Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

Optical-cavity manipulation strategies of singlet fission systems mediated by conical intersections: Insights from fully quantum simulations

We offer a theoretical perspective on simulation and engineering of polaritonic conical-intersection-driven singlet-fission (SF) materials. We begin by examining fundamental models, including Tavis-Cummings and Holstein-Tavis-Cummings Hamiltonians, exploring how disorder, non-Hermitian effects, and finite temperature conditions impact their dynamics, setting the stage for studying conical intersections and their crucial role in SF. Using rubrene as an example and applying the numerically accurate Davydov Ansatz methodology, we derive dynamic and spectroscopic responses of the system and demonstrate key mechanisms capable of SF manipulation, viz. cavity-induced enhancement/weakening/suppression of SF, population localization on the singlet state via engineering cavity-mode excitation, polaron/polariton decoupling, and collective enhancement of SF. We outline unsolved problems and challenges in the field and share our views on the development of the future lines of research. We emphasize the significance of careful modeling of cascades of polaritonic conical intersections in high excitation manifolds and envisage that collective geometric phase effects may remarkably affect the SF dynamics and yield. We argue that the microscopic interpretation of the main regulatory mechanisms of polaritonic conical-intersection-driven SF can substantially deepen our understanding of this process, thereby providing novel ideas and solutions for improving conversion efficiency in photovoltaics.

2D Electronic Spectroscopy Uncovers 2D Materials: Theoretical Study of Nanocavity-Integrated Monolayer Semiconductors

Transition metal dichalcogenides (TMDs) have emerged as promising 2D semiconductors due to their strong excitonic effects, spin-valley coupling, and tunable light-matter interactions. Here, we employ a fully quantum, numerically "exact" multi-Davydov Ansatz approach to simulate two-dimensional electronic spectroscopy signals in hBN-encapsulated WSe2 monolayers integrated with a tunable nanocavity. By incorporating both momentum-bright and momentum-dark excitons alongside detailed phonon dispersion, our model captures vibrational resonances and exciton-polariton behaviors, enabling the evaluation of beating maps (3D spectra) that disentangle ground-state bleach and stimulated emission pathways. The results highlight the essential role of vibronic coherence in TMD monolayers and offer quantitative guidance for the design of next-generation optoelectronic devices based on cavity-coupled 2D materials.

Radiative pumping vs vibrational relaxation of molecular polaritons: a bosonic mapping approach

We present a formalism to study molecular polaritons based on the bosonization of molecular vibronic states. This formalism accommodates an arbitrary number of molecules N, excitations and internal vibronic structures, making it ideal for investigating molecular polariton processes accounting for finite N effects. We employ this formalism to rigorously derive radiative pumping and vibrational relaxation rates. We show that radiative pumping is the emission from incoherent excitons and divide its rate into transmitted and re-absorbed components. On the other hand, the vibrational relaxation rate in the weak linear vibronic coupling regime is composed of a O ( 1 / N ) contribution already accounted for by radiative pumping, and a O ( 1 / N 2 ) contribution from a second-order process in the single-molecule light-matter coupling that we call polariton-assisted Raman scattering. This scattering is enhanced when the difference between fluorescence and lower polariton frequencies matches a Raman-active excitation.

Polariton-induced Purcell effects via a reduced semiclassical electrodynamics approach

Recent experiments have demonstrated that polariton formation provides a novel strategy for modifying local molecular processes when a large ensemble of molecules is confined within an optical cavity. Herein, a numerical strategy based on coupled Maxwell-Schrödinger equations is examined for simulating local molecular processes in a realistic cavity structure under collective strong coupling. In this approach, only a few molecules, referred to as quantum impurities, are treated quantum mechanically, while the remaining macroscopic molecular layer and the cavity structure are modeled using dielectric functions. When a single electronic two-level system embedded in a Lorentz medium is confined in a two-dimensional Bragg resonator, our numerical simulations reveal a polariton-induced Purcell effect: the radiative decay rate of the quantum impurity is significantly enhanced by the cavity when the impurity frequency matches the polariton frequency, while the rate can sometimes be greatly suppressed when the impurity is near resonance with the bulk molecules forming strong coupling. In addition, this approach demonstrates that the cavity absorption of light exhibits Rabi-splitting-dependent suppression due to the inclusion of a realistic cavity structure. Our simulations also identify a fundamental limitation of this approach-an inaccurate description of polariton dephasing rates into dark modes. This arises because the dark-mode degrees of freedom are not explicitly included when most molecules are modeled using simple dielectric functions. As the polariton-induced Purcell effect alters molecular radiative decay differently from the Purcell effect under weak coupling, this polariton-induced effect may facilitate understanding the origin of polariton-modified photochemistry under electronic strong coupling.

