Recent Progress in Vibropolaritonic Chemistry

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.

Molecular Strong Coupling and Cavity Finesse

Molecular strong coupling offers exciting prospects in physics, chemistry, and materials science. While attention has been focused on developing realistic models for the molecular systems, the important role played by the entire photonic mode structure of the optical cavities has been less explored. We show that the effectiveness of molecular strong coupling may be critically dependent on cavity finesse. Specifically we only see emission associated with a dispersive lower polariton for cavities with sufficient finesse. By developing an analytical model of cavity photoluminescence in a multimode structure we clarify the role of finite-finesse in polariton formation and show that lowering the finesse reduces the extent of the mixing of light and matter in polariton states. We suggest that the detailed nature of the photonic modes supported by a cavity will be as important in developing a coherent framework for molecular strong coupling as the inclusion of realistic molecular models.

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.

Strong coupling in molecular systems: a simple predictor employing routine optical measurements

We provide a simple method that enables readily acquired experimental data to be used to predict whether or not a candidate molecular material may exhibit strong coupling. Specifically, we explore the relationship between the hybrid molecular/photonic (polaritonic) states and the bulk optical response of the molecular material. For a given material, this approach enables a prediction of the maximum extent of strong coupling (vacuum Rabi splitting), irrespective of the nature of the confined light field. We provide formulae for the upper limit of the splitting in terms of the molar absorption coefficient, the attenuation coefficient, the extinction coefficient (imaginary part of the refractive index) and the absorbance. To illustrate this approach, we provide a number of examples, and we also discuss some of the limitations of our approach.

Fully Quantum Simulation of Polaritonic Vibrational Spectra of Large Cavity-Molecule System

The formation of molecular vibrational polaritons, arising from the interplay between molecular vibrations and infrared cavity modes, is a quantum phenomenon necessitating accurate quantum dynamical simulations. Here, we introduce the cavity vibrational self-consistent field/virtual state configuration interaction method, enabling quantum simulation of the vibrational spectra of many-molecule systems within the optical cavity. Focusing on the representative (H2O)21 system, we showcase this parameter-free quantum approach's ability to capture both linear and nonlinear vibrational spectral features. Our findings highlight the growing prominence of molecular couplings among OH stretches and bending excited bands with increased light-matter interaction, revealing distinctive nonlinear spectral features induced by vibrational strong coupling.

Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling

We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full nonrelativistic Pauli-Fierz problem of an ensemble of strongly coupled molecules in the dilute-gas limit reduces in the cavity Born-Oppenheimer approximation to a cavity-Hartree equation for the electronic structure. Consequently, each individual molecule experiences a self-consistent coupling to the dipoles of all other molecules, which amount to non-negligible values in the thermodynamic limit (large ensembles). Thus, collective vibrational strong coupling can alter individual molecules strongly for localized "hotspots" within the ensemble. Moreover, the discovered cavity-induced polarization pattern possesses a zero net polarization, which resembles a continuous form of a spin glass (or better polarization glass). Our findings suggest that the thorough understanding of polaritonic chemistry, requires a self-consistent treatment of dressed electronic structure, which can give rise to numerous, so far overlooked, physical mechanisms.

