Suppression and Enhancement of Thermal Chemical Rates in a Cavity

Vibrational weak and strong coupling modify a chemical reaction via cavity-mediated radiative energy transfer

Controlling reaction outcomes through external influences is a central goal in chemistry. Vibrational coupling between molecular vibrations and cavity modes is rapidly emerging as a distinct strategy compared with conventional thermochemical and photochemical methods; however, insight into the fundamental mechanisms remains limited. Here we investigate how vibrational weak and strong coupling in plasmonic nanocavities modifies the thermal dehydration of copper sulfate pentahydrate. We demonstrate that light-matter coupling reduces the onset temperature for dehydration by up to 14 °C, and we attribute this effect to enhanced radiative energy transport that is mediated by resonant electromagnetic modes, eliminating temperature gradients in the coupled system. Our findings provide direct evidence of localized energy transfer leading to modified chemical behaviour in specific regions of high optical density of states. This work establishes a mechanism for modifying thermally driven chemical processes using optical cavities, with implications for the development of catalytic systems that exploit these tailored interactions to achieve targeted reaction control.

Stochastic resonance in vibrational polariton chemistry

In this work, we systematically investigate the impact of ambient noise intensity on the rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. To achieve this, we utilize a numerically exact open quantum system approach-the hierarchical equations of motion in twin space, combined with a flexible tree tensor network state solver. Our findings reveal a stochastic resonance phenomenon in cavity-modified chemical reactivities: an optimal reaction rate enhancement occurs at an intermediate noise level. In other words, this enhancement diminishes if ambient noise, sensed by the cavity-molecule system through cavity leakage, is either too weak or excessively strong. In the collective coupling regime, when the cavity is weakly damped, rate enhancement strengthens as more molecules couple to the cavity. In contrast, under strong cavity damping, reaction rates decline as the number of molecules grows.

Cavity induced modulation of intramolecular vibrational energy flow pathways

Recent experiments in polariton chemistry indicate that reaction rates can be significantly enhanced or suppressed inside an optical cavity. One possible explanation for the rate modulation involves the cavity mode altering the intramolecular vibrational energy redistribution (IVR) pathways by coupling to specific molecular vibrations in the vibrational strong coupling (VSC) regime. However, the mechanism for such a cavity-mediated modulation of IVR is yet to be understood. In a recent study, Ahn et al. [Science 380, 1165 (2023)] observed that the rate of alcoholysis of phenyl isocyanate (PHI) is considerably suppressed when the cavity mode is tuned to be resonant with the isocyanate (NCO) stretching mode of PHI. Here, we analyze the quantum and classical IVR dynamics of a model effective Hamiltonian for PHI involving the high-frequency NCO-stretch mode and two of the key low-frequency phenyl ring modes. We compute various indicators of the extent of IVR in the cavity-molecule system and show that tuning the cavity frequency to the NCO-stretching mode strongly perturbs the cavity-free IVR pathways. Subsequent IVR dynamics involving the cavity and the molecular anharmonic resonances lead to efficient scrambling of an initial NCO-stretching overtone state over the molecular quantum number space. We also show that the hybrid light-matter states of the effective Hamiltonian undergo a localization-delocalization transition in the VSC regime.

Spectroscopic properties under vibrational strong coupling in disordered matter from path-integral Monte Carlo simulations

Vibrational strong coupling (VSC), the strong coupling between a Fabry-Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli-Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis-Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem.

Cavity-modified local and non-local electronic interactions in molecular ensembles under vibrational strong coupling