Trajectory-based non-adiabatic simulations of the polariton relaxation dynamics

We benchmark the accuracy of various trajectory-based non-adiabatic methods in simulating the polariton relaxation dynamics under the collective coupling regime. The Holstein-Tavis-Cummings Hamiltonian is used to describe the hybrid light-matter system of N molecules coupled to a single cavity mode. We apply various recently developed trajectory-based methods to simulate the population relaxation dynamics by initially exciting the upper polariton state and benchmark the results against populations computed from exact quantum dynamical propagation using the hierarchical equations of motion approach. In these benchmarks, we have systematically varied the number of molecules N, light-matter detunings, and the light-matter coupling strengths. Our results demonstrate that the symmetrical quasi-classical method with γ correction and spin-mapping linearized semi-classical approaches yield more accurate polariton population dynamics than traditional mixed quantum-classical methods, such as the Ehrenfest and surface hopping techniques.

Blackbody Radiation and Thermal Effects on Chemical Reactions and Phase Transitions in Cavities

An important question in polariton chemistry is whether reacting molecules are in thermal equilibrium with their surroundings. If not, can experimental changes observed in reaction rates of molecules in a cavity (even without optical pumping) be attributed to a higher/lower temperature inside the cavity? In this work, we address this question by computing the temperature differences between reacting molecules inside a cavity and the air outside. We found this temperature difference to be negligible for most reactions. On the other hand, for phase transitions inside cavities, as the temperature of the material is actively maintained by a heating/cooling source in experiments, we show that cavities can modify observed transition temperatures when mirrors and cavity windows are ideal (nonabsorbing); however, this modification vanishes when real mirrors and windows are used. This conclusion relies on having a low contact resistance between mirrors and molecules. Finally, we find substantial differences in blackbody spectral energy density between free space and infrared cavities, which reveal resonance effects and could potentially play a role in explaining changes in the chemical reactivity in the dark.

Exploiting Quantum Light-Matter Interaction for Probing and Controlling Molecules

Quantum mechanical properties of light, such as time-energy entanglement, quadrature squeezing, and non-Poisson statistics, can be exploited to develop novel spectroscopic signals that enhance the signal strength and spectrotemporal resolution. Moreover, quantum light also provides nonclassical control knobs for controlling the outcome of a chemical reaction. Here, we provide a perspective on how quantum light-matter interaction can be exploited to probe and control molecular events.

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

Molecular exciton polaritons, hybrid states formed through the strong coupling of molecular electronic excitations with optical cavity modes, offer a powerful avenue for controlling photophysical and photochemical processes in molecular systems. Here, we present a semiclassical framework for investigating the dynamics of molecular exciton polaritons using the truncated Wigner approximation (TWA). This approach extends the prior TWA method developed for molecular vibration-polariton dynamics ( J. Chem. Theory Comput. 2024, 20, 3019-3027) by incorporating semiclassical treatment of quantum coherence between ground and excited molecular states. To validate the framework, we first apply it to a simplified system of two-level (spin-1/2) molecules without vibronic coupling, demonstrating strong agreement between semiclassical and fully quantum simulations in systems with a large molecular ensemble. We further extend the model to include molecular vibronic coupling, revealing the dynamic polaron decoupling effect, where the quantum coherence between molecular excitations persists under strong light-matter coupling. These findings provide critical insights into the collective behavior and coherence preservation in polaritonic systems with implications for designing cavity-mediated molecular processes.

Polariton spectra under the collective coupling regime. II. 2D non-linear spectra

In our previous work [Mondal et al., J. Chem. Phys. 162, 014114 (2025)], we developed several efficient computational approaches to simulate exciton-polariton dynamics described by the Holstein-Tavis-Cummings (HTC) Hamiltonian under the collective coupling regime. Here, we incorporated these strategies into the previously developed Lindblad-partially linearized density matrix (L-PLDM) approach for simulating 2D electronic spectroscopy (2DES) of exciton-polariton under the collective coupling regime. In particular, we apply the efficient quantum dynamics propagation scheme developed in Paper I to both the forward and the backward propagations in the PLDM and develop an efficient importance sampling scheme and graphics processing unit vectorization scheme that allow us to reduce the computational costs from O(K2)O(T3) to O(K)O(T0) for the 2DES simulation, where K is the number of states and T is the number of time steps of propagation. We further simulated the 2DES for an HTC Hamiltonian under the collective coupling regime and analyzed the signal from both rephasing and non-rephasing contributions of the ground state bleaching, excited state emission, and stimulated emission pathways.

