Driving chemical reactions with polariton condensates

Light and matter couple strongly when a large number of molecules are placed within optical cavities that confine light. This results in hybrid light-matter excitations called polaritons, formed when a collective molecular transition and a photon mode coherently exchange energy faster than individual decay from each component. Light-matter strong coupling (SC) provides a new method for modifying material properties by controlling their electromagnetic environment. Vibrational strong coupling (VSC), where an infrared cavity mode couples to an ensemble of localized molecular vibrations, influences chemical reactivity even without external pumping. However, the microscopic mechanism for modifying molecular processes through hybridization with light is still poorly understood, potentially limited by numerous quasi-degenerate dark modes lacking photonic character, behaving similarly to uncoupled molecules. A Bose-Einstein condensate of polaritons offers a solution, as the macroscopic occupation of polaritonic states enhances SC effects. Room-temperature condensation has been demonstrated in various organic exciton-polariton systems, used in applications like polariton transistors. However, the impact of polariton condensation on chemical reactivity remained unaddressed before this study. Previous proposals for using Bose-Einstein condensates of molecules in chemistry required ultracold temperatures due to the large mass of the condensing entities. Polaritons' low effective mass (inherited from their photonic component) and the large binding energy of Frenkel excitons enable room-temperature condensation. Their partly photonic nature also offers benefits such as delocalization and remote action for manipulating chemistry. This research investigates the effect of polariton condensation on electron transfer (ET), focusing on how it amplifies the difference in reaction yield between infrared laser excitation (without SC) and thermal equilibrium conditions by unevenly altering the activation barrier for forward and backward reactions, thus tilting the equilibrium.

The influence of strong coupling on chemical reactions has been a subject of increasing interest. Previous studies have explored the effects of both electronic strong coupling (ESC) and vibrational strong coupling (VSC) on electron transfer processes. ESC studies have shown that the interaction of electronic excitations with cavity photons can alter the reaction dynamics. Similarly, VSC studies, such as the work by Campos-Gonzalez-Angulo et al. (2019), have demonstrated that coupling molecular vibrations to cavity modes can influence reaction rates. However, these studies did not consider the effect of Bose-Einstein condensation, which is a key aspect of the current research. The concept of using Bose-Einstein condensates in chemistry has been explored in previous work, though this typically requires ultra-low temperatures. The unique properties of polaritons, particularly their low effective mass and the possibility of room-temperature condensation, offer a novel pathway to explore this concept. The theoretical understanding of polariton condensation in organic microcavities has largely focused on systems under electronic strong coupling, necessitating a separate treatment for vibrational strong coupling due to differences in energy scales and relaxation pathways.

The researchers model the polariton system as *N* vibrational modes (*a*_vib) with frequency ω_vib, strongly coupled to a single photon mode (*a*_ph) with frequency ω_ph. The Hamiltonian uses the rotating wave approximation. Diagonalization yields normal modes: lower and upper polaritons (ω−, ω+), and *N* − 1 dark modes (ωk). Polariton population dynamics are modeled using Boltzmann rate equations, where the polariton system is weakly coupled to a low-frequency solvent bath, enabling scattering between modes. These equations account for final-state stimulation. The condensation transition is observed at a specific detuning (Δ ≈ −1.5*k*_B*T*), where a significant fraction of excitations resides in the lower polariton. Two factors determine the condensation threshold: (i) the rate of scattering between polariton and dark modes relative to system losses (thermalization rate); and (ii) the abundance of modes energetically close to the condensing mode. Fast thermalization is assumed for calculations. The average population per molecule at the condensation threshold (*ñ*) is a crucial indicator of experimental feasibility. This is analyzed across different light-matter coupling strengths and detunings. The model doesn't include disorder, simplifying the dark mode degeneracy. However, inhomogeneous broadening in experimental systems would affect the condensation threshold. To study the effect on electron transfer (ET), a VSC version of the Marcus-Levich-Jortner (MLJ) model is used. The system includes *N* molecules in a cavity with a single photon mode. Molecules can be in reactant (R) or product (P) electronic states. Each state is dressed with a high-frequency intramolecular vibrational mode coupling to the photon mode. An effective low-frequency solvent mode facilitates ET. The Hamiltonian accounts for photons, intramolecular vibrations, solvent modes, and light-matter couplings, along with a diabatic coupling term that induces reactive transitions between R and P states. The intramolecular vibrations are reorganized into a bright mode (coupling with light) and *N* − 1 dark modes (not coupling with light). The bright and photon modes form upper and lower polaritons (UP, LP). The rate constant for ET outside a cavity depends on intramolecular and solvent modes. The rate constant under laser driving is calculated, considering a coherent state in the vibrational mode. Under VSC, the ET process depends on vibrations in all molecules and the photon mode. The model simplifies this to three modes: a dark mode, LP, and UP, enabling rate constant calculation under polariton condensation. The calculations use parameters from the condensation threshold analysis, pumping the lower polariton. The initial vibrational state is described using a semiclassical approximation, and the rate constant is calculated by summing over contributions from different vibrational states. The activation energies for various reactive channels are computed, and to simplify calculation for large lower polariton occupation, channels are grouped by changes in vibrational quanta. Potential energy surfaces (PES) are plotted to illustrate the effect of the condensate on the reaction pathways. The net ET rate and steady-state solution are used to calculate the reaction yield, which is compared between the condensate and the laser-driven (no SC) cases.

