Polaritonic normal modes in transition state theory

Unraveling abnormal collective effects via the non-monotonic number dependence of electron transfer in confined electromagnetic fields

Strong light-matter coupling within an optical cavity leverages the collective interactions of molecules and confined electromagnetic fields, giving rise to the possibilities of modifying chemical reactivity and molecular properties. While collective optical responses, such as enhanced Rabi splitting, are often observed, the overall effect of the cavity on molecular systems remains ambiguous for a large number of molecules. In this paper, we investigate the non-adiabatic electron transfer process in electron donor-acceptor pairs influenced by collective excitation and local molecular dynamics. Using the timescale difference between reorganization and thermal fluctuations, we derive analytical formulas for the electron transfer rate constant and the polariton relaxation rate. These formulas apply to any number of molecules (N) and account for the collective effect as induced by cavity photon coupling. Our findings reveal a non-monotonic dependence of the rate constant on N, which can be understood by the interplay between electron transfer and polariton relaxation. As a result, the cavity-induced quantum yield increases linearly with N for small N (as predicted by a simple Dicke model) but shows a turnover and suppression for large N. We also interrelate the thermal bath frequency and the number of molecules, suggesting the optimal number for maximizing enhancement. The analysis provides an analytical insight for understanding the collective excitation of light and electron transfer, helping to predict the optimal condition for effective cavity-controlled chemical reactivity.

Quantum nature of reactivity modification in vibrational polariton chemistry

In this work, we present a mixed quantum-classical open quantum system dynamics method for studying rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. In this approach, the cavity radiation mode is treated classically with a mean-field nuclear force averaging over the remaining degrees of freedom, both within the system and the environment, which are handled quantum mechanically within the hierarchical equations of motion framework. Using this approach, we conduct a comparative analysis by juxtaposing the mixed quantum-classical results with fully quantum-mechanical simulations. After eliminating spurious peaks that can occur when not using the rigorous definition of the rate constant, we confirm the crucial role of the quantum nature of the cavity radiation mode in reproducing the resonant peak observed in the cavity frequency-dependent rate profile. In other words, it appears necessary to explicitly consider the quantized photonic states in studying reactivity modification in vibrational polariton chemistry (at least for the model systems studied in this work), as these phenomena stem from cavity-induced reaction pathways involving resonant energy exchanges between photons and molecular vibrational transitions.

Do Molecular Geometries Change Under Vibrational Strong Coupling?

As pioneering experiments have shown, strong coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current theoretical description is limited and far from complete. To explore the origin of this exciting observation, we investigate how the molecular structure changes under strong light-matter coupling using an ab initio method based on the cavity Born-Oppenheimer Hartree-Fock ansatz. By optimizing H2O and H2O2 resonantly coupled to cavity modes, we study the importance of reorientation and geometric relaxation. In addition, we show that the inclusion of one or two cavity modes can change the observed results. On the basis of our findings, we derive a simple concept to estimate the effect of the cavity interaction on the molecular geometry using the molecular polarizability and the dipole moments.

Insights into the mechanisms of optical cavity-modified ground-state chemical reactions

In this work, we systematically investigate the mechanisms underlying the rate modification of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. We employ a symmetric double-well description of the molecular potential energy surface and a numerically exact open quantum system approach-the hierarchical equations of motion in twin space with a matrix product state solver. Our results predict the existence of multiple peaks in the photon frequency-dependent rate profile for a strongly anharmonic molecular system with multiple vibrational transition energies. The emergence of a new peak in the rate profile is attributed to the opening of an intramolecular reaction pathway, energetically fueled by the cavity photon bath through a resonant cavity mode. The peak intensity is determined jointly by kinetic factors. Going beyond the single-molecule limit, we examine the effects of the collective coupling of two molecules to the cavity. We find that when two identical molecules are simultaneously coupled to the same resonant cavity mode, the reaction rate is further increased. This additional increase is associated with the activation of a cavity-induced intermolecular reaction channel. Furthermore, the rate modification due to these cavity-promoted reaction pathways remains unaffected, regardless of whether the molecular dipole moments are aligned in the same or opposite direction as the light polarization.

Controlling Molecular Photoisomerization in Photonic Cavities through Polariton Funneling

Strong coupling between photonic modes and molecular electronic excitations, creating hybrid light-matter states called polaritons, is an attractive avenue for controlling chemical reactions. Nevertheless, experimental demonstrations of polariton-modified chemical reactions remain sparse. Here, we demonstrate modified photoisomerization kinetics of merocyanine and diarylethene by coupling the reactant's optical transition with photonic microcavity modes. We leverage broadband Fourier-plane optical microscopy to noninvasively and rapidly monitor photoisomerization within microcavities, enabling systematic investigation of chemical kinetics for different cavity-exciton detunings and photoexcitation conditions. We demonstrate three distinct effects of cavity coupling: first, a renormalization of the photonic density of states, akin to a Purcell effect, leads to enhanced absorption and isomerization rates at certain wavelengths, notably red-shifting the onset of photoisomerization. This effect is present under both strong and weak light-matter couplings. Second, kinetic competition between polariton localization into reactive molecular states and cavity losses leads to a suppression of the photoisomerization yield. Finally, our key result is that in reaction mixtures with multiple reactant isomers, exhibiting partially overlapping optical transitions and distinct isomerization pathways, the cavity resonance can be tuned to funnel photoexcitations into specific reactant isomers. Thus, upon decoherence, polaritons localize into a chosen isomer, selectively triggering the latter's photoisomerization despite initially being delocalized across all isomers. This result suggests that careful tuning of the cavity resonance is a promising avenue to steer chemical reactions and enhance product selectivity in reaction mixtures.

