Probing voltage-induced chemical reactions and anharmonicity with a confined vacuum light field

TL;DR

This paper addresses how a confined vacuum electromagnetic field inside an optical cavity can modulate voltage-driven, non-equilibrium chemical reactions at a molecule–electrode interface. It develops a fully quantum-mechanical model using a Morse-potential reaction coordinate and two electronic surfaces, embedded in a dissipative environment, and solves the dynamics with numerically exact HEOM augmented by a tree tensor network state. The key findings show sharp resonant suppression of dissociation when cavity modes are tuned to vibrational transitions, and a proposed multi-mode scheme that cascades vibrational energy down the ladder to suppress bond rupture under bias. These results indicate a pathway to stabilize molecular junctions and probe molecular anharmonicity using cavity-enhanced, nonequilibrium polaritonic chemistry, with potential practical impact for designing robust nanoelectronic devices.

Abstract

In this work, we present a proof-of-concept investigation of non-equilibrium chemical reaction dynamics at a molecule-electrode interface, driven out of equilibrium by an applied votage bias and mediated by a confined, enhanced vacuum electromagnetic field inside an optical cavity. The coupled electron-vibration-photon system, together with the electrodes and a dissipative environment, is described within an open quantum system framework and solved using a numerically exact quantum dynamical approach. The reaction coordinate is modeled with a Morse potential, enabling explicit treatment of molecular anharmonicity and bond-breaking behavior. By varying the cavity frequency across the infrared regime to cover typical nuclear vibrational energies, we observe multiple resonant rate suppression features that emerge whenever the cavity mode is brought into resonance with a dipole-allowed vibrational transition along the anharmonic ladder up to the dissociation threshold. These findings open the door to extending polaritonic chemistry into genuinely nonequilibrium scenarios relevant to molecule-electrode interfaces. Moreover, building on these results, we further propose a multi-mode vibrational strong coupling strategy in which several cavity modes are individually matched to distinct vibrational transitions. This engineered multi-resonant cavity induces a stepwise vibrational ladder descending process that efficiently drains vibrational excited energy. The resulting cavity-assisted cooling suggests a potential route toward mitigating voltage-induced bond rupture and the long-standing instability issues of molecular junctions operating under high bias.

Figures (10)

• Figure 1: a) Schematic illustration of a single molecule bound to two electrodes under an applied bias voltage $\Phi$, and confined within an enhanced optical field provided by a nanoparticle-on-mirror cavity structure. b) Morse potential energy surfaces of the neutral and charged electronic states, characterized by $D_{\rm g}=D_{\rm e}=1.4$ eV, $a_{\rm g}=a_{\rm e}=3\text{\r{A}}$, $x_{\rm g}=1.8\text{\r{A}}$, and $x_{\rm m}^{e.0}=1.9\text{\r{A}}$. The charging energy is $E=1$ eV. The green shaded region shows the absolute value of the CAP $|V_{\rm CAP}(x_{\rm m})|$. Thin horizontal lines indicate the bound vibrational eigenstate energies of the isolated molecule below the dissociation barrier. The dotted red, purple, and olive-green vertical lines denote the nearest-neighbor, two-quantum, three-quantum vibrational transitions, respectively, with the corresponding energy gaps labeled on the side. We note that the coupling to the cavity and its associated bath, as well as the electrodes and solvent environment might broaden these levels and can shift the transition energies. c) Illustration of the tree tensor network state decomposition of the high-dimensional coefficient tensor $C_{\bf{s}, \bf{s}'}^{ \bf{n}, \bf{m}}(t)$ appearing in the extended wavefunction $|\Psi(t)\rangle$ [defined in Eq. (\ref{['ExtendedWaveFunction']})] for the full molecule-cavity-environment composite system.
• Figure 2: Electronic current $I_e$ and its value rescaled value by the surviving population $1-Q_{\rm loss}$ in panel a); Population of the neutral electronic state $P_g$ and its rescaling $P_g/(1-Q_{\rm loss})$ in panel b); Dissociation probability $Q_{\rm loss}$ in panel c). All quantities are shown as functions of the applied bias voltage $\Phi$, varied from 0 to 5 V. These observables are evaluated at time $t=10$ ps. The pink and blue lines correspond, respectively, to the cases without and with coupling to a dissipative bosonic bath ($\lambda_{\rm m}=0$ and $\lambda_{\rm m}=50\,\mathrm{cm}^{-1}$), representing solvent or surface phonon-induced vibrational relxation.
• Figure 3: Dissociation rate $k_{\rm o}$ in the radiation-free case as a function of the applied bias voltage $\Phi$. The inset provides a close-up view of the crossover region between non-resonant and resonant electronic transport. The pink curve corresponds to $\lambda_{\rm}=0$, where the dissipation is caused solely by electron-hole pair generation in the electrodes. The blue curve corresponds to $\lambda_{\rm m}=50\,\mathrm{cm}^{-1}$, which introduces an additional relaxation pathway through coupling to a dissipative bosonic bath.
• Figure 4: a) Ratio of dissociation rates inside and outside a single-mode cavity, $k_{\rm c}/k_{\rm o}$, as a function of the cavity frequency $\omega_{\rm c}$ spanning from $300$ to $3500\,\mathrm{cm}^{-1}$ in steps of $10\,\mathrm{cm}^{-1}$. The light-matter coupling strength is fixed at $\eta_{\rm c}=0.1$ a.u. The red, purple, and green dotted vertical lines mark the positions of distinct one-quantum ($v_i\leftrightarrow v_{i+1}$, two-quantum ($v_i\leftrightarrow v_{i+2}$, and three-quantum ($v_i\leftrightarrow v_{i+3}$) vibrational transitions, respectively. b) Cavity-induced rate modification ratio $k_{\rm c}/k_{\rm o}$ plotted as a function of $\eta_{\rm c}$ for seven different cavity frequencies chosen to be in close resonance with discrete vibrational transition energies along the vibrational energy ladder up to the dissciation barrier. The electronic dipole function is given by $u(x_{\rm m})=x_{\rm m}e^{-x^2_{\rm m}/a_{u}^2}$ with $a_{u}=2.5\,\text{\r{A}}$. Dissipation into the bosonic bath is neglected, i.e., $\lambda_{\rm m}=0$. The bias voltage is fixed at $\Phi=3$ V.
• Figure 5: Time evolution of the vibrational population distribution $P_{v_i}(t)$ for bound vibrational states below the dissociation barrier at the bias voltage of $\Phi=3$ V, shown for two different cavity frequencies: $\omega_{\rm c}=2310\,\mathrm{cm}^{-1}$ in panel a) and $\omega_{\rm c}=2010\,\mathrm{cm}^{-1}$ in panel b). All populations are rescaled by the surviving probability $1-Q_{\rm loss}(t)$. The dipole function is $u(x_{\rm m})=x_{\rm m}e^{-x^2_{\rm m}/a_{u}^2}$ with $a_{u}=2.5\,\text{\r{A}}$. Dissipation into the bosonic bath is neglected $(\lambda_{\rm m}=0)$. For comparison, the corresponding long-time steady vibrational populations outside the cavity are plotted as circles along the right axis.