Photon Many-Body Dispersion: Exchange-Correlation Functional for Strongly Coupled Light-Matter Systems

We introduce an electron-photon exchange-correlation functional for quantum electrodynamical density-functional theory (QEDFT). The approach, photon MBD (pMBD), is inspired by the many-body dispersion (MBD) method for weak intermolecular interactions, which is generalized to include both electronic and photonic (electromagnetic) degrees of freedom on the same footing. We demonstrate that pMBD accurately captures effects that arise in the context of strong light-matter interactions, such as anisotropic electron-photon interactions, beyond single-photon effects, and cavity-modulated van der Waals interactions. Moreover, we show that pMBD is computationally efficient and allows simulations of large complex systems coupled to optical cavities.

CUT-E as a 1/N expansion for multiscale molecular polariton dynamics

Molecular polaritons arise when the collective coupling between an ensemble of N molecules and an optical mode exceeds individual photon and molecular linewidths. The complexity of their description stems from their multiscale nature, where the local dynamics of each molecule can, in principle, be influenced by the collective behavior of the entire ensemble. To address this, we previously introduced a formalism called collective dynamics using truncated equations (CUT-E). CUT-E approaches the problem in two stages. First, it exploits permutational symmetries to obtain a substantial simplification of the problem. However, this is often insufficient for parameter regimes relevant to most experiments. Second, it takes the exact solution of the problem in the N → ∞ limit as a reference and derives systematic finite-N corrections. Here, we provide a novel derivation of CUT-E based on recently developed bosonization techniques. We lay down its connections with 1/N expansions that are ubiquitous in other fields of physics and present previously unexplored key aspects of this formalism, including various types of approximations and extensions to high-excitation manifolds.

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.

Quantum Dynamics Simulations of Exciton Polariton Transport

Recent experiments have shown that exciton transport can be significantly enhanced through hybridization with confined photonic modes in a cavity. The light-matter hybridization generates exciton-polariton (EP) bands, whose group velocity is significantly larger than the excitons. Dissipative mechanisms that affect the constituent states of EPs, such as exciton-phonon coupling and cavity loss, have been observed to reduce the group velocities in experiments. To elucidate the impacts of these dissipative mechanisms on polariton transport, we developed an efficient quantum dynamics approach that allows us to directly simulate polariton transport under the collective coupling regime and beyond long-wavelength approximation. Our numerical results suggest a renormalization of the group velocities with stronger exciton-phonon coupling strengths and a smaller Q-factor. We observe the transition from ballistic to diffusive propagation as well as the quality-factor-dependent behavior of the transient mean square displacement, agreeing well with the recent experimental measurements.

Impact of Dipole Self-Energy on Cavity-Induced Nonadiabatic Dynamics

The coupling of matter to the quantized electromagnetic field of a plasmonic or optical cavity can be harnessed to modify and control chemical and physical properties of molecules. In optical cavities, a term known as the dipole self-energy (DSE) appears in the Hamiltonian to ensure gauge invariance. The aim of this work is twofold. First, we introduce a method, which has its own merits and complements existing methods, to compute the DSE. Second, we study the impact of the DSE on cavity-induced nonadiabatic dynamics in a realistic system. For that purpose, various matrix elements of the DSE are computed as functions of the nuclear coordinates and the dynamics of the system after laser excitation is investigated. The cavity is known to induce conical intersections between polaritons, which gives rise to substantial nonadiabatic effects. The DSE is shown to slightly affect these light-induced conical intersections and, in particular, break their symmetry.

Molecular Assembly in Optical Cavities

Chemistry has traditionally focused on the synthesis of desired compounds, with organic synthesis being a key method for obtaining target molecules. In contrast, self-assembly -where molecules spontaneously organize into well-defined structures- has emerged as a powerful tool for fabricating intricate structures. Self-assembly was initially studied in biological systems but has been developed for synthetic methods, leading to the field of supramolecular chemistry, where non-covalent interactions/bonds guide molecular assembly. This has led to the development of complex molecular structures, such as metal-organic frameworks and hydrogen-bonded organic frameworks. Parallel to this field, cavity quantum electrodynamics (QED), developed in the mid-20th century, has recently intersected with molecular assembly. Early research in cavity strong coupling focused on inorganic solids and simple molecules, but has since extended to molecular assemblies. The strong coupling synergized with molecular assembly will generate new polaritonic phenomena and applications.