Theoretical formulation of chemical equilibrium under vibrational strong coupling

Experiments have suggested that strong interactions between molecular ensembles and infrared microcavities can be employed to control chemical equilibria. Nevertheless, the primary mechanism and key features of the effect remain largely unexplored. In this work, we develop a theory of chemical equilibrium in optical microcavities, which allows us to relate the equilibrium composition of a mixture in different electromagnetic environments. Our theory shows that in planar microcavities under strong coupling with polyatomic molecules, hybrid modes formed between all dipole-active vibrations and cavity resonances contribute to polariton-assisted chemical equilibrium shifts. To illustrate key aspects of our formalism, we explore a model SN2 reaction within a single-mode infrared resonator. Our findings reveal that chemical equilibria can be shifted towards either direction of a chemical reaction, depending on the oscillator strength and frequencies of reactant and product normal modes. Polariton-induced zero-point energy changes provide the dominant contributions, though the effects in idealized single-mode cavities tend to diminish quickly as the temperature and number of molecules increase. Our approach is valid in generic electromagnetic environments and paves the way for understanding and controlling chemical equilibria with microcavities.

Machine Learning for Polaritonic Chemistry: Accessing Chemical Kinetics

Altering chemical reactivity and material structure in confined optical environments is on the rise, and yet, a conclusive understanding of the microscopic mechanisms remains elusive. This originates mostly from the fact that accurately predicting vibrational and reactive dynamics for soluted ensembles of realistic molecules is no small endeavor, and adding (collective) strong light-matter interaction does not simplify matters. Here, we establish a framework based on a combination of machine learning (ML) models, trained using density-functional theory calculations and molecular dynamics to accelerate such simulations. We then apply this approach to evaluate strong coupling, changes in reaction rate constant, and their influence on enthalpy and entropy for the deprotection reaction of 1-phenyl-2-trimethylsilylacetylene, which has been studied previously both experimentally and using ab initio simulations. While we find qualitative agreement with critical experimental observations, especially with regard to the changes in kinetics, we also find differences in comparison with previous theoretical predictions. The features for which the ML-accelerated and ab initio simulations agree show the experimentally estimated kinetic behavior. Conflicting features indicate that a contribution of dynamic electronic polarization to the reaction process is more relevant than currently believed. Our work demonstrates the practical use of ML for polaritonic chemistry, discusses limitations of common approximations, and paves the way for a more holistic description of polaritonic chemistry.

Simulating Polaritonic Ground States on Noisy Quantum Devices

The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.

Resonance Enhancement of Vibrational Polariton Chemistry Obtained from the Mixed Quantum-Classical Dynamics Simulations

We applied a variety of mixed quantum-classical (MQC) approaches to simulate the VSC-influenced reaction rate constant. All of these MQC simulations treat the key vibrational levels associated with the reaction coordinate in the quantum subsystem (as quantum states), whereas all other degrees of freedom (DOFs) are treated inside the classical subsystem. We find that, as long as we have the quantum state descriptions for the vibrational DOFs, one can correctly describe the VSC resonance condition when the cavity frequency matches the bond vibrational frequency. This correct resonance behavior can be obtained regardless of the detailed MQC methods that one uses. The results suggest that the MQC approaches can generate semiquantitative agreement with the exact results for rate constant changes when changing the cavity frequency, the light-matter coupling strength, or the cavity lifetime. The finding of this work suggests that one can use computationally economic MQC approaches to explore the collective coupling scenario when many molecules are collectively coupled to many cavity modes in the future.

Ultrafast dynamics of CN radical reactions with chloroform solvent under vibrational strong coupling

Polariton chemistry may provide a new means to control molecular reactivity, permitting remote, reversible modification of reaction energetics, kinetics, and product yields. A considerable body of experimental and theoretical work has already demonstrated that strong coupling between a molecular vibrational mode and the confined electromagnetic field of an optical cavity can alter chemical reactivity without external illumination. However, the mechanisms underlying cavity-altered chemistry remain unclear in large part because the experimental systems examined previously are too complex for detailed analysis of their reaction dynamics. Here, we experimentally investigate photolysis-induced reactions of cyanide radicals with strongly-coupled chloroform (CHCl3) solvent molecules and examine the intracavity rates of photofragment recombination, solvent complexation, and hydrogen abstraction. We use a microfluidic optical cavity fitted with dichroic mirrors to facilitate vibrational strong coupling (VSC) of the C-H stretching mode of CHCl3 while simultaneously permitting optical access at visible wavelengths. Ultrafast transient absorption experiments performed with cavities tuned on- and off-resonance reveal that VSC of the CHCl3 C-H stretching transition does not significantly modify any measured rate constants, including those associated with the hydrogen abstraction reaction. This work represents, to the best of our knowledge, the first experimental study of an elementary bimolecular reaction under VSC. We discuss how the conspicuous absence of cavity-altered effects in this system may provide insights into the mechanisms of modified ground state reactivity under VSC and help bridge the divide between experimental results and theoretical predictions in vibrational polariton chemistry.