Molecular Polaritons for Chemistry, Photonics and Quantum Technologies

Molecular polaritons are quasiparticles resulting from the hybridization between molecular and photonic modes. These composite entities, bearing characteristics inherited from both constituents, exhibit modified energy levels and wave functions, thereby capturing the attention of chemists in the past decade. The potential to modify chemical reactions has spurred many investigations, alongside efforts to enhance and manipulate optical responses for photonic and quantum applications. This Review centers on the experimental advances in this burgeoning field. Commencing with an introduction of the fundamentals, including theoretical foundations and various cavity architectures, we discuss outcomes of polariton-modified chemical reactions. Furthermore, we navigate through the ongoing debates and uncertainties surrounding the underpinning mechanism of this innovative method of controlling chemistry. Emphasis is placed on gaining a comprehensive understanding of the energy dynamics of molecular polaritons, in particular, vibrational molecular polaritons─a pivotal facet in steering chemical reactions. Additionally, we discuss the unique capability of coherent two-dimensional spectroscopy to dissect polariton and dark mode dynamics, offering insights into the critical components within the cavity that alter chemical reactions. We further expand to the potential utility of molecular polaritons in quantum applications as well as precise manipulation of molecular and photonic polarizations, notably in the context of chiral phenomena. This discussion aspires to ignite deeper curiosity and engagement in revealing the physics underpinning polariton-modified molecular properties, and a broad fascination with harnessing photonic environments to control chemistry.

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.

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.

Collective Strong Coupling Modifies Aggregation and Solvation

Intermolecular (Coulombic) interactions are pivotal for aggregation, solvation, and crystallization. We demonstrate that the collective strong coupling of several molecules to a single optical mode results in notable changes in the molecular excitations around a single perturbed molecule, thus representing an impurity in an otherwise ordered system. A competition between short-range coulombic and long-range photonic correlations inverts the local transition density in a polaritonic state, suggesting notable changes in the polarizability of the solvation shell. Our results provide an alternative perspective on recent work in polaritonic chemistry and pave the way for the rigorous treatment of cooperative effects in aggregation, solvation, and crystallization.

Optical Cavity Design and Functionality for Molecular Strong Coupling

Optical cavity/molecule strong coupling offers attractive opportunities to modulate photochemical or photophysical processes. When atoms or molecules are placed in an optical cavity, they can coherently exchange photonic energy with optical cavity vacuum fields, entering the strong coupling interaction regime. Recent work suggests that the thermodynamic and kinetic properties of molecules can be significantly changed by strong coupling, resulting in the emergence of intriguing photochemical and photophysical phenomena. As more and more physico-chemical systems are studied under strong coupling conditions, optical cavities have also advanced in their sophistication, responsiveness, and (multi)functionality. In this review, we highlight some of these recent developments, particularly focusing on Fabry-Perot microcavities.

Ab Initio Vibro-Polaritonic Spectra in Strongly Coupled Cavity-Molecule Systems

Recent experiments have revealed the profound effect of strong light-matter interactions in optical cavities on the electronic ground state of molecular systems. This phenomenon, known as vibrational strong coupling, can modify reaction rates and induce the formation of molecular vibrational polaritons, hybrid states involving both photon modes, and vibrational modes of molecules. We present an ab initio methodology based on the cavity Born-Oppenheimer Hartree-Fock ansatz, which is specifically powerful for ensembles of molecules, to calculate vibro-polaritonic IR spectra. This method allows for a comprehensive analysis of these hybrid states. Our semiclassical approach, validated against full quantum simulations, reproduces key features of the vibro-polaritonic spectra. The underlying analytic gradients also allow for optimization of cavity-coupled molecular systems and performing semiclassical dynamics simulations.

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.

Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations

The first numerically exact simulation of a full ab initio molecular quantum system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the ground state but is quickly lost already in the deep cryogenic regime. This is in contrast to predictions from the Jaynes-Cummings model, which is the standard starting point to model collective strong-coupling chemistry phenomenologically. Moreover, we find that the fluctuations of matter remain modified by the quantum nature of the thermal and vacuum-field fluctuations for significant temperatures, e.g., at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) have implications for the understanding and control of polaritonic chemistry and materials science, since a semiclassical theoretical description of light-matter interaction becomes reasonable, but the typical (classical) canonical equilibrium assumption for the nuclear subsystem remains violated. This opens the door for quantum fluctuation-induced stochastic resonance phenomena under vibrational strong coupling, which have been suggested as a plausible theoretical mechanism to explain the experimentally observed resonance phenomena in the absence of periodic driving that has not yet been fully understood.