Toward Collective Chemistry under Strong Light-Matter Coupling

Collective strong light-matter coupling provides a versatile means to manipulate physicochemical properties of molecules and materials. Understanding collective polaritonic dynamics is hindered by the macroscopic number of molecules interacting collectively with photonic modes. We develop a many-body theory to investigate the spectroscopy and dynamics of a molecular ensemble embedded in an optical cavity in the collective strong coupling regime. This theory is constructed by a pseudoparticle representation of the molecular Hamiltonian, which maps the polaritonic Hamiltonian into a coupled fermion-boson model under particle number constraints. The mapped model is then analyzed using the nonequilibrium Green's function theory with the self-energy diagrams identified through a large N expansion. We demonstrate that in the thermodynamic limit, the necessary condition to have any collective effects is to have a macroscopic cavity field. Numerical illustrations are shown for the driven Tavis-Cummings model, which shows an excellent agreement with exact results.

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein-Tavis-Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

Multiple interacting photonic modes in strongly coupled organic microcavities

Room-temperature cavity quantum electrodynamics with molecular materials in optical cavities offers exciting prospects for controlling electronic, nuclear and photonic degrees of freedom for applications in physics, chemistry and materials science. However, achieving strong coupling with molecular ensembles typically requires high molecular densities and substantial electromagnetic-field confinement. These conditions usually involve a significant degree of molecular disorder and a highly structured photonic density of states. It remains unclear to what extent these additional complexities modify the usual physical picture of strong coupling developed for atoms and inorganic semiconductors. Using a microscopic quantum description of molecular ensembles in realistic multimode optical resonators, we show that the emergence of vacuum Rabi splitting in linear spectroscopy is a necessary but not sufficient metric of coherent admixing between light and matter. In low-finesse multi-mode situations, we find that molecular dipoles can be partially hybridized with photonic dissipation channels associated with off-resonant cavity modes. These vacuum-induced dissipative processes ultimately limit the extent of light-matter coherence that the system can sustain.This article is part of the theme issue 'The quantum theory of light'.

Photon-mediated energy transfer between molecules and atoms in a cavity: A numerical study

The molecular energy transfer is crucial for many different physicochemical processes. The efficiency of traditional resonance energy transfer relies on dipole-dipole distance between molecules and becomes negligible when the distance is larger than ∼10 nm, which is difficult to overcome. Cavity polariton, formed when placing molecules inside the cavity, is a promising way to surmount the distance limit. By hybridizing a two-level atom (TLA) and a lithium fluoride (LiF) molecule with a cavity, we numerically simulate the reaction process and the energy transfer between them. Our results show that the TLA can induce a deep potential well, which can be seen as a replica of the potential energy surface of bare LiF, acting as a reservoir to absorb/release the molecular kinetic energy. In addition, the energy transfer shows a molecular nuclear kinetic energy dependent behavior, namely, more nuclear kinetic energy igniting more energy transfer. These findings show us a promising way to manipulate the energy transfer process within the cavity using an intentional TLA, which can also serve as a knob to control the reaction process.

Revisiting cavity-coupled 2DIR: A classical approach implicates reservoir modes

Significant debate surrounds the origin of nonlinear optical responses from cavity-coupled molecular vibrations. Several groups, including our own, have previously assigned portions of the nonlinear response to polariton excited-state transitions. Here, we report a new method to approximate two-dimensional infrared spectra under vibrational strong coupling, which properly accounts for inhomogeneous broadening. We find excellent agreement between this model and experimental results for prototypical systems exhibiting both homogeneous and inhomogeneous broadening. This work implies that reservoir excitation is solely responsible for all optical response measured after the polariton modes dephase and represents an important new method for predicting and interpreting the nonlinear optical response of molecular vibrational polaritons.

Theory of molecular emission power spectra. III. Non-Hermitian interactions in multichromophoric systems coupled with polaritons

Based on our previous study [Wang et al., J. Chem. Phys. 153, 184102 (2020)], we generalize the theory of molecular emission power spectra (EPS) from one molecule to multichromophoric systems in the framework of macroscopic quantum electrodynamics. This generalized theory is applicable to ensembles of molecules, providing a comprehensive description of the molecular spontaneous emission spectrum in arbitrary inhomogeneous, dispersive, and absorbing media. In the far-field region, the analytical formula of EPS can be expressed as the product of a lineshape function (LF) and an electromagnetic environment factor (EEF). To demonstrate the polaritonic effect on multichromophoric systems, we simulate the LF and EEF for one to three molecules weakly coupled to surface plasmon polaritons above a silver surface. Our analytical expressions show that the peak broadening originates from not only the spontaneous emission rates but also the imaginary part of resonant dipole-dipole interactions (non-Hermitian interactions), which is associated with the superradiance of molecular aggregates, indicating that the superradiance rate can be controlled through an intermolecular distance and the design of dielectric environments. This study presents an alternative approach to directly analyze the hybrid-state dynamics of multichromophoric systems coupled with polaritons.