Beyond Cavity Born-Oppenheimer: On Nonadiabatic Coupling and Effective Ground State Hamiltonians in Vibro-Polaritonic Chemistry

The emerging field of vibro-polaritonic chemistry studies the impact of light-matter hybrid states known as vibrational polaritons on chemical reactivity and molecular properties. Here, we discuss vibro-polaritonic chemistry from a quantum chemical perspective beyond the cavity Born-Oppenheimer (CBO) approximation and examine the role of electron-photon correlation in effective ground state Hamiltonians. We first quantitatively review ab initio vibro-polaritonic chemistry based on the molecular Pauli-Fierz Hamiltonian in dipole approximation and a vibrational strong coupling (VSC) Born-Huang expansion. We then derive nonadiabatic coupling elements arising from both "slow" nuclei and cavity modes compared to "fast" electrons via the generalized Hellmann-Feynman theorem, discuss their properties, and reevaluate the CBO approximation. In the second part, we introduce a crude VSC Born-Huang expansion based on adiabatic electronic states, which provides a foundation for widely employed effective Pauli-Fierz Hamiltonians in ground state vibro-polaritonic chemistry. Those do not strictly respect the CBO approximation but an alternative scheme, which we name crude CBO approximation. We argue that the crude CBO ground state misses electron-photon correlation relative to the CBO ground state due to neglected cavity-induced nonadiabatic transition dipole couplings to excited states. A perturbative connection between both ground state approximations is proposed, which identifies the crude CBO ground state as a first-order approximation to its CBO counterpart. We provide an illustrative numerical analysis of the cavity Shin-Metiu model with a focus on nonadiabatic coupling under VSC and electron-photon correlation effects on classical activation barriers. We finally discuss the potential shortcomings of the electron-polariton Hamiltonian when employed in the VSC regime.

Modification of Thermal Chemical Rates in a Cavity via Resonant Effects in the Collective Regime

The modification of thermal chemical rates in Fabry-Perot cavities, as observed in experiments, still poses theoretical challenges. While we have a better grasp of how the reactivity of isolated molecules and model systems changes under strong coupling, we lack a comprehensive understanding of the combined effects and the specific roles played by activated and spectator molecules during reactive events. In this study, we investigate an ensemble of randomly oriented gas-phase HONO molecules undergoing a cis-trans isomerization reaction on an ab initio potential energy surface. One thermally activated molecule can overcome the reaction barrier, while the other molecules are nonactivated but coupled to the cavity as well. Using the classical reactive flux method, we analyze the transmission coefficient and determine the conditions that lead to accelerated rates within the collective regime. We identify two main mechanistic aspects: First, nonactivated molecules enhance the cavity's ability to dissipate excess energy from the activated molecule postreactive event. Second, the activated molecule couples with the polaritonic resonance created by the nonactivated molecules and the cavity at a shifted resonance frequency with respect to the bare cavity.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

On the Mechanism of Polaritonic Rate Suppression from Quantum Transition Paths

Polariton chemistry holds promise for facilitating mode-selective chemical reactions, but the underlying mechanism behind the rate modifications observed under strong vibrational coupling is not well understood. Using the recently developed quantum transition path theory, we have uncovered a mechanism of resonant suppression of a thermal reaction rate in a simple model polaritonic system consisting of a reactive mode in a bath confined to a lossless microcavity with a single photon mode. We observed the formation of a polariton during rate-limiting transitions on reactive pathways and identified the concomitant rate suppression as being due to hybridization between the reactive mode and the cavity mode, which inhibits bath-mediated tunneling. The transition probabilities that define the quantum master equation can be directly translated into a visualization of the corresponding polariton energy landscape. This landscape exhibits a double funnel structure with a large barrier between the initial and final states.

Molecular Chemistry in Cavity Strong Coupling

The coherent exchange of energy between materials and optical fields leads to strong light-matter interactions and so-called polaritonic states with intriguing properties, halfway between light and matter. Two decades ago, research on these strong light-matter interactions, using optical cavity (vacuum) fields, remained for the most part the province of the physicist, with a focus on inorganic materials requiring cryogenic temperatures and carefully fabricated, high-quality optical cavities for their study. This review explores the history and recent acceleration of interest in the application of polaritonic states to molecular properties and processes. The enormous collective oscillator strength of dense films of organic molecules, aggregates, and materials allows cavity vacuum field strong coupling to be achieved at room temperature, even in rapidly fabricated, highly lossy metallic optical cavities. This has put polaritonic states and their associated coherent phenomena at the fingertips of laboratory chemists, materials scientists, and even biochemists as a potentially new tool to control molecular chemistry. The exciting phenomena that have emerged suggest that polaritonic states are of genuine relevance within the molecular and material energy landscape.