Resonant vibrational strong coupling (VSC) between molecular vibrations and quantized field modes of low-frequency optical cavities constitutes the conceptual cornerstone of vibro-polaritonic chemistry. In this work, we theoretically investigate the role of complementary nonresonant electron-photon interactions in the cavity Born-Oppenheimer (CBO) approximation. In particular, we study cavity-induced modifications of local and non-local electronic interactions in dipole-coupled molecular ensembles under VSC. Methodologically, we combine CBO perturbation theory (CBO-PT) [E. W. Fischer and P. Saalfrank, J. Chem. Theory Comput. 19, 7215 (2023)] with non-perturbative CBO Hartree-Fock (HF) and coupled cluster (CC) theories. In a first step, we derive up to second-order CBO-PT cavity potential energy surfaces, which reveal non-trivial intra- and inter-molecular corrections induced by the cavity. We then introduce the concept of a cavity reaction potential (CRP), minimizing the electronic energy in the cavity subspace to discuss vibro-polaritonic reaction mechanisms. We present reformulations of CBO-HF and CBO-CC approaches for CRPs and derive second-order approximate CRPs from CBO-PT for unimolecular and bimolecular scenarios. In the unimolecular case, we find small local modifications of molecular potential energy surfaces for selected isomerization reactions dominantly captured by the first-order dipole fluctuation correction. Excellent agreement between CBO-PT and non-perturbative wave function results indicates minor VSC-induced state relaxation effects in the single-molecule limit. In the bimolecular scenario, CBO-PT reveals an explicit coupling of interacting dimers to cavity modes besides cavity-polarization dependent dipole-induced dipole and van der Waals interactions with enhanced long-range character. An illustrative CBO-coupled cluster theory with singles and doubles-based numerical analysis of selected molecular dimer models provides a complementary non-perturbative perspective on cavity-modified intermolecular interactions under VSC.

Conditions for enhancement of gas phase chemical reactions inside a dark microwave cavity

The ability to slow down or enhance chemical reactions, by a seemingly simple setup of reactions inside a cavity made of two parallel mirrors is fascinating. Unfortunately, currently, theory and experiment have not yet fully converged. Since theory and experiment perfectly match for atom/molecular collisions in gas phase the enhancing chemical reactions in gas phase through its coupling to quantized electromagnetic modes in a dark cavity is investigated. Here the conditions and guidelines for selecting the proper type of reactions that can be enhanced by a dark cavity are provided. Showing that the asymmetric reaction rates of O + D2 → [ODD]# → OD + D and H + ArCl → [ArHCl]# → H + Ar + Cl can be enhanced by a dark cavity. On the other hand, an effect of the dark cavity on the symmetric reaction of hydrogen exchange in methane is predicted to be negligible. Notice that the theory is not limited to microwave cavities only.

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.

More than just smoke and mirrors: Gas-phase polaritons for optical control of chemistry

Gas-phase molecules are a promising platform to elucidate the mechanisms of action and scope of polaritons for optical control of chemistry. Polaritons arise from the strong coupling of a dipole-allowed molecular transition with the photonic mode of an optical cavity. There is mounting evidence of modified reactivity under polaritonic conditions; however, the complex condensed-phase environment of most experimental demonstrations impedes mechanistic understanding of this phenomenon. While the gas phase was the playground of early efforts in atomic cavity quantum electrodynamics, we have only recently demonstrated the formation of molecular polaritons under these conditions. Studying the reactivity of isolated gas-phase molecules under strong coupling would eliminate solvent interactions and enable quantum state resolution of reaction progress. In this Perspective, we contextualize recent gas-phase efforts in the field of polariton chemistry and offer a practical guide for experimental design moving forward.

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.

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.

Direct Observation of Polaritonic Chemistry by Nuclear Magnetic Resonance Spectroscopy

Polaritonic chemistry is emerging as a powerful approach to modifying the properties and reactivity of molecules and materials. However, probing how the electronics and dynamics of molecular systems change under strong coupling has been challenging due to the narrow range of spectroscopic techniques that can be applied in situ. Here we develop microfluidic optical cavities for vibrational strong coupling (VSC) that are compatible with nuclear magnetic resonance (NMR) spectroscopy using standard liquid NMR tubes. VSC is shown to influence the equilibrium between two conformations of a molecular balance sensitive to London dispersion forces, revealing an apparent change in the equilibrium constant under VSC. In all compounds studied, VSC does not induce detectable changes in chemical shifts, J-couplings, or spin-lattice relaxation times. This unexpected finding indicates that VSC does not substantially affect molecular electron density distributions, and in turn has profound implications for the possible mechanisms at play in polaritonic chemistry under VSC and suggests that the emergence of collective behavior is critical.