Room-Temperature Exciton Polaritons in a Monolayer Molecular Crystal

Strong coupling between excitons and photons in optical microcavities leads to the formation of exciton polaritons, which maintain both the coherence of light and the interaction of matter. Recently, atomically thin monolayer semiconductors with a large exciton oscillator strength and high exciton binding energy have been widely used for realizing room-temperature exciton polaritons. Here, we demonstrated room-temperature exciton polaritons with a monolayer molecular crystal. The molecular monolayers behave as J-aggregates with comparable oscillator strength and narrow line width as inorganic monolayers, enabling exciton-photon strong coupling at the monolayer limit. Moreover, the coupling strength can be tuned systematically via engineering the in-plane polarization or by using a vertical stack of multiple molecular monolayers. Our research provides a new material platform for realizing strong light-matter interactions inside optical microcavities at room temperature and may motivate the development of molecular-crystal-based exciton-polaritonic devices with novel functions and new possibilities.

Plasmon-Exciton Strong Coupling in Colloidal Au Nanocubes with Layered Molecular J-Aggregates

Strong coupling between light and matter forms hybrid states, such as exciton-polaritons, which are crucial for advancements in quantum science and technology. Plasmonic metal nanoparticles, with their ultrasmall mode volumes, are effective for generating these states, but the coupling strength is often limited by surface saturation of excitonic materials. Additionally, cubic nanoparticles, which can generate strong local fields, have not been systematically explored. This study investigates strong coupling in Au nanocubes (AuNCs) coupled with J-aggregates, observing spectral splitting in both extinction and scattering spectra. Our findings suggest that smaller AuNCs, with higher-quality resonances and reduced mode volumes, achieve stronger coupling. Furthermore, a layer-by-layer (LBL) coating of J-aggregates on AuNCs results in a ∼21% increase in coupling strength. Simulations reveal the mechanism behind the enhanced coupling and confirm that the layering method effectively increases coupling, surpassing the limitations of the finite surface area of nanoparticles.

Mechanism of Molecular Polariton Decoherence in the Collective Light-Matter Couplings Regime

Molecular polaritons, the hybridization of electronic states in molecules with photonic excitation inside a cavity, play an important role in fundamental quantum science and technology. Understanding the decoherence mechanism of molecular polaritons is among the most significant fundamental questions. We theoretically demonstrate that hybridizing many molecular excitons in a cavity protects the overall quantum coherence from phonon-induced decoherence. The polariton coherence time can be prolonged up to 100 fs with a realistic collective Rabi splitting and quality factor at room temperature, compared to the typical electronic coherence time which is around 15 fs. Our numerically exact simulations and analytic theory suggest that the dominant decoherence mechanism is the population transfer from the upper polariton state to the dark state manifold. Increasing the collective coupling strength will increase the energy gap between these two sets of states and thus prolong the coherence lifetime. We further derived valuable scaling relations that directly indicate how polariton coherence depends on the number of molecules, Rabi splittings, and light-matter detunings.

Hamiltonian non-Hermicity: Accurate dynamics with the multiple Davydov D2Ansätze

We examine the applicability of the numerically accurate method of time dependent variation with multiple Davydov Ansätze (mDA) to non-Hermitian systems. As illustrative examples, three systems of interest have been studied, a non-Hermitian system of dissipative Landau-Zener transitions, a non-Hermitian multimode Jaynes-Cummings model, and a dissipative Holstein-Tavis-Cummings model, all of which are shown to be effectively described by the mDA method. Our findings highlight the versatility of the mDA as a powerful numerical tool for investigating complex many-body non-Hermitian systems, which can be extended to explore diverse phenomena such as skin effects, excited-state dynamics, and spectral topology in the non-Hermitian field.

Perturbative analysis of the coherent state transformation in ab initio cavity quantum electrodynamics

Experimental demonstrations of modified chemical structure and reactivity under strong light-matter coupling have spurred theoretical and computational efforts to uncover underlying mechanisms. Ab initio cavity quantum electrodynamics (QED) combines quantum chemistry with cavity QED to investigate these phenomena in detail. Unitary transformations of ab initio cavity QED Hamiltonians have been used to make them more computationally tractable. We analyze one such transformation, the coherent state transformation, using perturbation theory. Applying perturbation theory up to third order for ground state energies and potential energy surfaces of several molecular systems under electronic strong coupling, we show that the coherent state transformation yields better agreement with exact ground state energies. We examine one specific case using perturbation theory up to ninth order and find that coherent state transformation performs better up to fifth order but converges more slowly to the exact ground state energy at higher orders. In addition, we apply perturbation theory up to second order for cavity mode states under bilinear coupling, elucidating how the coherent state transformation accelerates the convergence of the photonic subspace toward the complete basis limit and renders molecular ion energies origin invariant. These findings contribute valuable insights into computational advantages of the coherent state transformation in the context of ab initio cavity quantum electrodynamics methods.