Manipulating hydrogen bond dissociation rates and mechanisms in water dimer through vibrational strong coupling

The vibrational strong coupling (VSC) between molecular vibrations and cavity photon modes has recently emerged as a promising tool for influencing chemical reactivities. Despite numerous experimental and theoretical efforts, the underlying mechanism of VSC effects remains elusive. In this study, we combine state-of-art quantum cavity vibrational self-consistent field/configuration interaction theory (cav-VSCF/VCI), quasi-classical trajectory method, along with the quantum-chemical CCSD(T)-level machine learning potential, to simulate the hydrogen bond dissociation dynamics of water dimer under VSC. We observe that manipulating the light-matter coupling strength and cavity frequencies can either inhibit or accelerate the dissociation rate. Furthermore, we discover that the cavity surprisingly modifies the vibrational dissociation channels, with a pathway involving both water fragments in their ground vibrational states becoming the major channel, which is a minor one when the water dimer is outside the cavity. We elucidate the mechanisms behind these effects by investigating the critical role of the optical cavity in modifying the intramolecular and intermolecular coupling patterns. While our work focuses on single water dimer system, it provides direct and statistically significant evidence of VSC effects on molecular reaction dynamics.

Computational study on the catalytic control of endo/exo Diels-Alder reactions by cavity quantum vacuum fluctuations

Achieving control over chemical reaction's rate and stereoselectivity realizes one of the Holy Grails in chemistry that can revolutionize chemical and pharmaceutical industries. Strong light-matter interaction in optical or nanoplasmonic cavities might provide the knob to reach such control. In this work, we demonstrate the catalytic and selectivity control of an optical cavity for two selected Diels-Alder cycloaddition reactions using the quantum electrodynamics coupled cluster (QED-CC) method. Herein, we find that by changing the molecular orientation with respect to the polarization of the cavity mode the reactions can be significantly inhibited or selectively enhanced to produce major endo or exo products on demand. This work highlights the potential of utilizing quantum vacuum fluctuations of an optical cavity to modulate the rate of Diels-Alder cycloaddition reactions and to achieve stereoselectivity in a practical and non-intrusive way. We expect that the present findings will be applicable to a larger set of relevant reactions, including the click chemical reactions.

Quantum dynamical effects of vibrational strong coupling in chemical reactivity

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.

Nonadiabatic Wave Packet Dynamics with Ab Initio Cavity-Born-Oppenheimer Potential Energy Surfaces

Strong coupling of molecules with quantized electromagnetic fields can reshape their potential energy surfaces by forming dressed states. In such a scenario, it is possible to manipulate the dynamics of the molecule and open new photochemical reaction pathways. A theoretical approach to describe such coupled molecular-photon systems is the Cavity-Born-Oppenheimer (CBO) approximation. Similarly to the standard Born-Oppenheimer (BO) approximation, the system is partitioned and the electronic part of the system is treated quantum mechanically. This separation leads to CBO surfaces that depend on both nuclear and photonic coordinates. In this work, we demonstrated, for two molecular examples, how the concept of the CBO approximation can be used to perform nonadiabatic wave packet dynamics of a coupled molecular-cavity system. The light-matter interaction is incorporated in the CBO surfaces and the associated nonadiabatic coupling elements. We show that molecular and cavity contributions can be treated on the same numerical footing. This approach gives a new perspective on the description of light-matter coupling in molecular systems.

Dissociation dynamics of a diatomic molecule in an optical cavity

We study the dissociation dynamics of a diatomic molecule, modeled as a Morse oscillator, coupled to an optical cavity. A marked suppression of the dissociation probability, both classical and quantum, is observed for cavity frequencies significantly below the fundamental transition frequency of the molecule. We show that the suppression in the probability is due to the nonlinearity of the dipole function. The effect can be rationalized entirely in terms of the structures in the classical phase space of the model system.

Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity

Strong light-matter interaction in cavity environments is emerging as a promising approach to control chemical reactions in a non-intrusive and efficient manner. The underlying mechanism that distinguishes between steering, accelerating, or decelerating a chemical reaction has, however, remained unclear, hampering progress in this frontier area of research. We leverage quantum-electrodynamical density-functional theory to unveil the microscopic mechanism behind the experimentally observed reduced reaction rate under cavity induced resonant vibrational strong light-matter coupling. We observe multiple resonances and obtain the thus far theoretically elusive but experimentally critical resonant feature for a single strongly coupled molecule undergoing the reaction. While we describe only a single mode and do not explicitly account for collective coupling or intermolecular interactions, the qualitative agreement with experimental measurements suggests that our conclusions can be largely abstracted towards the experimental realization. Specifically, we find that the cavity mode acts as mediator between different vibrational modes. In effect, vibrational energy localized in single bonds that are critical for the reaction is redistributed differently which ultimately inhibits the reaction.

Multidimensional Quantum Dynamical Simulation of Infrared Spectra under Polaritonic Vibrational Strong Coupling

Recent experimental and theoretical studies demonstrate that the chemical reactivity of molecules can be modified inside an optical cavity. Here, we provide a theoretical framework for conducting multidimensional quantum simulations of the infrared (IR) spectra for molecules interacting with cavity modes. A single water molecule under polaritonic vibrational strong coupling serves as an illustrative example. Combined with accurate potential energy and dipole moment surfaces, our cavity vibrational self-consistent field/virtual state configuration interaction (cav-VSCF/VCI) approach can predict the IR spectra when the molecule is inside or outside the cavity. The spectral signatures of Rabi splittings and shifts of certain bands are found to be strongly dependent on the frequency and polarization direction of the cavity modes. Analyses of the simulated spectra show that polaritonic vibrational strong coupling can induce unconventional couplings among the molecule's vibrational modes, suggesting that intramolecular vibrational energy transfer can be significantly accelerated by the cavity.