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 Control of Molecular Spectroscopy and Photophysics

ConspectusOptical cavities have been established as a powerful platform for manipulating the spectroscopy and photophysics of molecules. Molecules placed inside an optical cavity will interact with the cavity field, even if the cavity is in the vacuum state with no photons. When the coupling strength between matter excitations, either electronic or vibrational, and a cavity photon mode surpasses all decay rates in the system, hybrid light-matter excitations known as cavity polaritons emerge. Originally studied in atomic systems, there has been growing interest in studying polaritons in molecules. Numerous studies, both experimental and theoretical, have demonstrated that the formation of molecular polaritons can significantly alter the optical, electronic, and chemical properties of molecules in a noninvasive manner.This Account focuses on novel studies that reveal how optical cavities can be employed to control electronic excitations, both valence and core, in molecules and the spectroscopic signatures of molecular polaritons. We first discuss the capacity of optical cavities to manipulate and control the intrinsic conical intersection dynamics in polyatomic molecules. Since conical intersections are responsible for a wide range of photochemical and photophysical processes such as internal conversion, photoisomerization, and singlet fission, this provides a practical strategy to control molecular photodynamics. Two examples are given for the internal conversion in pyrazine and singlet fission in a pentacene dimer. We further show how X-ray cavities can be exploited to control the core-level excitations of molecules. Core polaritons can be created from inequivalent core orbitals by exchanging X-ray cavity photons. The core polaritons can also alter the selection rules in nonlinear spectroscopy.Polaritonic states and dynamics can be monitored by nonlinear spectroscopy. Quantum light spectroscopy is a frontier in nonlinear spectroscopy that exploits the quantum-mechanical properties of light, such as entanglement and squeezing, to extract matter information inaccessible by classical light. We discuss how quantum spectroscopic techniques can be employed for probing polaritonic systems. In multimolecule polaritonic systems, there exist two-polariton states that are dark in the two-photon absorption spectrum due to destructive interference between transition pathways. We show that a time-frequency entangled photon pair can manipulate the interference between transition pathways in the two-photon absorption signal and thus capture classically dark two-polariton states. Finally, we discuss cooperative effects among molecules in spectroscopy and possibly in chemistry. When many molecules are involved in forming the polaritons, while the cooperative effects clearly manifest in the dependence of the Rabi splitting on the number of molecules, whether they can show up in chemical reactivity, which is intrinsically local, is an open question. We explore the cooperative nature of the charge migration process in a cavity and show that, unlike spectroscopy, polaritonic charge dynamics is intrinsically local and does not show collective many-molecule effects.

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

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.

Light-responsive organic polaritons from first principles

Controlling the optical properties of light-responsive organic molecules is essential for their application in photonics. We demonstrate how light-responsive organic polaritons formed inside an optical cavity can be used to modify these properties based on first principles. Specifically, we study the excited state properties of the trans-azobenzene molecule and the free base tetraphenyl porphyrin (H2TPP) molecule under weak to strong light-matter coupling. Our results show that the cavity can modulate the dispersion and absorption properties of organic molecules. Compared to the case outside the cavity, the anomalous dispersion of the trans-azobenzene molecule inside the cavity is suppressed and this suppression decreases with increasing coupling strength, showing the potential of strong light-matter coupling in manipulating the optical dipole trap of organic molecules. Moreover, by adjusting the cavity parameters to tune the strength of the light-matter coupling, we achieve free switching between symmetric Lorentz and asymmetric Fano line shapes for H2TPP polaritonic excitations. During the switching between these spectral features, we also find that the cavity can be used to control the spontaneous radiation of organic molecules via the Purcell effect. These findings provide a new pathway to manipulate the optical properties of light-responsive organic molecules.

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.