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.

Role of cavity strong coupling on single electron transfer reaction rate at electrode-electrolyte interface

The physicochemical properties of molecules can be modulated through polariton formation under strong electromagnetic confinement. Here, we discuss the possibility of exploiting this phenomenon to increase the electron transfer rate at an electrode-electrolyte interface. Electron transfer theory under strong electromagnetic confinement can be extended to the electrode-electrolyte interface, and single-electron transfer reactions can be simulated using Gerischer's theory. Although single electron transfer in free space is well described using Marcus theory, the vacuum electric field can facilitate an additional electron transfer pathway via virtual photon excitation under cavity strong coupling conditions. Therefore, this binary reaction pathway for single electron transfer can yield a quasi-two-particle electron transfer process. This quantum behavior can dominate when the mode volume is small and when there are a large number of molecules in the vacuum electric field. Exploitation of polaritons in single electron transfer reactions can lead to enhanced electrochemical energy conversion systems.

Comparing parameterized and self-consistent approaches to ab initio cavity quantum electrodynamics for electronic strong coupling

Molecules under strong or ultra-strong light-matter coupling present an intriguing route to modify chemical structure, properties, and reactivity. A rigorous theoretical treatment of such systems requires handling matter and photon degrees of freedom on an equal quantum mechanical footing. In the regime of molecular electronic strong or ultra-strong coupling to one or a few molecules, it is desirable to treat the molecular electronic degrees of freedom using the tools of ab initio quantum chemistry, yielding an approach referred to as ab initio cavity quantum electrodynamics (ai-QED), where the photon degrees of freedom are treated at the level of cavity QED. We analyze two complementary approaches to ai-QED: (1) a parameterized ai-QED, a two-step approach where the matter degrees of freedom are computed using existing electronic structure theories, enabling the construction of rigorous ai-QED Hamiltonians in a basis of many-electron eigenstates, and (2) self-consistent ai-QED, a one-step approach where electronic structure methods are generalized to include coupling between electronic and photon degrees of freedom. Although these approaches are equivalent in their exact limits, we identify a disparity between the projection of the two-body dipole self-energy operator that appears in the parameterized approach and its exact counterpart in the self-consistent approach. We provide a theoretical argument that this disparity resolves only under the limit of a complete orbital basis and a complete many-electron basis for the projection. We present numerical results highlighting this disparity and its resolution in a particularly simple molecular system of helium hydride cation, where it is possible to approach these two complete basis limits simultaneously. In this same helium hydride system, we examine and compare the practical issue of the computational cost required to converge each approach toward the complete orbital and many-electron bases limit. Finally, we assess the aspect of photonic convergence for polar and charged species, finding comparable behavior between parameterized and self-consistent approaches.

Impact of Cavity Length Non-uniformity on Reaction Rate Extraction in Strong Coupling Experiments

Reports of altered chemical phenomena under vibrational strong coupling, including reaction rates, product distributions, intermolecular forces, and cavity-mediated vibrational energy transfer, have been met with a great deal of skepticism due to several irreproducible results and the lack of an accepted theoretical framework. In this work, we add some insight by identifying a UV-vis measurement artifact that distorts observed absorption peak positions, amplitudes, and consequently, chemical reaction rates extracted in optical microcavities. We predict and characterize the behavior of this artifact using the Transfer Matrix (TM) method and confirm its presence experimentally. We then present a correction technique whereby an effective molar absorption coefficient is assigned to an absorbing species within the cavity. These revelations have important implications for many existing examples of cavity-modified chemistry and establishing best practices for carrying out robust future investigations.

Quantized embedding approaches for collective strong coupling-Connecting ab initio and macroscopic QED to simple models in polaritonics

Collective light-matter interactions have been used to control chemistry and energy transfer, yet accessible approaches that combine ab initio methodology with large many-body quantum optical systems are missing due to the fast increase in computational cost for explicit simulations. We introduce an accessible ab initio quantum embedding concept for many-body quantum optical systems that allows us to treat the collective coupling of molecular many-body systems effectively in the spirit of macroscopic quantum electrodynamics while keeping the rigor of ab initio quantum chemistry for the molecular structure. Our approach fully includes the quantum fluctuations of the polaritonic field and yet remains much simpler and more intuitive than complex embedding approaches such as dynamical mean-field theory. We illustrate the underlying assumptions by comparison to the Tavis-Cummings model. The intuitive application of the quantized embedding approach and its transparent limitations offer a practical framework for the field of ab initio polaritonic chemistry to describe collective effects in realistic molecular ensembles.

