Ground state properties and infrared spectra of anharmonic vibrational polaritons of small molecules in cavities

Semiclassical dynamics in Wigner phase space I: Adiabatic hybrid Wigner dynamics

The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In Paper I, focusing on adiabatic single surface processes, we derive the well-known double Herman-Kluk (DHK) approximation for real-time correlation functions in Wigner phase space and connect it to the linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important "system" degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the "bath") at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators and the decoherence of vibrational probability density of a model I2 Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign problem and employs reduced dimensional prefactors bringing calculations of complex system-bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes.

Exciton energy transfer inside cavity-A benchmark study of polaritonic dynamics using the surface hopping method

Strong coupling between the molecular system and photon inside the cavity generates polaritons, which can alter reaction rates by orders of magnitude. In this work, we benchmark the surface hopping method to simulate non-adiabatic dynamics in a cavity. The comparison is made against a numerically exact method (the hierarchical equations of motion) for a model system investigating excitonic energy transfer for a broad range of parameters. Surface hopping captures the effects of the radiation mode well, both at resonance and off-resonance. We have further investigated parameters that can increase or decrease the rate of population transfer, and we find that surface hopping in general can capture both effects well. Finally, we show that the dipole self-energy term within our parameter regime does not significantly affect the system's dynamics.

Mesoscale Molecular Simulations of Fabry-Pérot Vibrational Strong Coupling

Developing theoretical frameworks for vibrational strong coupling (VSC) beyond the single-mode approximation is crucial for a comprehensive understanding of experiments with planar Fabry-Pérot cavities. Herein, a generalized cavity molecular dynamics (CavMD) scheme is developed to simulate VSC of a large ensemble of realistic molecules coupled to an arbitrary 1D or 2D photonic environment. This approach is built upon the Power-Zienau-Woolley Hamiltonian in the normal mode basis and uses a grid representation of the molecular ensembles to reduce the computational cost. When simulating the polariton dispersion relation for a homogeneous distribution of molecules in planar Fabry-Pérot cavities, our data highlight the importance of preserving the in-plane translational symmetry of the molecular distribution. In this homogeneous limit, CavMD yields the consistent polariton dispersion relation as an analytic theory, i.e., incorporating many cavity modes with varying in-plane wave vectors (k∥) produces the same spectrum as the system with a single cavity mode. Furthermore, CavMD reveals that the validity of the single-mode approximation is challenged when nonequilibrium polariton dynamics are considered, as polariton-polariton scattering occurs between modes with the nearest neighbor k∥. The procedure for numerically approaching the macroscopic limit is also demonstrated with CavMD by increasing the system size. Looking forward, our generalized CavMD approach may facilitate understanding vibrational polariton transport and condensation.

Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description

The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schrödinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work, we compare numerically the Lindblad and Schrödinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schrödinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.

Impact of Cavity on Molecular Ionization Spectra

Ionization phenomena have been widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of a cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.

A Quantum Chemistry Approach to Linear Vibro-Polaritonic Infrared Spectra with Perturbative Electron-Photon Correlation

In the vibrational strong coupling (VSC) regime, molecular vibrations and resonant low-frequency cavity modes form light-matter hybrid states, vibrational polaritons, with characteristic infrared (IR) spectroscopic signatures. Here, we introduce a molecular quantum chemistry-based computational scheme for linear IR spectra of vibrational polaritons in polyatomic molecules, which perturbatively accounts for nonresonant electron-photon interactions under VSC. Specifically, we formulate a cavity Born-Oppenheimer perturbation theory (CBO-PT) linear response approach, which provides an approximate but systematic description of such electron-photon correlation effects in VSC scenarios while relying on molecular ab initio quantum chemistry methods. We identify relevant electron-photon correlation effects at the second order of CBO-PT, which manifest as static polarizability-dependent Hessian corrections and an emerging polarizability-dependent cavity intensity component providing access to transmission spectra commonly measured in vibro-polaritonic chemistry. Illustratively, we address electron-photon correlation effects perturbatively in IR spectra of CO2 and Fe(CO)5 vibro-polaritonic models in sound agreement with nonperturbative CBO linear response theory.

Coherent state switching using vibrational polaritons in an asymmetric double-well potential

The quantum dynamics of vibrational polaritonic states arising from the interaction of a bistable molecule with the quantized mode of a Fabry-Perot microcavity is investigated using a generic asymmetric double-well potential as a simplified one-dimensional model of a reactive molecule. After discussing the role of the light-matter coupling strength in the emergence of avoided crossings between polaritonic states, we investigate the possibility of using these crossings to trigger a dynamical switching of these states from one potential well to the other. Two schemes are proposed to achieve this coherent state switching, either by preparing the molecule in an appropriate vibrational excited state before inserting it into the cavity, or by applying a short laser pulse inside the cavity to obtain a coherent superposition of polaritonic states. The respective influences of dipole moment amplitude and potential asymmetry on the coherent switching process are also discussed.