A path towards single molecule vibrational strong coupling in a Fabry-Pérot microcavity

Interaction between light and molecular vibrations leads to hybrid light-matter states called vibrational polaritons. Even though many intriguing phenomena have been predicted for single-molecule vibrational strong coupling (VSC), several studies suggest that these effects tend to be diminished in the many-molecule regime due to the presence of dark states. Achieving single or few-molecule vibrational polaritons has been constrained by the need for fabricating extremely small mode volume infrared cavities. In this theoretical work, we propose an alternative strategy to achieve single-molecule VSC in a cavity-enhanced Raman spectroscopy (CERS) setup, based on the physics of cavity optomechanics. We then present a scheme harnessing few-molecule VSC to thermodynamically couple two reactions, such that a spontaneous electron transfer can now fuel a thermodynamically uphill reaction that was non-spontaneous outside the cavity.

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.

Theoretical Analysis of Exciton Wave Packet Dynamics in Polaritonic Wires

We present a comprehensive study of the exciton wave packet evolution in disordered lossless polaritonic wires. Our simulations reveal signatures of ballistic, diffusive, and subdiffusive exciton dynamics under strong light-matter coupling and identify the typical time scales associated with the transitions between these qualitatively distinct transport phenomena. We determine optimal truncations of the matter and radiation subsystems required for generating reliable time-dependent data from computational simulations at an affordable cost. The time evolution of the photonic part of the wave function reveals that many cavity modes contribute to the dynamics in a nontrivial fashion. Hence, a sizable number of photon modes is needed to describe exciton propagation with a reasonable accuracy. We find and discuss an intriguingly common lack of dominance of the photon mode on resonance with matter in both the presence and absence of disorder. We discuss the implications of our investigations for the development of theoretical models and analysis of experiments where coherent intermolecular energy transport and static disorder play an important role.

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.

Molecular Vibrational Polariton Dynamics: What Can Polaritons Do?

ConspectusWhen molecular vibrational modes strongly couple to virtual states of photonic modes, new molecular vibrational polariton states are formed, along with a large population of dark reservoir modes. The polaritons are much like the bonding and antibonding molecular orbitals when atomic orbitals form molecular bonds, while the dark modes are like nonbonding orbitals. Because the polariton states are half-matter and half-light, whose energy is shifted from the parental states, polaritons are predicted to modify chemistry under thermally activated conditions, leading to an exciting and emerging field known as polariton chemistry that could potentially shift paradigms in chemistry. Despite several published results supporting this concept, the chemical physics and mechanism of polariton chemistry remain elusive. One reason for this challenge is that previous works cannot differentiate polaritons from dark modes. This limitation makes delineating the contributions to chemistry from polaritons and dark states difficult. However, this level of insight is critical for developing a solid mechanism for polariton chemistry to design and predict the outcome of strong coupling with any given reaction. My group addressed the challenge of differentiating the dynamics of polaritons and dark modes by ultrafast two-dimensional infrared (2D IR) spectroscopy. Specifically, (1) we found that polaritons can facilitate intra- and intermolecular vibrational energy transfer, opening a pathway to control vibrational energy flow in liquid-phase molecular systems, and (2) by studying a single-step isomerization event, we verified that indeed polaritons can modify chemical dynamics under strong coupling conditions, but in contrast, the dark modes behave like uncoupled molecules and do not change the dynamics. This finding confirmed the central concept of polariton chemistry: polaritons modify the potential energy landscape of reactions. The result also clarified the role of dark modes, which lays a critical foundation for designing cavities for future polariton chemistry. Aside from using 2D IR spectroscopy to study polariton chemistry, we also used the same technique to develop molecular polaritons into a potential quantum simulation platform. We demonstrated that polaritons have Rabi oscillations, and using a checkerboard cavity design, we showed that polaritons could have large nonlinearity across space. We further used the checkerboard polaritons to simulate coherence transfer and visualize it. A unidirectional coherence transfer was observed, indicating non-Hermitian dynamics. The highlighted efforts in this Account provide a solid understanding of the capability of polaritons for chemistry and quantum information science. I conclude this Account by discussing a few challenges for moving polariton chemistry toward being predictable and making the polariton quantum platform a complement to existing systems.