Electronic structure simulations in the cloud computing environment

The transformative impact of modern computational paradigms and technologies, such as high-performance computing (HPC), quantum computing, and cloud computing, has opened up profound new opportunities for scientific simulations. Scalable computational chemistry is one beneficiary of this technological progress. The main focus of this paper is on the performance of various quantum chemical formulations, ranging from low-order methods to high-accuracy approaches, implemented in different computational chemistry packages and libraries, such as NWChem, NWChemEx, Scalable Predictive Methods for Excitations and Correlated Phenomena, ExaChem, and Fermi-Löwdin orbital self-interaction correction on Azure Quantum Elements, Microsoft's cloud services platform for scientific discovery. We pay particular attention to the intricate workflows for performing complex chemistry simulations, associated data curation, and mechanisms for accuracy assessment, which is demonstrated with the Arrows automated workflow for high throughput simulations. Finally, we provide a perspective on the role of cloud computing in supporting the mission of leadership computational facilities.

Optical force and torque in near-field excitation of C3H6: A first-principles study using RT-TDDFT

Optical trapping is an effective tool for manipulating micrometer-sized particles, although its application to nanometer-sized particles remains difficult. The field of optical trapping has advanced significantly, incorporating more advanced techniques such as plasmonic structures. However, single-molecule trapping remains a challenge. To achieve a deeper understanding of optical forces acting on molecular systems, a first-principles approach to analyze the optical force on molecules interacting with a plasmonic field is crucial. In our study, the optical force and torque induced by the near-field excitation of C3H6 were investigated using real-time time-dependent density functional theory calculations on real-space grids. The near field from the scanning tunneling probe was adopted as the excitation source for the molecule. The optical force was calculated using the polarization charges induced in the molecule based on Lorentz force. While the optical force and torque calculated as functions of the light energy were in moderate agreement with the oscillator strengths obtained from the far-field excitation of C3H6, a closer correspondence was achieved with the power spectrum of the induced dipole moment using near-field excitation. Time-domain analysis of the optical force suggests that the simultaneous excitation of multiple excited states generally weakens the force because of mismatches between the directions of the induced polarization and the electric field. This study revealed a subtle damping mechanism for the optical force arising from intrinsic electronic states and the influence of beating.

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.

Non-equilibrium rate theory for polariton relaxation dynamics

We derive an analytic expression of the non-equilibrium Fermi's golden rule (NE-FGR) expression for a Holstein-Tavis-Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi's golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.

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

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

Cavity-Mediated Enhancement of the Energy Transfer in the Reduced Fenna-Matthews-Olson Complex

Strong light-matter interaction leads to the formation of hybrid polariton states and can alter the light-harvesting properties of natural photosynthetic systems without modifying their chemical structure. In the present study, we computationally investigate the effect of the resonant cavity on the efficiency and the rate of the population transfer in a quantum system coupled to the cavity and the dissipative environment. The parameters of the model system were chosen to represent the Fenna-Matthews-Olson natural light-harvesting complex reduced to the three essential sites. The dynamics of the total system was propagated using the hierarchical equations of motion. Our results show that the strong light-matter interaction can accelerate the population transfer process compared to the cavity-free case but at the cost of lowering the transfer efficiency. The transition to the strong coupling regime was found to coincide with the degeneracy of polariton eigenvalues. Our findings indicate the potential and the limit of tuning the energy transfer in already efficient natural light-harvesting systems.

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.

Cavity-Tuned Exciton Dynamics in Transition Metal Dichalcogenides Monolayers

A fully quantum, numerically accurate methodology is presented for the simulation of the exciton dynamics and time-resolved fluorescence of cavity-tuned two-dimensional (2D) materials at finite temperatures. This approach was specifically applied to a monolayer WSe2 system. Our methodology enabled us to identify the dynamical and spectroscopic signatures of polaronic and polaritonic effects and to elucidate their characteristic timescales across a range of exciton-cavity couplings. The approach employed can be extended to simulation of various cavity-tuned 2D materials, specifically for exploring finite temperature nonlinear spectroscopic signals.