Generalized Resonance Energy Transfer Theory: Applications to Vibrational Energy Flow in Optical Cavities

A general rate theory for resonance energy transfer (gRET) is formulated to incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and polariton) as well as coherently coupled composite donor or acceptor states. The compact rate expression allows us to establish useful relationships: (i) detailed balance condition when the donor and acceptor are at the same temperature; (ii) proportionality to the product of dipole correlation tensors, which is not necessarily equivalent to spectral overlap; (iii) scaling with the effective coherent size, i.e., the number of coherently coupled molecules or modes; (iv) decomposition of collective rate in homogeneous systems into the monomer and coherence contributions such that the ratio of the two defines the quantum enhancement factor F; (v) spatial and orientational dependences as derived from the interaction potential. For the special case of exciton transfer, the general rate formalism reduces to FRET or its multichromophoric extension. When applied to cavity-assisted vibrational energy transfer between molecules or within a molecule, the general rate expression provides an intuitive explanation of intriguing phenomena such as cooperativity, resonance, and nonlinearity in the collective vibrational strong coupling (VSC) regime, as demonstrated in recent simulations. The relevance of gRET to cavity-catalyzed reactions and intramolecular vibrational redistribution is discussed and will lead to further theoretical developments.

Cavity-enabled enhancement of ultrafast intramolecular vibrational redistribution over pseudorotation

Vibrational strong coupling (VSC) between molecular vibrations and microcavity photons yields a few polaritons (light-matter modes) and many dark modes (with negligible photonic character). Although VSC is reported to alter thermally activated chemical reactions, its mechanisms remain opaque. To elucidate this problem, we followed ultrafast dynamics of a simple unimolecular vibrational energy exchange in iron pentacarbonyl [Fe(CO) 5 ] under VSC, which showed two competing channels: pseudorotation and intramolecular vibrational-energy redistribution (IVR). We found that under polariton excitation, energy exchange was overall accelerated, with IVR becoming faster and pseudorotation being slowed down. However, dark-mode excitation revealed unchanged dynamics compared with those outside of the cavity, with pseudorotation dominating. Thus, despite controversies around thermally activated VSC modified chemistry, our work shows that VSC can indeed alter chemistry through a nonequilibrium preparation of polaritons.

Exact Results for the Tavis-Cummings and Hückel Hamiltonians with Diagonal Disorder

We present an exact method to calculate the electronic states of one electron Hamiltonians with diagonal disorder. We show that in cases where the disorder has a Cauchy distribution, the disorder averaged one particle Green's function can be calculated directly, using a deterministic, complex (non-Hermitian) Hamiltonian. For this we use the supersymmetric method which has already been used in problems of solid state physics. Using the method we find exact solution for the case of N molecules with site disorder, confined to a microcavity, for any value of N. Our analysis shows that the width of the polaritonic states as a function of N depends on the nature of disorder, and hence it can be used to probe the way molecular energy levels are distributed. We also show how one can find exact results for Hückel type Hamiltonians with on-site Cauchy disorder and demonstrate its use.

Resonant Cavity Modification of Ground-State Chemical Kinetics

Recent experiments have suggested that ground-state chemical kinetics can be suppressed or enhanced by coupling molecular vibrations with a cavity radiation mode. Here, we develop an analytical rate theory for cavity-modified chemical kinetics based on the Pollak-Grabert-Hänggi 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 chemical kinetics is enhanced when bath friction is weak and suppressed when bath friction is strong. For weak bath friction, the resonant photon frequency (at which the maximum modification of the chemical rate is achieved) is close to the reactant well. In the strong friction limit, the resonant photon frequency is instead close to the barrier frequency. Finally, we observe that rate changes as a function of the photon frequency are much sharper and more sizable in the weak friction limit than in the strong friction limit.

Energy-efficient pathway for selectively exciting solute molecules to high vibrational states via solvent vibration-polariton pumping

Selectively exciting target molecules to high vibrational states is inefficient in the liquid phase, which restricts the use of IR pumping to catalyze ground-state chemical reactions. Here, we demonstrate that this inefficiency can sometimes be solved by confining the liquid to an optical cavity under vibrational strong coupling conditions. For a liquid solution of ¹³CO₂ solute in a ¹²CO₂ solvent, cavity molecular dynamics simulations show that exciting a polariton (hybrid light-matter state) of the solvent with an intense laser pulse, under suitable resonant conditions, may lead to a very strong (>3 quanta) and ultrafast (<1 ps) excitation of the solute, even though the solvent ends up being barely excited. By contrast, outside a cavity the same input pulse fluence can excite the solute by only half a vibrational quantum and the selectivity of excitation is low. Our finding is robust under different cavity volumes, which may lead to observable cavity enhancement on IR photochemical reactions in Fabry–Pérot cavities.

Hybrid light-matter states formed in the strong light-matter coupling regime can alter the molecular ground-state reactivity. Here, Li et al. computationally demonstrate that pumping a collection of solvent molecules forming hybrid vibrational light-matter states in an optical cavity can excite solute molecules to very high excited states.