Resonance theory of vibrational polariton chemistry at the normal incidence

We present a theory that explains the resonance effect of the vibrational strong coupling (VSC) modified reaction rate constant at the normal incidence of a Fabry-Pérot (FP) cavity. This analytic theory is based on a mechanistic hypothesis that cavity modes promote the transition from the ground state to the vibrational excited state of the reactant, which is the rate-limiting step of the reaction. This mechanism for a single molecule coupled to a single-mode cavity has been confirmed by numerically exact simulations in our recent work in [J. Chem. Phys. 159, 084104 (2023)]. Using Fermi's golden rule (FGR), we formulate this rate constant for many molecules coupled to many cavity modes inside a FP microcavity. The theory provides a possible explanation for the resonance condition of the observed VSC effect and a plausible explanation of why only at the normal incident angle there is the resonance effect, whereas, for an oblique incidence, there is no apparent VSC effect for the rate constant even though both cases generate Rabi splitting and forming polariton states. On the other hand, the current theory cannot explain the collective effect when a large number of molecules are collectively coupled to the cavity, and future work is required to build a complete microscopic theory to explain all observed phenomena in VSC.

Extracting kinetic information from short-time trajectories: relaxation and disorder of lossy cavity polaritons

The emerging field of molecular cavity polaritons has stimulated a surge of experimental and theoretical activities and presents a unique opportunity to develop the many-body simulation methodology. This paper presents a numerical scheme for the extraction of key kinetic information of lossy cavity polaritons based on the transfer tensor method (TTM). Steady state, relaxation timescales, and oscillatory phenomena can all be deduced directly from a set of transfer tensors without the need for long-time simulation. Moreover, we generalize TTM to disordered systems by sampling dynamical maps and achieve fast convergence to disordered-averaged dynamics using a small set of realizations. Together, these techniques provide a toolbox for characterizing the interplay of cavity loss, disorder, and cooperativity in polariton relaxation and allow us to predict unusual dependences on the initial excitation state, photon decay rate, strength of disorder, and the type of cavity models. Thus, using the example of cavity polaritons, we have demonstrated significant potential in the use of the TTM toward both the efficient computation of long-time polariton dynamics and the extraction of crucial kinetic information about polariton relaxation from a small set of short-time trajectories.

Investigating the collective nature of cavity-modified chemical kinetics under vibrational strong coupling

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

Exploring the impact of vibrational cavity coupling strength on ultrafast CN + c-C6H12 reaction dynamics

Molecular polaritons, hybrid light-matter states resulting from strong cavity coupling of optical transitions, may provide a new route to guide chemical reactions. However, demonstrations of cavity-modified reactivity in clean benchmark systems are still needed to clarify the mechanisms and scope of polariton chemistry. Here, we use transient absorption to observe the ultrafast dynamics of CN radicals interacting with a cyclohexane (c-C6H12) and chloroform (CHCl3) solvent mixture under vibrational strong coupling of a C-H stretching mode of c-C6H12. By modulating the c-C6H12:CHCl3 ratio, we explore how solvent complexation and hydrogen (H)-abstraction processes proceed under collective cavity coupling strengths ranging from 55 to 85 cm-1. Reaction rates remain unchanged for all extracavity, on-resonance, and off-resonance cavity coupling conditions, regardless of coupling strength. These results suggest that insufficient vibrational cavity coupling strength may not be the determining factor for the negligible cavity effects observed previously in H-abstraction reactions of CN with CHCl3.

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.

Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities

It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.

