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Recent experiments demonstrate the control of chemical reactivities by coupling molecules inside an optical microcavity. In contrast, transition state theory predicts no change of the reaction barrier height during this process. Here, we present a theoretical explanation of the cavity modification of the ground state reactivity in the vibrational strong coupling (VSC) regime in polariton chemistry. Our theoretical results suggest that the VSC kinetics modification is originated from the non-Markovian dynamics of the cavity radiation mode that couples to the molecule, leading to the dynamical caging effect of the reaction coordinate and the suppression of reaction rate constant for a specific range of photon frequency close to the barrier frequency. We use a simple analytical non-Markovian rate theory to describe a single molecular system coupled to a cavity mode. We demonstrate the accuracy of the rate theory by performing direct numerical calculations of the transmission coefficients with the same model of the molecule-cavity hybrid system. Our simulations and analytical theory provide a plausible explanation of the photon frequency dependent modification of the chemical reactivities in the VSC polariton chemistry. Vibrational strong coupling controls the ground-state reactivity of molecules in optical cavities, but the underlying theory is still elusive. The authors analyze a molecular system coupled to a cavity mode and find that the reaction rate is suppressed for a particular cavity frequency, related to the topology of the reaction barrier region, analogously to a solvent caging effect.

Recent experiments suggest that ground state chemical reactivity can be modified when placing molecular systems inside infrared cavities where molecular vibrations are strongly coupled to electromagnetic radiation. This phenomenon lacks a firm theoretical explanation. Here, we employ an exact quantum dynamics approach to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry. Experiments suggest that placing molecules in an infrared cavity alters their reactivity, an effect lacking a clear theoretical explanation. Here, the authors show that the key to understanding this process may lie in quantum light-matter interactions.

Semiconductor excitations can hybridize with cavity photons to form exciton-polaritons (EPs) with remarkable properties, including light-like energy flow combined with matter-like interactions. To fully harness these properties, EPs must retain ballistic, coherent transport despite matter-mediated interactions with lattice phonons. Here we develop a nonlinear momentum-resolved optical approach that directly images EPs in real space on femtosecond scales in a range of polaritonic architectures. We focus our analysis on EP propagation in layered halide perovskite microcavities. We reveal that EP–phonon interactions lead to a large renormalization of EP velocities at high excitonic fractions at room temperature. Despite these strong EP–phonon interactions, ballistic transport is maintained for up to half-exciton EPs, in agreement with quantum simulations of dynamic disorder shielding through light-matter hybridization. Above 50% excitonic character, rapid decoherence leads to diffusive transport. Our work provides a general framework to precisely balance EP coherence, velocity, and nonlinear interactions. Exciton-polaritons are part-light part-matter states in semiconductors. Here the authors leverage momentum-resolved optical microscopy to image ballistic and diffusive propagation of exciton-polaritons on femtosecond scales.

In this paper, we develop quantum dynamical methods capable of treating the dynamics of chemically reacting systems in an optical cavity in the vibrationally strong-coupling (VSC) limit at finite temperatures and in the presence of a dissipative solvent in both the few and many molecule limits. In the context of two simple models, we demonstrate how reactivity in the VSC regime does not exhibit altered rate behavior in equilibrium but may exhibit resonant cavity modification of reactivity when the system is explicitly out of equilibrium. Our results suggest experimental protocols that may be used to modify reactivity in the collective regime and point to features not included in the models studied, which demand further scrutiny.

