Cavity-Correlated Electron-Nuclear Dynamics from First Principles

Reverse Intersystem Crossing Dynamics in Vibronically Modulated Inverted Singlet-Triplet Gap System: A Wigner Phase Space Study

We inspect the origin of the inverted singlet-triplet gap (INVEST) and slow change in the reverse intersystem crossing (rISC) rate with temperature, as recently observed. A Wigner phase space study reveals that, though INVEST is found at equilibrium geometry, variation in the exchange interaction and the doubles-excitation for other geometries in the harmonic region leads to non-INVEST behavior. This highlights the importance of nuclear degrees of freedom for the INVEST phenomenon, and in this case, geometric puckering of the studied molecule determines INVEST and the associated rISC dynamics.

Do Molecular Geometries Change Under Vibrational Strong Coupling?

As pioneering experiments have shown, strong coupling between molecular vibrations and light modes in an optical cavity can significantly alter molecular properties and even affect chemical reactivity. However, the current theoretical description is limited and far from complete. To explore the origin of this exciting observation, we investigate how the molecular structure changes under strong light-matter coupling using an ab initio method based on the cavity Born-Oppenheimer Hartree-Fock ansatz. By optimizing H2O and H2O2 resonantly coupled to cavity modes, we study the importance of reorientation and geometric relaxation. In addition, we show that the inclusion of one or two cavity modes can change the observed results. On the basis of our findings, we derive a simple concept to estimate the effect of the cavity interaction on the molecular geometry using the molecular polarizability and the dipole moments.

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

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

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.

Simulating the Excited-State Dynamics of Polaritons with Ab Initio Multiple Spawning

Over the past decade, there has been a growth of interest in polaritonic chemistry, where the formation of hybrid light-matter states (polaritons) can alter the course of photochemical reactions. These hybrid states are created by strong coupling between molecules and photons in resonant optical cavities and can even occur in the absence of light when the molecule is strongly coupled with the electromagnetic fluctuations of the vacuum field. We present a first-principles model to simulate nonadiabatic dynamics of such polaritonic states inside optical cavities by leveraging graphical processing units (GPUs). Our first implementation of this model is specialized for a single molecule coupled to a single-photon mode confined inside the optical cavity but with any number of excited states computed using complete active space configuration interaction (CASCI) and a Jaynes-Cummings-type Hamiltonian. Using this model, we have simulated the excited-state dynamics of a single salicylideneaniline (SA) molecule strongly coupled to a cavity photon with the ab initio multiple spawning (AIMS) method. We demonstrate how the branching ratios of the photodeactivation pathways for this molecule can be manipulated by coupling to the cavity. We also show how one can stop the photoreaction from happening inside of an optical cavity. Finally, we also investigate cavity-based control of the ordering of two excited states (one optically bright and the other optically dark) inside a cavity for a set of molecules, where the dark and bright states are close in energy.

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

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

Cavity-Modified Chemiluminescent Reaction of Dioxetane

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

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

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

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics

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

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

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

Light-responsive organic polaritons from first principles

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

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

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

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

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.

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

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

Polaritonic Chemistry from First Principles via Embedding Radiation Reaction

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

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

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

Frequency-Dependent Sternheimer Linear-Response Formalism for Strongly Coupled Light-Matter Systems

The rapid progress in quantum-optical experiments, especially in the field of cavity quantum electrodynamics and nanoplasmonics, allows one to substantially modify and control chemical and physical properties of atoms, molecules, and solids by strongly coupling to the quantized field. Alongside such experimental advances has been the recent development of ab initio approaches such as quantum electrodynamical density-functional theory (QEDFT), which is capable of describing these strongly coupled systems from first principles. To investigate response properties of relatively large systems coupled to a wide range of photon modes, ab initio methods that scale well with system size become relevant. In light of this, we extend the linear-response Sternheimer approach within the framework of QEDFT to efficiently compute excited-state properties of strongly coupled light-matter systems. Using this method, we capture features of strong light-matter coupling both in the dispersion and absorption properties of a molecular system strongly coupled to the modes of a cavity. We exemplify the efficiency of the Sternheimer approach by coupling the matter system to the continuum of an electromagnetic field. We observe changes in the spectral features of the coupled system as Lorentzian line shapes turn into Fano resonances when the molecule interacts strongly with the continuum of modes. This work provides an alternative approach for computing efficiently excited-state properties of large molecular systems interacting with the quantized electromagnetic field.

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalize recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed based on well-established methods from molecular dynamics. It suggests the emergence of cavity-induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe that the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling from the collective quantum interpretation toward a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions toward a refined description of cavity-modified chemistry are introduced in the context of QEDFT, and future directions of the field are sketched.