Theoretical formulation of chemical equilibrium under vibrational strong coupling

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

Machine Learning for Polaritonic Chemistry: Accessing Chemical Kinetics

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

Non-Polaritonic Effects in Cavity-Modified Photochemistry

Strong coupling of molecules to vacuum fields is widely reported to lead to modified chemical properties such as reaction rates. However, some recent attempts to reproduce infrared strong coupling results have not been successful, suggesting that factors other than strong coupling may sometimes be involved. In the first vacuum-modified chemistry experiment, changes to a molecular photoisomerization process in the ultraviolet-visible spectral range are attributed to strong coupling of the molecules to visible light. Here, this process is re-examined, finding significant variations in photoisomerization rates consistent with the original work. However, there is no evidence that these changes need to be attributed to strong coupling. Instead, it is suggested that the photoisomerization rates involved are most strongly influenced by the absorption of ultraviolet radiation in the cavity. These results indicate that care must be taken to rule out non-polaritonic effects before invoking strong coupling to explain any changes of properties arising in cavity-based experiments.

Cavity Click Chemistry: Cavity-Catalyzed Azide-Alkyne Cycloaddition

Click chemistry, which refers to chemical reactions that are fast and selective with high product yields, has become a powerful approach in organic synthesis and chemical biology. Due to the cytotoxicity of the transition metals employed in click chemistry reactions, a search for novel metal-free alternatives continues. Herein, we demonstrate that an optical cavity can be utilized as a metal-free alternative in the click chemistry cycloaddition reaction between cyanoacetylene and formylazide using the quantum electrodynamics coupled cluster method. We show that by changing the molecular orientation with respect to the polarization of the cavity mode(s), the reaction can be selectively catalyzed to form a major 1,4-disubstituted or 1,5-disubstituted product. This work highlights that a cavity has the same effect on the investigated cycloaddition as the transition metal catalysts traditionally employed in click chemistry reactions. We expect our findings to further stimulate research on cavity-assisted click chemistry reactions.

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

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

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

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

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.

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

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

How Quantum is the Resonance Behavior in Vibrational Polariton Chemistry?

Recent experiments in polariton chemistry have demonstrated that reaction rates can be modified by vibrational strong coupling to an optical cavity mode. Importantly, this modification occurs only when the frequency of the cavity mode is tuned to closely match a molecular vibrational frequency. This sharp resonance behavior has proved to be difficult to capture theoretically. Only recently did Lindoy et al. [ Nat. Commun. 2023, 14, 2733] report the first instance of a sharp resonant effect in the cavity-modified rate simulated in a model system using exact quantum dynamics. We investigate the same model system with a different method, ring-polymer molecular dynamics (RPMD), which captures quantum statistics but treats dynamics classically. We find that RPMD does not reproduce this sharp resonant feature at the well frequency, and we discuss the implications of this finding for future studies of vibrational polariton chemistry.

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.

QED Theory for Controlling the Molecule-Cavity Interaction: From Solvable Analytical Models to Realistic Ones

The study of the interactions of chemical systems in a cavity and the ability to control the reactions inside the cavities become an evolving and hot field of research. Despite that, there is still a significant gap between experiment and theory. Herein, we aim to bridge this gap by starting with the analysis of solvable analytical models for reactions inside a cavity, then continuing to realistic models for many molecules inside a single mode and in a multimode cavity. In addition, we investigate different ways to control the strength of the molecule-cavity coupling term, which in turn allows controlling chemical reactions. Our analysis can benefit the development of ab initio computational methods to simulate molecular systems in polariton cavities; in addition, we show how to parameterize the model Hamiltonians in order to simulate a specific molecular system. Finally, we demonstrate the possibility of achieving isomerization, in case it is prohibited out of the cavity, by placing the reaction inside a cavity.

Modification of ground-state chemical reactivity via light-matter coherence in infrared cavities

Reaction-rate modifications for chemical processes due to strong coupling between reactant molecular vibrations and the cavity vacuum have been reported; however, no currently accepted mechanisms explain these observations. In this work, reaction-rate constants were extracted from evolving cavity transmission spectra, revealing resonant suppression of the intracavity reaction rate for alcoholysis of phenyl isocyanate with cyclohexanol. We observed up to an 80% suppression of the rate by tuning cavity modes to be resonant with the reactant isocyanate (NCO) stretch, the product carbonyl (CO) stretch, and cooperative reactant-solvent modes (CH). These results were interpreted using an open quantum system model that predicted resonant modifications of the vibrational distribution of reactants from canonical statistics as a result of light-matter quantum coherences, suggesting links to explore between chemistry and quantum science.