The study demonstrates that vibrational polariton condensation significantly amplifies the modification of reaction yields observed under infrared laser excitation without strong coupling. This amplification stems from the emergence of numerous additional reactive channels, whose energies differ by approximately ħΩ/2 (where Ω is the Rabi splitting), instead of the usual ħωvib. The condensation transition occurs near a detuning of Δ ≈ −1.5kB T, where a substantial portion of excitations occupy the lower polariton mode. The average population per molecule at the condensation threshold (ñ) is a critical factor in determining the experimental feasibility of vibrational polariton condensation. The researchers find that this condensation is attainable for experimentally realistic pumping powers and Rabi splittings. A key contribution is the development of a methodology to compute multidimensional Franck-Condon factors under conditions of significant lower polariton occupation, which is necessary to analyze the system at the condensation threshold. Analysis of potential energy surfaces (PES) reveals that the condensate introduces additional final PESs, effectively broadening the range of accessible reaction pathways and lowering the activation barriers. The reaction yield exhibits a periodic dependence on the free energy difference (ΔG) with a period of approximately ħωvib. This periodic modulation, which is absent or weak in the absence of condensation, highlights the unique capacity of the condensate to tune the reaction outcome. Notably, the condensate enables originally endergonic reactions to become exergonic, and vice-versa. These effects are much weaker under laser driving alone, highlighting both the energetic and entropic advantages of exploiting polariton condensates. The impact of condensation on the reaction rate is particularly pronounced in the inverted Marcus regime. Even with asymmetric light-matter coupling, where only the reactant or product molecules strongly interact with light, the condensate enhances the modification of the reaction yield.

The findings address the research question by demonstrating that vibrational polariton condensation enhances the control over chemical reaction rates and yields, surpassing the effects achievable through simple infrared laser excitation. This advancement is particularly significant because it overcomes the limitations imposed by the multitude of dark modes typically present in vibrational strong coupling systems. The significance of the results lies in their potential to enable mode-selective chemistry at room temperature, a challenging goal in conventional vibrational dynamics due to fast intramolecular vibrational redistribution (IVR). The results suggest that the condensate effectively bypasses IVR by concentrating energy in a specific normal mode (the lower polariton). The periodic modulation of reaction yield with ΔG, enabled by the condensate, offers new possibilities for controlling chemical reactions. The relevance to the field lies in its potential to revolutionize catalysis and chemical synthesis by providing a new tool for manipulating reaction pathways and outcomes.

This work demonstrates for the first time the theoretical feasibility of using vibrational polariton condensates to drive and control chemical reactions at room temperature, exceeding the capabilities of simple infrared excitation. The method overcomes the challenge of numerous dark modes by harnessing the macroscopic occupation of a single polariton mode in a Bose-Einstein condensate. Future research should focus on identifying suitable experimental systems that can achieve vibrational polariton condensation and validating these theoretical predictions. Exploring the generalizability of the findings to other molecular systems and spectral ranges would also be valuable.

The model used in this study simplifies the complex interplay between various modes and does not incorporate effects such as disorder, anharmonicity, or other energy relaxation processes that may affect the condensation threshold and reaction dynamics in real-world systems. The semiclassical approximation used for the vibrational state distribution could also introduce some inaccuracies, particularly when considering interactions with high-frequency vibrational modes. Further experimental validation is needed to fully understand the potential and limitations of using polariton condensates to drive chemical reactions.