Theory and quantum dynamics simulations of exciton-polariton motional narrowing

The motional narrowing effect has been extensively studied for cavity exciton-polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior and (2) the asymmetric linewidths for the upper polariton and the lower polariton. However, a minimal theoretical model that is clear and adequate to address all these effects as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein-Tavis-Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion approach. The results reveal that under collective light-matter coupling between a cavity mode and N molecules, the polariton linewidth scales as 1/N under the slow limit, while scales as 1/N under the fast limit, due to the polaron decoupling effect. Furthermore, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions [Eqs. (34) and (35)] agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton-polariton motional narrowing based on the HTC model.

i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations

Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.

Cavity Controlled Upconversion in CdSe Nanoplatelet Polaritons

Exciton-polaritons provide a versatile platform for investigating quantum electrodynamics effects in chemical systems, such as polariton-altered chemical reactivity. However, using polaritons in chemical contexts will require a better understanding of their photophysical properties under ambient conditions, where chemistry is typically performed. Here, we used cavity quality factor to control strong light-matter interactions and in particular the excited state dynamics of colloidal CdSe nanoplatelets (NPLs) coupled to a Fabry-Pérot optical cavity. With increasing cavity quality factor, we observe significant population of the upper polariton (UP) state, exemplified by the rare observation of substantial UP photoluminescence (PL). Excitation of the lower polariton (LP) states results in upconverted PL emission from the UP branch due to efficient exchange of population between the LP, UP and the reservoir of dark states present in collectively coupled polaritonic systems. In addition, we measure time scales for polariton dynamics ∼100 ps, implying great potential for NPL based polariton systems to affect photochemical reaction rates. State-of-the-art quantum dynamical simulations show outstanding quantitative agreement with experiments, and thus provide important insight into polariton photophysical dynamics of collectively coupled nanocrystal-based systems. These findings represent a significant step toward the development of practical polariton photochemistry platforms.

Kadanoff-Baym Equations for Interacting Systems with Dissipative Lindbladian Dynamics

The extraordinary quantum properties of nonequilibrium systems governed by dissipative dynamics have become a focal point in contemporary scientific inquiry. The nonequilibrium Green's functions (NEGF) theory provides a versatile method for addressing driven nondissipative systems, utilizing the powerful diagrammatic technique to incorporate correlation effects. We here present a second-quantization approach to the dissipative NEGF theory, reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation theory for many-body Lindblad operators, the formalism enables correlated and dissipative real-time simulations for the exploration of transient and steady-state changes in the electronic, transport, and optical properties of materials.

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.

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

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

Quantum rates in dissipative systems with spatially varying friction

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.

Room-temperature strong coupling between CdSe nanoplatelets and a metal-DBR Fabry-Pérot cavity

The generation of exciton-polaritons through strong light-matter interactions represents an emerging platform for exploring quantum phenomena. A significant challenge in colloidal nanocrystal-based polaritonic systems is the ability to operate at room temperature with high fidelity. Here, we demonstrate the generation of room-temperature exciton-polaritons through the coupling of CdSe nanoplatelets (NPLs) with a Fabry-Pérot optical cavity, leading to a Rabi splitting of 74.6 meV. Quantum-classical calculations accurately predict the complex dynamics between the many dark state excitons and the optically allowed polariton states, including the experimentally observed lower polariton photoluminescence emission, and the concentration of photoluminescence intensities at higher in-plane momenta as the cavity becomes more negatively detuned. The Rabi splitting measured at 5 K is similar to that at 300 K, validating the feasibility of the temperature-independent operation of this polaritonic system. Overall, these results show that CdSe NPLs are an excellent material to facilitate the development of room-temperature quantum technologies.

Mesoscale Molecular Simulations of Fabry-Pérot Vibrational Strong Coupling

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

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.

Cavity Quantum Electrodynamics Enables para- and ortho-Selective Electrophilic Bromination of Nitrobenzene

Coupling molecules to a quantized radiation field inside an optical cavity has shown great promise to modify chemical reactivity. In this work, we show that the ground-state selectivity of the electrophilic bromination of nitrobenzene can be fundamentally changed by strongly coupling the reaction to the cavity, generating ortho- or para-substituted products instead of the meta product. Importantly, these are products that are not obtained from the same reaction outside the cavity. A recently developed ab initio approach was used to theoretically compute the relative energies of the cationic Wheland intermediates, which indicate the kinetically preferred bromination site for all products. Performing an analysis of the ground-state electron density for the Wheland intermediates inside and outside the cavity, we demonstrate how strong coupling induces reorganization of the molecular charge distribution, which in turn leads to different bromination sites directly dependent on the cavity conditions. Overall, the results presented here can be used to understand cavity induced changes to ground-state chemical reactivity from a mechanistic perspective as well as to directly connect frontier theoretical simulations to state-of-the-art, but realistic, experimental cavity conditions.