Ab Initio Linear-Response Approach to Vibro-Polaritons in the Cavity Born-Oppenheimer Approximation

Recent years have seen significant developments in the study of strong light-matter coupling including the control of chemical reactions by altering the vibrational normal modes of molecules. In the vibrational strong coupling regime, the normal modes of the system become hybrid modes which mix nuclear, electronic, and photonic degrees of freedom. First-principles methods capable of treating light and matter degrees of freedom on the same level of theory are an important tool in understanding such systems. In this work, we develop and apply a generalized force constant matrix approach to the study of mixed vibration-photon (vibro-polariton) states of molecules based on the cavity Born-Oppenheimer approximation and quantum-electrodynamical density-functional theory. With this method, vibro-polariton modes and infrared spectra can be computed via linear-response techniques analogous to those widely used for conventional vibrations and phonons. We also develop an accurate model that highlights the consistent treatment of cavity-coupled electrons in the vibrational strong coupling regime. These electronic effects appear as new terms previously disregarded by simpler models. This effective model also allows for an accurate extrapolation of single and two molecule calculations to the collective strong coupling limit of hundreds of molecules. We benchmark these approaches for single and many CO2 molecules coupled to a single photon mode and the iron pentacarbonyl Fe(CO)5 molecule coupled to a few photon modes. Our results are the first ab initio results for collective vibrational strong coupling effects. This framework for efficient computations of vibro-polaritons paves the way to a systematic description and improved understanding of the behavior of chemical systems in vibrational strong coupling.

Quantum Simulations of Vibrational Strong Coupling via Path Integrals

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. This result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.

Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution

While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.

Shortcut to Self-Consistent Light-Matter Interaction and Realistic Spectra from First Principles

We introduce a simple approach to how an electromagnetic environment can be efficiently embedded into state-of-the-art electronic structure methods, taking the form of radiation-reaction forces. We demonstrate that this self-consistently provides access to radiative emission, natural linewidth, Lamb shifts, strong coupling, electromagnetically induced transparency, Purcell-enhanced and superradiant emission. As an example, we illustrate its seamless integration into time-dependent density-functional theory with virtually no additional cost, presenting a convenient shortcut to light-matter interactions.

Semiclassical Real-Time Nuclear-Electronic Orbital Dynamics for Molecular Polaritons: Unified Theory of Electronic and Vibrational Strong Couplings

Molecular polaritons have become an emerging platform for remotely controlling molecular properties through strong light-matter interactions. Herein, a semiclassical approach is developed for describing molecular polaritons by self-consistently propagating the real-time dynamics of classical cavity modes and a quantum molecular subsystem described by the nuclear-electronic orbital (NEO) method, where electrons and specified nuclei are treated quantum mechanically on the same level. This semiclassical real-time NEO approach provides a unified description of electronic and vibrational strong couplings and describes the impact of the cavity on coupled nuclear-electronic dynamics while including nuclear quantum effects. For a single o-hydroxybenzaldehyde molecule under electronic strong coupling, this approach shows that the cavity suppression of excited state intramolecular proton transfer is influenced not only by the polaritonic potential energy surface but also by the time scale of the chemical reaction. This work provides the foundation for exploring collective strong coupling in nuclear-electronic quantum dynamical systems within optical cavities.

Optical Cavity Manipulation and Nonlinear UV Molecular Spectroscopy of Conical Intersections in Pyrazine

Optical cavities provide a versatile platform for manipulating the excited-state dynamics of molecules via strong light-matter coupling. We employ optical absorption and two-multidimensional electronic spectroscopy simulations to investigate the effect of optical cavity coupling in the nonadiabatic dynamics of photoexcited pyrazine. We observe the emergence of a novel polaritonic conical intersection (PCI) between the electronic dark state and photonic surfaces as the cavity frequency is tuned. The PCI could significantly change the nonadiabatic dynamics of pyrazine by doubling the decay rate constant of the S₂ state population. Moreover, the absorption spectrum and excited-state dynamics could be systematically manipulated by tuning the strong light-matter interaction, e.g., the cavity frequency and cavity coupling strength. We propose that a tunable optical cavity-molecule system may provide promising approaches for manipulating the photophysical properties of molecules.

Non-Hermitian Cavity Quantum Electrodynamics - Configuration Interaction Singles Approach for Polaritonic Structure with ab initio Molecular Hamiltonians

We combine ab initio molecular electronic Hamiltonians with a cavity quantum electrodynamics model for dissipative photonic modes and apply mean-field theories to the ground- and excited-states of resulting polaritonic systems. In particular, we develop a non-Hermitian configuration interaction singles theory for mean-field ground- and excited-states of the molecular system strongly interacting with a photonic mode, and apply these methods to elucidating the phenomenology of paradigmatic polaritonic systems. We leverage the Psi4Numpy framework to yield open-source and accessible reference implementations of these methods.