Shaping the laser control landscape of a hydrogen transfer reaction by vibrational strong coupling. A direct optimal control approach

Controlling molecular reactivity by shaped laser pulses is a long-standing goal in chemistry. Here, we suggest a direct optimal control approach that combines external pulse optimization with other control parameters arising in the upcoming field of vibro-polaritonic chemistry for enhanced controllability. The direct optimal control approach is characterized by a simultaneous simulation and optimization paradigm, meaning that the equations of motion are discretized and converted into a set of holonomic constraints for a nonlinear optimization problem given by the control functional. Compared with indirect optimal control, this procedure offers great flexibility, such as final time or Hamiltonian parameter optimization. A simultaneous direct optimal control theory will be applied to a model system describing H-atom transfer in a lossy Fabry-Pérot cavity under vibrational strong coupling conditions. Specifically, optimization of the cavity coupling strength and, thus, of the control landscape will be demonstrated.

Cavity-Modified Chemiluminescent Reaction of Dioxetane

Chemiluminescence is a thermally activated chemical process that emits a photon of light by forming a fraction of products in the electronic excited state. A well-known example of this spectacular phenomenon is the emission of light in the firefly beetle, where the formation of a four-membered cyclic peroxide compound and subsequent dissociation produce a light-emitting product. The smallest cyclic peroxide, dioxetane, also exhibits chemiluminescence but with a low quantum yield as compared to that of firefly dioxetane. Employing the strong light-matter coupling has recently been found to be an alternative strategy to modify the chemical reactivity. In the presence of an optical cavity, the molecular degrees of freedom greatly mix with the cavity mode to form hybrid cavity-matter states called polaritons. These newly generated hybrid light-matter states manipulate the potential energy surfaces and significantly change the reaction dynamics. Here, we theoretically investigate the effects of a strong light-matter interaction on the chemiluminescent reaction of dioxetane using the extended Jaynes-Cummings model. The cavity couplings corresponding to the electronic and vibrational degrees of freedom have been included in the interaction Hamiltonian. We explore how the cavity alters the ground- and excited-state path energy barriers and reaction rates. Our results demonstrate that the formation of excited-state products in the dioxetane decomposition process can be either accelerated or suppressed, depending on the molecular orientation with respect to the cavity polarization.

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.

Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles

Experimental studies indicate that optical cavities can affect chemical reactions through either vibrational or electronic strong coupling and the quantized cavity modes. However, the current understanding of the interplay between molecules and confined light modes is incomplete. Accurate theoretical models that take into account intermolecular interactions to describe ensembles are therefore essential to understand the mechanisms governing polaritonic chemistry. We present an ab initio Hartree-Fock ansatz in the framework of the cavity Born-Oppenheimer approximation and study molecules strongly interacting with an optical cavity. This ansatz provides a nonperturbative, self-consistent description of strongly coupled molecular ensembles, taking into account the cavity-mediated dipole self-energy contributions. To demonstrate the capability of the cavity Born-Oppenheimer Hartree-Fock ansatz, we study the collective effects in ensembles of strongly coupled diatomic hydrogen fluoride molecules. Our results highlight the importance of the cavity-mediated intermolecular dipole-dipole interactions, which lead to energetic changes of individual molecules in the coupled ensemble.

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.

The role of dephasing for dark state coupling in a molecular Tavis-Cummings model

The collective coupling of an ensemble of molecules to a light field is commonly described by the Tavis-Cummings model. This model includes numerous eigenstates that are optically decoupled from the optically bright polariton states. Accessing these dark states requires breaking the symmetry in the corresponding Hamiltonian. In this paper, we investigate the influence of non-unitary processes on the dark state dynamics in the molecular Tavis-Cummings model. The system is modeled with a Lindblad equation that includes pure dephasing, as it would be caused by weak interactions with an environment, and photon decay. Our simulations show that the rate of pure dephasing, as well as the number of two-level systems, has a significant influence on the dark state population.

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.

