proton transfer reactions can be probed through the time- and energy-resolved cavity emission of a multimode cavity. Under strong coupling conditions, the cavity can modify the dynamics, in some cases suppressing proton transfer and exhibiting Rabi-like oscillations of the cavity emission due to polariton formation. Utilizing the spectral density for an experimentally relevant nanoparticle-on-mirror single-molecule cavity, we show that an excited-state proton transfer system can evolve into resonance with the cavity even when initially out of resonance with the dominant cavity peak. In this case, tuning the dominant cavity peak to be resonant with the electronic transition leads to polariton formation for a small collection of molecules. The RT-NEO framework with multimode cavities enables the efficient simulation of chemical reactions in physically realistic electromagnetic environments, providing fundamental insights into the dynamics and associated spectroscopic signatures.

Figures (6)

• Figure 1: Upper portion: Structure of oHBA at (A) the conventional DFT optimized ground-state (S$_0$) geometry and (B) the conventional TDDFT S$_1$ excited-state geometry with the transferring proton constrained to have the same distance from the donor oxygen O$_\mathrm{D}$ as in the ground state. The isosurface of the transferring proton density computed with NEO-DFT is shown in cyan. The cyan arrow depicts the proton transfer coordinate used for computing the potential energy profiles. Lower plots: Proton potential energy profiles for the S$_0$ and S$_1$ states in the (C) S$_0$ geometry and (D) constrained S$_1$ geometry, as computed with conventional TDDFT by scanning the proton coordinate along the axis connecting its optimized ground state position to O$_\text{A}$.
• Figure 2: Upper plots: Mode-specific cavity emission, $I_k$, indicated by color intensity, as a function of mode frequency $\omega_k$ and time, for oHBA in the (A) S$_0$ geometry and (B) constrained S$_1$ geometry. The cavity environment is represented by a Gaussian spectral density peaked at the initial NEO-TDDFT vertical S$_0$ to S$_1$ excitation energy, $\Delta E_{\text{S}_1}$, with $g_0/\mu_0=0.03$ eV$\cdot$nm$^{-1}$$e^{-1}$ and $\sigma=0.25$ eV. The frequency of the cavity mode with the largest emission as a function of time is $\omega^\text{max}_k$. Emission is normalized by the single largest intensity observed across the entire time series. Lower plots: H--O$_\mathrm{D}$ and H--O$_\mathrm{A}$ distances in Å ngstroms as a function of time for oHBA in the (C) S$_0$ geometry and (D) constrained S$_1$ geometry. The distances are computed using the proton position expectation value. The results are shown with the cavity off (blue) and on (red). Note that in this case the cavity has no effect on the proton transfer dynamics, and therefore the results with the cavity on and off are indistinguishable.
• Figure 3: Upper plots: Mode-specific cavity emission, $I_k$, indicated by color intensity, as a function of mode frequency $\omega_k$ and time, for oHBA in the (A) S$_0$ geometry and (B) constrained S$_1$ geometry. The cavity environment is represented by a Gaussian spectral density peaked at the initial NEO-TDDFT vertical S$_0$ to S$_1$ excitation energy, $\Delta E_{\text{S}_1}$, with $g_0/\mu_0=0.3$ eV$\cdot$nm$^{-1}$$e^{-1}$ and $\sigma=0.25$ eV. The frequency of the cavity mode with the largest emission as a function of time is $\omega^\text{max}_k$. Emission is normalized by the single largest intensity observed across the entire time series. Lower plots: H--O$_\mathrm{D}$ and H--O$_\mathrm{A}$ distances in Å ngstroms as a function of time for oHBA in the (C) S$_0$ geometry and (D) S$_1$ geometry. The distances are computed using the proton position expectation value. The results are shown with the cavity off (blue) and on (red).
• Figure 4: (A) Schematic depiction of gold nanoparticle-on-mirror setup (not to scale). $\epsilon_\text{Au}(\omega)$ is the dielectric function for gold, $\epsilon_\text{env}$ is the dielectric constant of the solvent environment, $\delta$ is the distance between the nanoparticle and the mirror, and $\mu$ is the emitter dipole. (B) Mode-specific cavity emission $I_k$, indicated by color intensity, as a function of mode frequency $\omega_k$ and time, for AMIEP in the constrained S$_1$ geometry. The frequency of the cavity mode with the largest emission as a function of time is $\omega^\text{max}_k$. Emission is normalized by the single largest intensity observed across the entire time series. $\Delta E_{\text{S}_1}$ is the initial NEO-TDDFT vertical S$_0$ to S$_1$ excitation energy of AMIEP. (C) Spectral density $J(\omega)$ for the NPoM setup depicted in (A). The emitter dipole is oriented parallel to the mirror at $\delta/2$, and the spectral density is plotted with a dipole value of 1 $e\cdot$nm and $\epsilon_\text{env}=4$. Each individual Lorentzian mode is shown in gray, while the total summation from Eq. \ref{['eq:specdens']} is shown in red. (D) H--O$_\mathrm{D}$ and H--N$_\text{a}$ distances in Å ngstroms as a function of time for AMIEP in the constrained S$_1$ geometry. The distances are computed using the proton position expectation value. The results are shown with the cavity off (blue), but the curves are indistinguishable with the cavity on.
• Figure 5: (A) The structure of the Schiff base, 4-amino-2-[(1-(methylimino)ethyl)]phenol (AMIEP), in the constrained S$_1$ geometry. The isosurface of the transferring proton density computed with NEO-DFT is shown in cyan. The cyan arrow depicts the proton transfer coordinate used for computing the potential energy profiles. (B) S$_0$ and S$_1$ proton potential energy profiles for AMIEP at the constrained S$_1$ geometry, as computed with conventional TDDFT by scanning the proton coordinate along the axis connecting its optimized ground state position to N$_\text{A}$.