Direct quantum dynamics simulation is often an essential tool for investigating complex chemical reactivities that involve the quantum mechanical interplay of electrons, protons, phonons, and photons. Quantum dynamics simulations can provide crucial mechanistic insights which can reveal the basic principles of new chemical reactivities, lead to new strategies for controlling or enabling chemical reactivities and help resolve mysteries in emerging fields such as polariton chemistry. One of the challenges for performing an on-the-fly quantum dynamics simulation is that it requires combining quantum dynamics methods with electronic structure approaches which are usually formulated under two different representations. While many quantum dynamics methods are developed in the diabatic representation, most of the electronic structure approaches provide outputs in the adiabatic representation. In this thesis, we have resolved this incompatibility challenge by developing the quasi-diabatic (QD) propagation scheme that allows a seamless interface between any adiabatic electronic structure method with a diabatic quantum dynamics approach. This is the first key finding in this thesis. With this new theoretical tool, we investigated proton-coupled electron trans- fer (PCET) reactions. We combined the instantaneous adiabatic electron-proton vibronic states, with path-integral quantum dynamics approaches using the QD propagation scheme. We found that this approach is accurate in obtaining population dynamics and provides reliable mechanistic insights of thermal as well as photoinduced PCET reactions. This is the second key finding in this thesis. With the success in simulating quantum dynamics molecular systems, we decided to investigate new chemical reactivities in light-matter hybrid systems. In particular, we investigated polariton chemistry, where new chemical reactivities are enabled by coupling molecular systems to quantized radiation in an optical cavity. We demonstrated that an isomerization reaction can be tuned by coupling molecules to radiation modes in a cavity. Using direct quantum dynamics simulations and analytical rate theories, we also demonstrated that the kinetics of photoinduced electron-transfer reaction can be suppressed or enhanced by coupling molecular system to quantized radiation in an optical cavity. This is the third key finding in this thesis. We found that the existing theoretical models for describing light-matter interactions between atoms and photons is inadequate for describing light-molecule hybrid systems. We developed the polarized-Fock state (PFS) representation for describing molecule-cavity interactions. The PFS representation provides an intuitive understanding of new phenomena and at the same time provides numerical convenience. We also discovered that the light-matter Hamiltonian in the PFS representation resolves the gauge ambiguity as it reduces to a coulomb gauge Hamiltonian that provides consistent result compared to the dipole gauge Hamiltonian under finite electronic truncation. This is the fourth key finding in this thesis. Finally, we explored vibrational polaritonic chemistry where ground-state chemical kinetics is modified when the vibrational degrees of freedom (DOF) of molecular systems are coupled to radiation modes inside an optical cavity. Such chemical kinetics modification has been demonstrated in recent experiments. However, a clear theoretical understanding of such an effect remains elusive. We found that the radiation mode can dynamically cage a solvent coordinate near the dividing surface suppressing the rate of a chemical reaction. We developed a non-Markovian rate theory for vibrational polaritonic chemistry. We extended this theory to show the same effect arises when collectively coupling radiation mode to the vibrational DOF of solvent molecules that strongly couples to a reaction coordinate. This is the final key finding in this thesis.

We theoretically demonstrate that chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity-frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

We employ an exact quantum mechanical simulation technique to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically in order to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

We generalize the quasi-diabatic (QD) propagation scheme to simulate the non-adiabatic polariton dynamics in molecule-cavity hybrid systems. The adiabatic-Fock states, which are the tensor product states of the adiabatic electronic states of the molecule and photon Fock states, are used as the locally well-defined diabatic states for the dynamics propagation. These locally well-defined diabatic states allow using any diabatic quantum dynamics methods for dynamics propagation, and the definition of these states will be updated at every nuclear time step. We use several recently developed non-adiabatic mapping approaches as the diabatic dynamics methods to simulate polariton quantum dynamics in a Shin-Metiu model coupled to an optical cavity. The results obtained from the mapping approaches provide very accurate population dynamics compared to the numerically exact method and outperform the widely used mixed quantum-classical approaches, such as the Ehrenfest dynamics and the fewest switches surface hopping approach. We envision that the generalized QD scheme developed in this work will provide a powerful tool to perform the non-adiabatic polariton simulations by allowing a direct interface between the diabatic dynamics methods and ab initio polariton information.

Recent experiments have suggested that ground state chemical kinetics can be suppressed or enhanced by coupling the vibrational degrees of freedom of a molecular system with a radiation mode inside an optical cavity. Experiments show that the chemical rate is strongly modified when the photon frequency is close to characteristic vibrational frequencies. The origin of this remarkable effect remains unknown. In this work, we develop an analytical rate theory for cavity-modified ground state chemical kinetics based on the Pollak-Grabert-H\"anggi rate theory. Unlike previous work, our theory covers the complete range of solvent friction values, from the energy-diffusion limited to the spatial-diffusion limited regimes. We show that the chemical reaction rate can either be enhanced or suppressed depending on the bath friction; when bath friction is weak chemical kinetics is enhanced as opposed to the case of strong bath friction, where chemical kinetics is suppressed. Further, we show that the photon frequency at which maximum modification of chemical rate is achieved is close to the reactant well, and hence resonant rate modification occurs. In the strong friction limit the {\\it resonant} photon frequency is instead close to the barrier frequency, as obtained using the Grote-Hynes rate theory. Finally, we observe that the rate changes (as a function of photon frequency) are much sharper and more sizable in the weak friction limit than in the strong friction limit, and become increasingly sharp with decreasing well frequency.

Recent progress in enabling new chemical reactivities by strongly coupling molecular systems to quantized radiation has stimulated theoretical developments in molecular quantum electrodynamics As this field of cavity quantum electrodynamics (cQED) is highly interdisciplinary drawing from both quantum optics and physical chemistry, the appropriate choice of Hamiltonian can be obfuscated for those new to the field. Often, the relationships between Hamiltonians and exact levels of approximation consequentially become unclear. In this review, we seek to put in one place all the major gauges and representations commonly used in the field in one place with detailed derivations that relate them to each other, helping to bridge the gap between quantum optics and physical chemistry.