Driving chemical reactions with polariton condensates

The study addresses how macroscopic occupation of vibrational polariton modes (Bose–Einstein condensation) can influence chemical reactivity, specifically intramolecular electron transfer (ET), under vibrational strong coupling (VSC) conditions. Strong coupling between molecular vibrations and confined cavity photon modes creates hybrid light–matter excitations (polaritons) that can alter material and chemical properties. However, the presence of many quasi-degenerate dark modes often obscures polaritonic effects on chemistry. The authors propose that forming a polariton condensate—particularly in the lower polariton (LP)—amplifies light–matter coupling effects by concentrating energy into a single delocalized mode and opening additional reactive channels. They aim to quantify how such condensation changes ET kinetics and reaction yields at room temperature relative to conventional infrared laser excitation without strong coupling.

Prior work established strong coupling in organic microcavities and demonstrated vibrational strong coupling (VSC) can influence chemical reactivity even without external pumping. Yet, mechanisms remain debated due to the role of dark states. Bose–Einstein condensation of polaritons has been observed in electronic (exciton–polariton) systems at room temperature and enabled devices like polariton transistors. Theoretical studies suggested polariton condensates may affect charge transport, but their implications for chemical reactivity were not previously explored. Earlier proposals for using molecular Bose–Einstein condensates in chemistry required ultracold temperatures; polaritons, with low effective mass and partial photonic character, enable room-temperature condensation and offer delocalization and remote action. Electron transfer under electronic and vibrational strong coupling has been modeled (including MLJ-based approaches), but not under polariton condensation. Relaxation pathways differ between ESC and VSC (high-frequency intramolecular vs low-frequency solvent modes), and thermal effects are crucial for VSC because Rabi splittings are on the order of kBT. These contexts motivate the present theoretical investigation.

Two interconnected models are developed: (1) a kinetic model for vibrational polariton condensation, and (2) a cavity-modified electron transfer (ET) model under condensation using a VSC Marcus–Levich–Jortner (MLJ) framework. - Polariton condensation model: N molecular vibrational modes (frequency ωvib) are strongly coupled to a single cavity photon mode (frequency ωph) with coupling g under the rotating wave approximation. Diagonalization yields lower/upper polaritons (LP/UP) with frequencies ω−, ω+ and N−1 dark modes at ωvib. Population dynamics are modeled via Boltzmann rate equations with solvent-assisted scattering Wij obeying detailed balance, mode-dependent decay γi = |cvib,i|2Γ + |cph,i|2κ, and external pumping Pi. Final-state stimulation is included. Thermalization is assumed fast relative to losses. The condensation threshold depends on scattering vs losses and the density of modes near the condensing LP. Numerical solutions map the excitation distribution across detuning Δ = ωph − ωvib and coupling strength, identifying threshold behavior and feasibility regions. - Electron transfer under VSC and condensation: The system comprises N molecules each in reactant (R) or product (P) electronic states, each dressed by an intramolecular high-frequency vibrational mode (frequency ωvib) linearly coupled to the photon mode, and a classical low-frequency solvent coordinate facilitating ET. The Hamiltonian extends the polariton model to include electronic states and diabatic coupling for ET (JRP). Vibrational operators for R and P are related via a displacement with Huang–Rhys factor S. Bright and dark molecular vibrational modes are constructed: a single bright mode couples to light and forms LP/UP with the photon mode; N−1 dark modes remain uncoupled. Potential energy surfaces (PES) are constructed by diagonalizing the non-reactive Hamiltonian parametrically in the solvent coordinate. Rate constants follow a generalized MLJ approach: outside the cavity under IR pumping, the rate is an average over Poisson-distributed intramolecular vibrational quanta; inside the cavity under condensation, initial vibrational populations for UP, LP, and a localized dark mode are approximated by thermal distributions with average populations taken from the kinetic model steady state (semiclassical approximation valid for N+, N− ≪ Np ≪ 1). The authors derive analytical expressions for multimode Franck–Condon (FC) factors using generating functions combined with the Lagrange–Bürmann formula, addressing computational challenges due to large LP occupation. Activation energies for many reactive channels are evaluated, grouping channels by total change f in intramolecular vibrational quanta to simplify summations. - Assumptions and parameters: Fast cavity leakage and mode scattering relative to reaction kinetics (e.g., ~100 ps cavity lifetime, ET timescale 10^6–10^7 ps). Numerical examples use N = 10^7, room temperature (kBT = 0.1389 ħωvib at T = 298 K for ħωvib = 185 meV), symmetric coupling unless otherwise noted, pumping P = 0.08 N Γ (yielding N+ ≈ 0.064, N− ≈ 1.94×10^4, Np ≈ 0.078; ~2.4% of excitations in LP). Threshold mapping is presented across Δ and 2ħg/√N, with discussion of disorder effects (not included) and strategies (direct LP pumping or Raman schemes) to lower thresholds experimentally.

