Resonant Cavity Modification of Ground-State Chemical Kinetics

Simulating Cavity-Modified Electron Transfer Dynamics on NISQ Computers

We present an algorithm based on the quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) method for simulating cavity-modified electron transfer dynamics on noisy intermediate-scale quantum (NISQ) computers. The utility and accuracy of the proposed methodology is demonstrated on a model for the photoinduced intramolecular electron transfer reaction within the carotenoid-porphyrin-C60 molecular triad in tetrahydrofuran (THF) solution. The electron transfer rate is found to increase significantly with increasing coupling strength between the molecular system and the cavity. The rate process is also seen to shift from overdamped monotonic decay to under-damped oscillatory dynamics. The electron transfer rate is seen to be highly sensitive to the cavity frequency, with the emergence of a resonance cavity frequency for which the effect of coupling to the cavity is maximal. Finally, an implementation of the algorithm on the IBM Osaka quantum computer is used to demonstrate how TT-TFD-based electron transfer dynamics can be simulated accurately on NISQ computers.

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.

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.

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.

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.

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

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

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

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

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.

Recent Developments in Kramers' Theory of Reaction Rates

In this short review, we provide an update of recent developments in Kramers' theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers' theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.

On the Mechanism of Polaritonic Rate Suppression from Quantum Transition Paths

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

Investigating Molecular Exciton Polaritons Using Ab Initio Cavity Quantum Electrodynamics

Coupling molecules to the quantized radiation field inside an optical cavity creates a set of new photon-matter hybrid states called polariton states. We combine electronic structure theory with quantum electrodynamics (QED) to investigate molecular polaritons using ab initio simulations. This framework joins unperturbed electronic adiabatic states with the Fock state basis to compute the eigenstates of the QED Hamiltonian. The key feature of this "parametrized QED" approach is that it provides the exact molecule-cavity interactions, limited by only approximations made in the electronic structure. Using time-dependent density functional theory, we demonstrated comparable accuracy with QED coupled cluster benchmark results for predicting potential energy surfaces in the ground and excited states and showed selected applications to light-harvesting and light-emitting materials. We anticipate that this framework will provide a set of general and powerful tools that enable direct ab initio simulation of exciton polaritons in molecule-cavity hybrid systems.

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.

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.

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.

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.