Molecular Electron Transfer in Optical Cavities: From Excitonic to Vibronic Polaritons

Abstract

Strong coupling between molecular excitations and quantized electromagnetic fields in optical cavities provides a powerful means to control the physical and chemical properties of molecular systems. Here, we study electron transfer (ET) dynamics in cavity-coupled molecules using the numerically exact hierarchical equations of motion (HEOM) method, which captures nonperturbative and non-Markovian effects beyond standard perturbative theories. We identify distinct resonance and collective effects associated with polariton formation and show that the ET rate saturates in the strong-coupling regime, a feature not captured by perturbative approaches. We further extend the cavity-modified ET model by incorporating the nuclear-coordinate dependence of molecular electric dipole moments, which gives rise to a three-body interaction involving molecular electronic and vibrational degrees of freedom and cavity photons. This vibronic polariton formation leads to non-monotonic, oscillatory dependencies of the ET rate on the light-matter coupling strength and cavity frequency, which we attribute to quantum interference among multiple transfer pathways. These findings establish cavity-modified electron transfer as a multichannel quantum process governed by the interplay of electronic, vibrational, and photonic degrees of freedom.

Figures (9)

• Figure 1: Relative change $k_\text{cav}/k_\text{non-cav}$ in electron transfer rate as a function of reorganization energy $\lambda_0$ and driving force $-\Delta G$ for a single molecule ($N_\text{mol}=1$). (a) Direct transition coupling only ($t_\text{DA}\neq 0$, $g_\text{D}=g_\text{A}=0$). (b) Energy-fluctuation coupling only ($t_\text{DA}=0$, $g_\text{D,A}\neq 0$).
• Figure 2: Time evolution of the donor population $p_\text{D}(t)$ for the direct transition coupling with $\lambda_0=50\,\text{cm}^{-1}$ and $-\Delta G=100\,\text{cm}^{-1}$. Red solid line: cavity-coupled system ($\hbar\omega_\text{c}|t_\text{DA}|=50\,\text{cm}^{-1}$). Black dashed line: uncoupled system. Cavity coupling accelerates transfer and extends coherence time through the dynamic polaron decoupling effect.
• Figure 3: Comparison of ET rates as a function of driving force $-\Delta G$ for (a) the direct transition coupling channel ($t_\text{DA}$) and (b) the energy-fluctuation coupling channel ($g_\text{D,A}$), with $\lambda_0=50\,\text{cm}^{-1}$. Solid lines: Fermi's golden rule predictions. Dots: numerically exact HEOM results. While FGR captures qualitative trends, it fails to reproduce the quantitative rates and spectral widths due to neglect of nonperturbative and non-Markovian effects.
• Figure 4: Cavity-induced change in ET rate, $\delta k_\text{DA}=k_\text{cav}-k_\text{non-cav}$ (normalized by $k_\text{non-cav}$) as a function of direct transition coupling strength $|t_\text{DA}|$ for $\lambda_0=50\,\text{cm}^{-1}$ and $-\Delta G=100\,\text{cm}^{-1}$. Red dots: HEOM results. Blue solid curve: FGR prediction (Eq. \ref{['eq: analytic expression, t-channel']}). The quadratic scaling $\delta k_\text{DA}\propto |t_\text{DA}|^2$ breaks down beyond $|t_\text{DA}|\sim 0.3$, where the rate saturates as the system enters the ultrastrong coupling regime.
• Figure 5: Resonance behavior of the ET rate as a function of cavity frequency $\omega_\text{c}$ with coupling parameters rescaled as $t_\text{DA}, g_\text{D,A}\propto 1/\sqrt{\omega_\text{c}}$ at fixed mode volume. (a) Direct transition coupling channel ($t_\text{DA}$): cavity-transition resonance. (b) Energy-fluctuation coupling channel ($g_\text{D,A}$): resonance reflects optimal cavity-induced modulation of the activation barrier. The different resonance frequencies underscore the distinct physical mechanisms of the two coupling channels.