- Condensation feasibility under VSC: A condensation transition occurs near detuning Δ ≈ −1.5 kBT for representative parameters, with a large fraction of excitations accumulating in the LP above threshold. Mapping of the average per-molecule threshold population ñ = Pth/(NΓ) over detuning and coupling shows feasible condensation at room temperature for systems like water (2ħg√N ≈ 700 cm−1) even up to zero detuning, while thresholds are high (ñ ≥ 1) for Δ > 0 and weaker coupling (2ħg/√N/kBT < 2). - Additional reactive channels: Under condensation, the LP's macroscopic occupation opens many additional ET channels via energy exchange among LP, UP, and dark modes. These channels are separated in energy by approximately ħΩ/2 (rather than ħωvib) and include pathways with both higher and lower activation energies relative to the dominant uncoupled channel, enabling enhancement in both Marcus normal and inverted regimes. - Reduced activation barriers and enhanced FC factors: Channels that change LP quanta during reaction exhibit dramatically larger FC factors under condensation (∼10^20 times) compared to no pumping, contributing significantly to the rate constants. Activation energy expressions show grouping by total quantum change f clarifies which channels dominate. - Periodic yield modulation: Reaction yields under condensation display a periodic dependence on ΔG with period ~ħωvib, with observable multiple fringes at room temperature and experimentally attainable pumping; outside the cavity under laser driving, typically only the first fringe appears unless extremely strong pumping is used. - Significant yield and rate changes at room temperature: For symmetric coupling with ~2.4% excitation in LP (example parameters), condensation substantially amplifies deviations from thermal yields compared to IR pumping alone. Rate enhancements (kcond/kp) are especially large for small solvent reorganization (As/ħωvib small) and when ΔG/ħωvib ≈ n/2 (n odd), reflecting strong activation-energy and FC-factor effects. - Robustness to asymmetric coupling: Yield modifications persist when only reactants or only products couple strongly to light, indicating generality beyond symmetric coupling cases.

The work shows that polariton Bose–Einstein condensation can overcome the typical limitation of VSC chemistry posed by quasi-degenerate dark states. By macroscopically populating the lower polariton, energy is concentrated into a specific delocalized mode, providing energetic advantages (lower activation barriers via additional channels at energies spaced by ~ħΩ/2) and entropic benefits (vibrational energy redistribution among many polariton/dark modes during reaction). These effects lead to marked changes in electron transfer kinetics and yields at room temperature, including periodic yield modulation with ΔG and the possibility of rendering originally endergonic reactions effectively exergonic (and vice versa) under nonequilibrium conditions. Compared with laser-driven chemistry without strong coupling, the condensate allows access to many more reactive pathways with substantial Franck–Condon overlap, leading to larger modifications in rates and yields. The threshold analysis suggests realistic routes to achieving vibrational polariton condensation (e.g., in water), while recognizing that disorder and mode density near LP can influence practicality; targeted LP pumping or Raman schemes could lower thresholds. Overall, the findings support condensate-enabled control of reactivity and suggest a strategy to circumvent fast intramolecular vibrational redistribution by accumulating energy in a well-defined normal mode.

This study theoretically demonstrates that vibrational polariton condensation can strongly modify and in many cases enhance electron transfer reactivity at room temperature by (i) enabling numerous additional reaction channels with reduced activation barriers spaced by ~ħΩ/2, (ii) greatly increasing Franck–Condon factors for channels involving LP quanta, and (iii) producing a periodic dependence of yields on ΔG (period ~ħωvib). Condensation feasibilities are mapped across detuning and coupling strengths, indicating realistic experimental regimes (e.g., water). The results highlight both energetic and entropic advantages of condensate-driven chemistry and provide guidance for materials and cavity designs to realize vibrational polariton condensates. Future work should include explicit treatment of disorder and inhomogeneous broadening, exploration of different spectral ranges and molecular systems, detailed quantum-statistical descriptions of condensate populations beyond semiclassical approximations, and experimental validation of predicted rate and yield modulations.

- The model neglects disorder and inhomogeneous broadening, treating all dark modes as degenerate at ωvib; in practice, dark-state density near the LP bottom may increase thresholds and alter kinetics. - Fast thermalization and cavity leakage relative to reaction rates are assumed; deviations could affect steady-state populations and rate predictions. - The initial vibrational population under condensation is approximated semiclassically with thermal distributions based on average populations (N+, N−, Np), not full number-state distributions. - The ET description relies on the generalized MLJ framework and displacement (Huang–Rhys) model; non-Condon effects and anharmonicities beyond included approximations may change quantitative outcomes. - The reaction is reduced to three effective modes (LP, UP, localized dark) using symmetry; residual couplings to other dark modes or multimode solvent dynamics are not fully resolved. - No experimental demonstration is provided; threshold estimates and yields are theoretical and parameter-dependent. - Disorder and potential energy landscape complexities that could enable or hinder condensation are discussed qualitatively but not modeled quantitatively.