Inherent Promotion of Ionic Conductivity via Collective Vibrational Strong Coupling of Water with the Vacuum Electromagnetic Field

Hydrogen bonding interactions among water molecules play a critical role in chemical reactivity, dynamic proton mobility, static dielectric behavior, and the thermodynamic properties of water. In this study, we demonstrate the modification of ionic conductivity of water through hybridization with a vacuum electromagnetic field by strongly coupling the O─H stretching mode of H₂O to a Fabry-Perot cavity mode. The hybridization generates collective vibro-polaritonic states, thereby enhancing the proton conductivity by an order of magnitude at resonance. In addition, the dielectric constants increase at resonance in the coupled state. The findings presented herein reveal how a vacuum electromagnetic environment can be engineered to control the ground-state properties of water.

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalize recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed based on well-established methods from molecular dynamics. It suggests the emergence of cavity-induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe that the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling from the collective quantum interpretation toward a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions toward a refined description of cavity-modified chemistry are introduced in the context of QEDFT, and future directions of the field are sketched.

Suppression and Enhancement of Thermal Chemical Rates in a Cavity

The observed modification of thermal chemical rates in Fabry-Perot cavities remains a poorly understood effect theoretically. Recent breakthroughs explain some of the observations through the Grote-Hynes theory, where the cavity introduces friction with the reaction coordinate, thus reducing the transmission coefficient and the rate. The regime of rate enhancement, the observed sharp resonances at varying cavity frequencies, and the survival of these effects in the collective regime remain mostly unexplained. In this Letter, we consider the cis-trans isomerization of HONO atomistically using an ab initio potential energy surface. We evaluate the transmission coefficient using the reactive flux method and identify the conditions for rate acceleration. In the underdamped, low-friction regime of the reaction coordinate, the cavity coupling enhances the rate with increasing coupling strength until reaching the Kramers turnover point. Sharp resonances in this regime are related to cavity-enabled energy redistribution channels.

Effects of disorder on polaritonic and dark states in a cavity using the disordered Tavis-Cummings model

We consider molecules confined to a microcavity of dimensions such that an excitation of the molecule is nearly resonant with a cavity mode. The molecular excitation energies are assumed to be Gaussianly distributed with mean ϵ_a and variance σ. We find an asymptotically exact solution for large number density N. Conditions for the existence of the polaritonic states and expressions for their energies are obtained. Polaritonic states are found to be quite stable against disorder. Our results are verified by comparison with simulations. When ϵ_a is equal to energy of the cavity state ϵ_c, the Rabi splitting is found to increase by 2σ²N|Ṽ|, where Ṽ is the coupling of a molecular excitation to the cavity state. An analytic expression is found for the disorder-induced width of the polaritonic peak. Results for various densities of states and the absorption spectrum are presented. The dark states turn "gray" in the presence of disorder with their contribution to the absorption increasing with σ. Lifetimes of the cavity and molecular states are found to be important, and for sufficiently large Rabi splitting, the width of the polaritonic peaks is dominated by them. We also give analytical results for the case where the molecular levels follow a uniform distribution. We conclude that the study of the width of the polaritonic peaks as a function of the Rabi splitting can give information on the distribution of molecular energy levels. Finally, the effects of (a) orientational disorder and (b) spatial variation on the cavity field are presented.

Ab Initio Linear-Response Approach to Vibro-Polaritons in the Cavity Born-Oppenheimer Approximation

Recent years have seen significant developments in the study of strong light-matter coupling including the control of chemical reactions by altering the vibrational normal modes of molecules. In the vibrational strong coupling regime, the normal modes of the system become hybrid modes which mix nuclear, electronic, and photonic degrees of freedom. First-principles methods capable of treating light and matter degrees of freedom on the same level of theory are an important tool in understanding such systems. In this work, we develop and apply a generalized force constant matrix approach to the study of mixed vibration-photon (vibro-polariton) states of molecules based on the cavity Born-Oppenheimer approximation and quantum-electrodynamical density-functional theory. With this method, vibro-polariton modes and infrared spectra can be computed via linear-response techniques analogous to those widely used for conventional vibrations and phonons. We also develop an accurate model that highlights the consistent treatment of cavity-coupled electrons in the vibrational strong coupling regime. These electronic effects appear as new terms previously disregarded by simpler models. This effective model also allows for an accurate extrapolation of single and two molecule calculations to the collective strong coupling limit of hundreds of molecules. We benchmark these approaches for single and many CO2 molecules coupled to a single photon mode and the iron pentacarbonyl Fe(CO)5 molecule coupled to a few photon modes. Our results are the first ab initio results for collective vibrational strong coupling effects. This framework for efficient computations of vibro-polaritons paves the way to a systematic description and improved understanding of the behavior of chemical systems in vibrational strong coupling.

Quantum Simulations of Vibrational Strong Coupling via Path Integrals

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. This result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.

Cavity-altered thermal isomerization rates and dynamical resonant localization in vibro-polaritonic chemistry

It has been experimentally demonstrated that reaction rates for molecules embedded in microfluidic optical cavities are altered when compared to rates observed under "ordinary" reaction conditions. However, precise mechanisms of how strong coupling of an optical cavity mode to molecular vibrations affects the reactivity and how resonance behavior emerges are still under dispute. In the present work, we approach these mechanistic issues from the perspective of a thermal model reaction, the inversion of ammonia along the umbrella mode, in the presence of a single-cavity mode of varying frequency and coupling strength. A topological analysis of the related cavity Born-Oppenheimer potential energy surface in combination with quantum mechanical and transition state theory rate calculations reveals two quantum effects, leading to decelerated reaction rates in qualitative agreement with experiments: the stiffening of quantized modes perpendicular to the reaction path at the transition state, which reduces the number of thermally accessible reaction channels, and the broadening of the barrier region, which attenuates tunneling. We find these two effects to be very robust in a fluctuating environment, causing statistical variations of potential parameters, such as the barrier height. Furthermore, by solving the time-dependent Schrödinger equation in the vibrational strong coupling regime, we identify a resonance behavior, in qualitative agreement with experimental and earlier theoretical work. The latter manifests as reduced reaction probability when the cavity frequency ω_c is tuned resonant to a molecular reactant frequency. We find this effect to be based on the dynamical localization of the vibro-polaritonic wavepacket in the reactant well.

Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.

Polariton relaxation under vibrational strong coupling: Comparing cavity molecular dynamics simulations against Fermi's golden rule rate

Under vibrational strong coupling (VSC), the formation of molecular polaritons may significantly modify the photo-induced or thermal properties of molecules. In an effort to understand these intriguing modifications, both experimental and theoretical studies have focused on the ultrafast dynamics of vibrational polaritons. Here, following our recent work [Li et al., J. Chem. Phys. 154, 094124 (2021)], we systematically study the mechanism of polariton relaxation for liquid CO₂ under a weak external pumping. Classical cavity molecular dynamics (CavMD) simulations confirm that polariton relaxation results from the combined effects of (i) cavity loss through the photonic component and (ii) dephasing of the bright-mode component to vibrational dark modes as mediated by intermolecular interactions. The latter polaritonic dephasing rate is proportional to the product of the weight of the bright mode in the polariton wave function and the spectral overlap between the polariton and dark modes. Both these factors are sensitive to parameters such as the Rabi splitting and cavity mode detuning. Compared to a Fermi's golden rule calculation based on a tight-binding harmonic model, CavMD yields a similar parameter dependence for the upper polariton relaxation lifetime but sometimes a modest disagreement for the lower polariton. We suggest that this disagreement results from polariton-enhanced molecular nonlinear absorption due to molecular anharmonicity, which is not included in our analytical model. We also summarize recent progress on probing nonreactive VSC dynamics with CavMD.

Multimode polariton effects on molecular energy transport and spectral fluctuations

Despite the potential paradigm breaking capability of microcavities to control chemical processes, the extent to which photonic devices change properties of molecular materials is still unclear, in part due to challenges in modeling hybrid light-matter excitations delocalized over many length scales. We overcome these challenges for a photonic wire under strong coupling with a molecular ensemble. Our simulations provide a detailed picture of the effect of photonic wires on spectral and transport properties of a disordered molecular material. We find stronger changes to the probed molecular observables when the cavity is redshifted relative to the molecules and energetic disorder is weak. These trends are expected to hold also in higher-dimensional cavities, but are not captured with theories that only include a single cavity-mode. Therefore, our results raise important issues for future experiments and model building focused on unraveling new ways to manipulate chemistry with optical cavities.

Cavity quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis. II. Analytic energy gradient

Following the formulation of cavity quantum-electrodynamical time-dependent density functional theory (cQED-TDDFT) models [Flick et al., ACS Photonics 6, 2757–2778 (2019) and Yang et al., J. Chem. Phys. 155, 064107 (2021)], here, we report the derivation and implementation of the analytic energy gradient for polaritonic states of a single photochrome within the cQED-TDDFT models. Such gradient evaluation is also applicable to a complex of explicitly specified photochromes or, with proper scaling, a set of parallel-oriented, identical-geometry, and non-interacting molecules in the microcavity.

Driving chemical reactions with polariton condensates

When molecular transitions strongly couple to photon modes, they form hybrid light-matter modes called polaritons. Collective vibrational strong coupling is a promising avenue for control of chemistry, but this can be deterred by the large number of quasi-degenerate dark modes. The macroscopic occupation of a single polariton mode by excitations, as observed in Bose-Einstein condensation, offers promise for overcoming this issue. Here we theoretically investigate the effect of vibrational polariton condensation on the kinetics of electron transfer processes. Compared with excitation with infrared laser sources, the vibrational polariton condensate changes the reaction yield significantly at room temperature due to additional channels with reduced activation barriers resulting from the large accumulation of energy in the lower polariton, and the many modes available for energy redistribution during the reaction. Our results offer tantalizing opportunities to use condensates for driving chemical reactions, kinetically bypassing usual constraints of fast intramolecular vibrational redistribution in condensed phase.

Catalysis by Dark States in Vibropolaritonic Chemistry

Collective strong coupling between a disordered ensemble of N localized molecular vibrations and a resonant optical cavity mode gives rise to two polariton and N-1≫2 dark modes. Thus, experimental changes in thermally activated reaction kinetics due to polariton formation appear entropically unlikely and remain a puzzle. Here we show that the overlooked dark modes, while parked at the same energy as bare molecular vibrations, are robustly delocalized across ∼2-3 molecules, yielding enhanced channels of vibrational cooling, concomitantly catalyzing a chemical reaction. As an illustration, we theoretically show an ≈50% increase in an electron transfer rate due to enhanced product stabilization. The reported effects can arise when the homogeneous linewidths of the dark modes are smaller than their energy spacings.