Dissociation slowdown by collective optical response under strong coupling conditions

We consider an ensemble of diatomic molecules resonantly coupled to an optical cavity under strong coupling conditions at normal incidence. Photodissociation dynamics is examined via direct numerical integration of the coupled Maxwell-Schrödinger equations with molecular rovibrational degrees of freedom explicitly taken into account. It is shown that the dissociation is significantly affected (slowed down) when the system is driven at its polaritonic frequencies. The observed effect is demonstrated to be of transient nature and has no classical analog. An intuitive explanation of the dissociation slowdown at polaritonic frequencies is proposed.

Solvent Dependence on Cooperative Vibrational Strong Coupling and Cavity Catalysis

Strong light-matter coupling offers a unique way to control chemical reactions at the molecular level. Here, we compare the solvent effect on an ester solvolysis process under cooperative vibrational strong coupling (VSC). Three reactants, para-nitrophenylacetate, 3-methyl-para-nitrophenylbenzoate, and bis-(2, 4-dinitrophenyl) oxalate are chosen to study the effect of VSC on the solvolysis reaction rates. Two solvents, ethyl acetate and cyclopentanone, are also considered to compare the cavity catalysis by coupling the C=O stretching band of the reactant and the solvent molecules to a Fabry-Perot cavity mode. Interestingly, both solvents enhance the chemical reaction rate of para-nitrophenylacetate and 3-methyl-para-nitrophenylbenzoate under cooperative VSC conditions. However, the resonance effect is observed at different temperatures for different solvents, which is further confirmed by thermodynamic studies. Bis-(2, 4-dinitrophenyl) oxalate doesn't respond to VSC in either of the solvent systems due to poor overlap of reactant and solvent C=O vibrational bands. Cavity detuning and other control experiments suggest that cooperative VSC of the solvent plays a crucial role in modifying the activation free-energy of the reaction. These findings, along with other observations, cement the concept of polaritonic chemistry.

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.

Collective response in light-matter interactions: The interplay between strong coupling and local dynamics

Strong molecule-radiation field coupling is often reached when a large number N of molecules respond collectively to the radiation field. In electronic strong coupling, molecular nuclear dynamics following polariton excitation reflects (a) the timescale separation between the fast electronic and photonic dynamics and the slow nuclear motion on one hand, and (b) the interplay between the collective nature of the molecule-field coupling and the local nature of the molecules nuclear response on the other. The first implies that the electronic excitation takes place, in the spirit of the Born approximation, at an approximately fixed nuclear configuration. The second can be rephrased as the intriguing question, can the collective nature of the optical excitation lead to collective nuclear motion following polariton formation, resulting in so-called polaron decoupled dynamics. We address this issue by studying the dynamical properties of a simplified Holstein-Tavis-Cummings type model, in which boson modes representing molecular vibrations are replaced by two-level systems while the boson frequency and the vibronic coupling are represented by the coupling between these levels (that induces Rabi oscillations between them) and electronic state dependence of this coupling. We investigate the short-time behavior of this model following polariton excitation as well as its response to CW driving and its density of states spectrum. We find that, while some aspects of the dynamical behavior appear to adhere to the polaron decoupling picture, the observed dynamics mostly reflect the local nature of the nuclear configuration of the electronic polariton rather than this picture.

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.

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.

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.

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.

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.