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.

Quantum dynamical effects of vibrational strong coupling in chemical reactivity

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

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.

Vibrational Energy Redistribution and Polaritonic Fermi Resonances in the Strong Coupling Regime

Intramolecular vibrational energy redistribution (IVR) plays a significant role in cavity-modified chemical reaction rates. As such, understanding the fundamental mechanisms by which the cavity modifies the IVR pathways is a fundamental step toward engineering the effect of the confined electromagnetic modes on the outcome of chemical processes. Here we consider an ensemble of M two-mode molecules with intramolecular anharmonic couplings interacting with an infrared cavity mode and consider their quantum dynamics and infrared spectra. Polaritonic Fermi resonances involving fundamental and overtone states of the polaritonic subsystem mediate efficient energy transfer pathways between otherwise off-resonant molecular states. These pathways are of collective nature, yet enabled by the intramolecular anharmonic couplings. Hence, through polaritonic Fermi resonances, cavity excitation can efficiently spread toward low-frequency modes while becoming delocalized over several molecules.

Dissociation dynamics of a diatomic molecule in an optical cavity

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

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

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

Chemical reactivity under collective vibrational strong coupling

Recent experiments of chemical reactions in optical cavities have shown great promise to alter and steer chemical reactions, but still remain poorly understood theoretically. In particular, the origin of resonant effects between the cavity and certain vibrational modes in the collective limit is still subject to active research. In this paper, we study the unimolecular dissociation reactions of many molecules, collectively interacting with an infrared cavity mode, through their vibrational dipole moment. We find that the reaction rate can slow down by increasing the number of aligned molecules, if the cavity mode is resonant with a vibrational mode of the molecules. We also discover a simple scaling relation that scales with the collective Rabi splitting, to estimate the onset of reaction rate modification by collective vibrational strong coupling and numerically demonstrate these effects for up to 104 molecules.

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.

Interference between Molecular and Photon Field-Mediated Electron Transfer Coupling Pathways in Cavities

Cavity polaritonics creates novel opportunities to direct chemical reactions. Electron transfer (ET) reactions are among the simplest reactions, and they underpin energy conversion. New strategies to manipulate and direct electron flow at the nanoscale are of particular interest in biochemistry, energy science, bioinspired materials science, and chemistry. We show that optical cavities can modulate electron transfer pathway interferences and ET rates in donor-bridge-acceptor (DBA) systems. We derive the rate for DBA electron transfer when the molecules are coupled to cavity modes, emphasizing novel cavity-induced pathway interferences with the molecular electronic coupling pathways, as these interferences allow a new kind of ET rate tuning. The interference between the cavity-induced coupling pathways and the intrinsic molecular coupling pathway is dependent on the cavity properties. Thus, manipulating the interference between the cavity-induced DA coupling and the bridge-mediated coupling offers an approach to direct and manipulate charge flow at the nanoscale.

Polaritonic Chemistry from First Principles via Embedding Radiation Reaction

The coherent interaction of a large collection of molecules with a common photonic mode results in strong light-matter coupling, a feature that has proven highly beneficial for chemistry and has introduced the research topics polaritonic and QED chemistry. Here, we demonstrate an embedding approach to capture the collective nature while retaining the full ab initio representation of single molecules─an approach ideal for polaritonic chemistry. The accuracy of the embedding radiation-reaction ansatz is demonstrated for time-dependent density-functional theory. Then, by virtue of a simple proton-tunneling model, we illustrate that the influence of collective strong coupling on chemical reactions features a nontrivial dependence on the number of emitters and can alternate between strong catalyzing and an inhibiting effect. Bridging classical electrodynamics, quantum optical descriptions, and the ab initio description of realistic molecules, this work can serve as a guiding light for future developments and investigations in the quickly growing fields of QED chemistry and QED material design.

Resonant Cavity Modification of Ground-State Chemical Kinetics

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