Vibration-Cavity Polariton Chemistry and Dynamics

Molecular polaritons result from light-matter coupling between optical resonances and molecular electronic or vibrational transitions. When the coupling is strong enough, new hybridized states with mixed photon-material character are observed spectroscopically, with resonances shifted above and below the uncoupled frequency. These new modes have unique optical properties and can be exploited to promote or inhibit physical and chemical processes. One remarkable result is that vibrational strong coupling to cavities can alter reaction rates and product branching ratios with no optical excitation whatsoever. In this work we review the ability of vibration-cavity polaritons to modify chemical and physical processes including chemical reactivity, as well as steady-state and transient spectroscopy. We discuss the larger context of these works and highlight their most important contributions and implications. Our goal is to provide insight for systematically manipulating molecular polaritons in photonic and chemical applications. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Theory of vibrational polariton chemistry in the collective coupling regime

We theoretically demonstrate that the 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.

Negligible rate enhancement from reported cooperative vibrational strong coupling catalysis

We report the results of an attempt to reproduce a reported cavity catalysis of the ester hydrolysis of para-nitrophenyl acetate due to vibrational strong coupling. While we achieved the same light-matter coupling strength and detuning, we did not observe the reported ten-fold increase in the reaction rate constant. Furthermore, no obvious detuning dependence was observed. The inconsistency with the reported literature suggests that cavity catalysis is sensitive to experimental details beyond the onset of vibrational strong coupling. This indicates that other important factors are involved and have been overlooked so far. We find that more investigation into the limits, key factors, and mechanisms to reliably actualize cavity modified reactions is needed.

Molecular Polaritonics: Chemical Dynamics Under Strong Light-Matter Coupling

Chemical manifestations of strong light-matter coupling have recently been a subject of intense experimental and theoretical studies. Here we review the present status of this field. Section 1 is an introduction to molecular polaritonics and to collective response aspects of light-matter interactions. Section 2 provides an overview of the key experimental observations of these effects, while Section 3 describes our current theoretical understanding of the effect of strong light-matter coupling on chemical dynamics. A brief outline of applications to energy conversion processes is given in Section 4. Pending technical issues in the construction of theoretical approaches are briefly described in Section 5. Finally, the summary in Section 6 outlines the paths ahead in this exciting endeavor. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light-matter coupling

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density-type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

Quantum Effects in Chemical Reactions under Polaritonic Vibrational Strong Coupling

The electromagnetic field in an optical cavity can dramatically modify and even control chemical reactivity via vibrational strong coupling (VSC). Since the typical vibration and cavity frequencies are considerably larger than thermal energy, it is essential to adopt a quantum description of cavity-catalyzed adiabatic chemical reactions. Using quantum transition state theory (TST), we examine the coherent nature of adiabatic reactions in cavities and derive the cavity-induced changes in eigenfrequencies, zero-point energy, and quantum tunneling. The resulting quantum TST calculation allows us to explain and predict the resonance effect (i.e., maximal kinetic modification via tuning the cavity frequency), collective effect (i.e., linear scaling with the molecular density), and selectivity (i.e., cavity-induced control of the branching ratio). The TST calculation is further supported by perturbative analysis of polariton normal modes, which not only provides physical insights to cavity-catalyzed chemical reactions but also presents a general approach to treat other VSC phenomena.

Molecular vibrational polariton: Its dynamics and potentials in novel chemistry and quantum technology

Molecular vibrational polaritons, a hybridized quasiparticle formed by the strong coupling between molecular vibrational modes and photon cavity modes, have attracted tremendous attention in the chemical physics community due to their peculiar influence on chemical reactions. At the same time, the half-photon half-matter characteristics of polaritons make them suitable to possess properties from both sides and lead to new features that are useful for photonic and quantum technology applications. To eventually use polaritons for chemical and quantum applications, it is critical to understand their dynamics. Due to the intrinsic time scale of cavity modes and molecular vibrational modes in condensed phases, polaritons can experience dynamics on ultrafast time scales, e.g., relaxation from polaritons to dark modes. Thus, ultrafast vibrational spectroscopy becomes an ideal tool to investigate such dynamics. In this Perspective, we give an overview of recent ultrafast spectroscopic works by our group and others in the field. These recent works show that molecular vibrational polaritons can have distinct dynamics from its pure molecular counterparts, such as intermolecular vibrational energy transfer and hot vibrational dynamics. We then discuss some current challenges and future opportunities, such as the possible use of ultrafast vibrational dynamics, to understand cavity-modified reactions and routes to develop molecular vibrational polaritons as new room temperature quantum platforms.

Theory of Mode-Selective Chemistry through Polaritonic Vibrational Strong Coupling

Recent experiments have demonstrated remarkable mode-selective reactivities by coupling molecular vibrations with a quantized radiation field inside an optical cavity. The fundamental mechanism behind such effects, on the other hand, remains elusive. In this work, we provide a theoretical explanation of the basic principle of how cavity frequency can be tuned to achieve mode-selective reactivities. We find that the dynamics of the radiation mode leads to a cavity frequency-dependent dynamical caging effect of a reaction coordinate, resulting in suppression of the rate constant. In the presence of competitive reactions, it is possible to preferentially cage a reaction coordinate when the barrier frequencies of competing reactions are different, resulting in a selective slow down of a given reaction. Our theoretical results illustrate the cavity-induced mode-selective chemistry through polaritonic vibrational strong couplings, revealing the fundamental mechanism for changing chemical selectivities through cavity quantum electrodynamics.