Cavity catalysis: modifying linear free-energy relationship under cooperative vibrational strong coupling

Here, we used an unconventional idea of cooperative vibrational strong coupling of solute and solvent molecules to enhance the rate of an esterification reaction. Different derivatives of p-nitrophenyl benzoate (solute) and isopropyl acetate (solvent) are cooperatively coupled to an infrared Fabry–Perot cavity mode. The apparent rates are increased by more than six times at the ON resonance condition, and the rate enhancement follows the lineshape of the vibrational envelope. Very interestingly, a strongly coupled system doesn't obey the Hammett relations. Thermodynamics suggests that the reaction mechanism remains intact for cavity and non-cavity conditions. Temperature-dependent experiments show an entropy-driven process for the coupled molecules. Vacuum field coupling decreases the free energy of activation by 2–5 kJ mol⁻¹, supporting a catalysis process. The non-linear rate enhancement can be due to the reshuffling of the energy distribution between the substituents and the reaction center across the aromatic ring. These findings underline the non-equilibrium behavior of cavity catalysis.

Cavity catalysis: vibrational strong coupling of solute and solvent molecules enhanced the rate of an esterification reaction. Hammett relation breaks under strong light-matter coupling conditions suggesting its potential applications in catalysis.

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.

Selective crystallization via vibrational strong coupling

The coupling of (photo)chemical processes to optical cavity vacuum fields is an emerging method for modulating molecular and material properties. Recent reports have shown that strong coupling of the vibrational modes of solvents to cavity vacuum fields can influence the chemical reaction kinetics of dissolved solutes. This suggests that vibrational strong coupling might also effect other important solution-based processes, such as crystallization from solution. Here we test this hitherto unexplored notion, investigating pseudopolymorphism in the crystallization from water of ZIF metal-organic frameworks inside optical microcavities. We find that ZIF-8 crystals are selectively obtained from solution inside optical microcavities, where the OH stretching vibration of water is strongly coupled to cavity vacuum fields, whereas mixtures of ZIF-8 and ZIF-L are obtained otherwise. Moreover, ZIF crystallization is accelerated by solvent vibrational strong coupling. This work suggests that cavity vacuum fields might become a tool for materials synthesis, biasing molecular self-assembly and driving macroscopic material outcomes.

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.

Modifying Woodward-Hoffmann Stereoselectivity Under Vibrational Strong Coupling

Vibrational strong coupling (VSC) has recently been shown to change the rate and chemoselectivity of ground-state chemical reactions via the formation of light-matter hybrid polaritonic states. However, the observation that vibrational-mode symmetry has a large influence on charge-transfer reactions under VSC suggests that symmetry considerations could be used to control other types of chemical selectivity through VSC. Here, we show that VSC influences the stereoselectivity of the thermal electrocyclic ring opening of a cyclobutene derivative, a reaction which follows the Woodward-Hoffmann rules. The direction of the change in stereoselectivity depends on the vibrational mode that is coupled, as do changes in rate and reaction thermodynamics. These results on pericyclic reactions confirm that symmetry plays a key role in chemistry under VSC.

Nonequilibrium effects of cavity leakage and vibrational dissipation in thermally activated polariton chemistry

In vibrational strong coupling (VSC), molecular vibrations strongly interact with the modes of an optical cavity to form hybrid light-matter states known as vibrational polaritons. Experiments show that the kinetics of thermally activated chemical reactions can be modified by VSC. Transition-state theory, which assumes that internal thermalization is fast compared to reactive transitions, has been unable to explain the observed findings. Here, we carry out kinetic simulations to understand how dissipative processes, namely, those introduced by VSC to the chemical system, affect reactions where internal thermalization and reactive transitions occur on similar timescales. Using the Marcus-Levich-Jortner type of electron transfer as a model reaction, we show that such dissipation can change reactivity by accelerating internal thermalization, thereby suppressing nonequilibrium effects that occur in the reaction outside the cavity. This phenomenon is attributed mainly to cavity decay (i.e., photon leakage), but a supporting role is played by the relaxation between polaritons and dark states. When nonequilibrium effects are already suppressed in the bare reaction (the reactive species are essentially at internal thermal equilibrium throughout the reaction), we find that reactivity does not change significantly under VSC. Connections are made between our results and experimental observations.