QM/MM Modeling of Vibrational Polariton Induced Energy Transfer and Chemical Dynamics

Vibrational strong coupling (VSC) provides a novel means to modify chemical reactions and energy transfer pathways. To efficiently model chemical dynamics under VSC in the collective regime, herein a hybrid quantum mechanical/molecular mechanical (QM/MM) cavity molecular dynamics (CavMD) scheme is developed and applied to an experimentally studied chemical system. This approach can achieve linear scaling with respect to the number of molecules for a dilute solution under VSC by assuming that each QM solute molecule is surrounded by an independent MM solvent bath. Application of this approach to a dilute solution of Fe(CO)₅ in n-dodecane under VSC demonstrates polariton dephasing to the dark modes and polariton-enhanced molecular nonlinear absorption. These simulations predict that strongly exciting the lower polariton may provide an energy transfer pathway that selectively excites the equatorial CO vibrations rather than the axial CO vibrations. Moreover, these simulations also directly probe the cavity effect on the dynamics of the Fe(CO)₅ Berry pseudorotation reaction for comparison to recent two-dimensional infrared spectroscopy experiments. This theoretical approach is applicable to a wide range of other polaritonic systems and provides a tool for exploring the use of VSC for selective infrared photochemistry.

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.

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.

Cavity-induced non-adiabatic dynamics and spectroscopy of molecular rovibrational polaritons studied by multi-mode quantum models

We study theoretically the quantum dynamics and spectroscopy of rovibrational polaritons formed in a model system composed of a single rovibrating diatomic molecule, which interacts with two degenerate, orthogonally polarized modes of an optical Fabry–Pérot cavity. We employ an effective rovibrational Pauli–Fierz Hamiltonian in length gauge representation and identify three-state vibro-polaritonic conical intersections (VPCIs) between singly excited vibro-polaritonic states in a two-dimensional angular coordinate branching space. The lower and upper vibrational polaritons are of mixed light–matter hybrid character, whereas the intermediate state is purely photonic in nature. The VPCIs provide effective population transfer channels between singly excited vibrational polaritons, which manifest in rich interference patterns in rotational densities. Spectroscopically, three bright singly excited states are identified when an external infrared laser field couples to both a molecular and a cavity mode. The non-trivial VPCI topology manifests as pronounced multi-peak progression in the spectral region of the upper vibrational polariton, which is traced back to the emergence of rovibro-polaritonic light–matter hybrid states. Experimentally, ubiquitous spontaneous emission from cavity modes induces a dissipative reduction of intensity and peak broadening, which mainly influences the purely photonic intermediate state peak as well as the rovibro-polaritonic progression.

Generalization of the Tavis-Cummings model for multi-level anharmonic systems: Insights on the second excitation manifold

Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light-matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis-Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N² × N² Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.

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.

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.

Theoretical Challenges in Polaritonic Chemistry

Polaritonic chemistry exploits strong light-matter coupling between molecules and confined electromagnetic field modes to enable new chemical reactivities. In systems displaying this functionality, the choice of the cavity determines both the confinement of the electromagnetic field and the number of molecules that are involved in the process. While in wavelength-scale optical cavities the light-matter interaction is ruled by collective effects, plasmonic subwavelength nanocavities allow even single molecules to reach strong coupling. Due to these very distinct situations, a multiscale theoretical toolbox is then required to explore the rich phenomenology of polaritonic chemistry. Within this framework, each component of the system (molecules and electromagnetic modes) needs to be treated in sufficient detail to obtain reliable results. Starting from the very general aspects of light-molecule interactions in typical experimental setups, we underline the basic concepts that should be taken into account when operating in this new area of research. Building on these considerations, we then provide a map of the theoretical tools already available to tackle chemical applications of molecular polaritons at different scales. Throughout the discussion, we draw attention to both the successes and the challenges still ahead in the theoretical description of polaritonic chemistry.

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.

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.

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.

Chemistry under Vibrational Strong Coupling

Over the past decade, the possibility of manipulating chemistry and material properties using hybrid light-matter states has stimulated considerable interest. Hybrid light-matter states can be generated by placing molecules in an optical cavity that is resonant with a molecular transition. Importantly, the hybridization occurs even in the dark because the coupling process involves the zero-point fluctuations of the optical mode (a.k.a. vacuum field) and the molecular transition. In other words, unlike photochemistry, no real photon is required to induce this strong coupling phenomenon. Strong coupling in general, but vibrational strong coupling (VSC) in particular, offers exciting possibilities for molecular and, more generally, material science. Not only is it a new tool to control chemical reactivity, but it also gives insight into which vibrations are involved in a reaction. This Perspective gives the underlying fundamentals of light-matter strong coupling, including a mini-tutorial on the practical issues to achieve VSC. Recent advancements in "vibro-polaritonic chemistry" and related topics are presented along with the challenges for this exciting new field.

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.