Stochastic Variational Approach to Small Atoms and Molecules Coupled to Quantum Field Modes in Cavity QED

In this work, we present a stochastic variational calculation (SVM) of energies and wave functions of few particle systems coupled to quantum fields in cavity QED. The spatial wave function and the photon spaces are optimized by a random selection process. Using correlated basis functions, the SVM approach solves the problem accurately and opens the way to the same precision that is reached the nonlight coupled quantum systems. Examples for a two-dimensional trion and confined electrons as well as for the He atom and the H_{2} molecule are presented showing that the light-matter coupling drastically changes the electronic states.

Deformed explicitly correlated Gaussians

Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli-Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light-matter coupled systems in cavity QED.

Molecular Polaritonics: Chemical Dynamics Under Strong Light-Matter Coupling

Chemical manifestations of strong light-matter coupling have recently been a subject of intense experimental and theoretical studies. Here we review the present status of this field. Section 1 is an introduction to molecular polaritonics and to collective response aspects of light-matter interactions. Section 2 provides an overview of the key experimental observations of these effects, while Section 3 describes our current theoretical understanding of the effect of strong light-matter coupling on chemical dynamics. A brief outline of applications to energy conversion processes is given in Section 4. Pending technical issues in the construction of theoretical approaches are briefly described in Section 5. Finally, the summary in Section 6 outlines the paths ahead in this exciting endeavor. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Defect Polaritons from First Principles

Control over the optical properties of defects in solid-state materials is necessary for their application in quantum technologies. In this study, we demonstrate, from first principles, how to tune these properties via the formation of defect polaritons in an optical cavity. We show that the polaritonic splitting that shifts the absorption energy of the lower polariton is much higher than can be expected from a Jaynes-Cummings interaction. We also find that the absorption intensity of the lower polariton increases by several orders of magnitude, suggesting a possible route toward overcoming phonon-limited single-photon emission from defect centers. These findings are a result of an effective continuum of electronic transitions near the lowest-lying electronic transition that dramatically enhances the strength of the light-matter interaction. We expect our findings to spur experimental investigations of strong light-matter coupling between defect centers and cavity photons for applications in quantum technologies.

Changing Vibration Coupling Strengths of Liquid Acetonitrile with an Angle-Tuned Etalon

This work is the first report on nonzero molecular vibration-vibration coupling in an infrared cavity-vibration experiment. Vibration-vibration coupling strength is determined as a cavity mode of parallel spaced mirrors (etalon mode or fringe) is angle-tuned in the region between two vibrations of liquid acetonitrile which are Fermi coupled, namely, a CN stretch dominated vibration and a nearby combination band dominated by the symmetric CH₃ bend and C-C stretch. All other infrared cavity-vibration work to date involving more than one vibration has used a value of zero for vibration-vibration coupling; however, this work starts with Fermi coupled vibrations and reveals that there are changes in the vibration-vibration coupling and cavity-vibration couplings as the cavity mode is angle-tuned between the interacting vibrations. The ability to change fundamental vibrational dynamics within a cavity is an exciting result which helps to build a foundation for understanding molecular vibrational dynamics in parallel plate etalon cavities.

Boosting Self-interaction of Molecular Vibrations under Ultrastrong Coupling Condition

In this letter, we investigated the modification of the oscillator strength of an asymmetric stretching band of CS₂ by strong coupling to an infrared cavity photon. This is achieved by placing liquid CS₂ in a Fabry-Perot resonator and tuning the cavity mode position to match the molecular vibrational transition. Ultrastrong coupling leads to an increase in the effective oscillator strength of the asymmetric stretching band of CS₂. We proved this experimentally by taking the area ratio of the asymmetric stretching and combination bands by selectively coupling the former. A nonlinear increase in the oscillator strength of the asymmetric stretching band is observed upon varying the coupling strength. This is explained by a quantum mechanical model that predicts quadratic behavior under ultrastrong coupling conditions. These findings will set up a new paradigm for understanding chemical reaction modifications by vacuum field coupling.

Light-matter interaction of a molecule in a dissipative cavity from first principles

Cavity-mediated light-matter coupling can dramatically alter opto-electronic and physico-chemical properties of a molecule. Ab initio theoretical predictions of these systems need to combine non-perturbative, many-body electronic structure theory-based methods with cavity quantum electrodynamics and theories of open-quantum systems. Here, we generalize quantum-electrodynamical density functional theory to account for dissipative dynamics of the cavity and describe coupled cavity-single molecule interactions in the weak-to-strong-coupling regimes. Specifically, to establish this generalized technique, we study excited-state dynamics and spectral responses of benzene and toluene under weak-to-strong light-matter coupling. By tuning the coupling, we achieve cavity-mediated energy transfer between electronically excited states. This generalized ab initio quantum-electrodynamical density functional theory treatment can be naturally extended to describe cavity-mediated interactions in arbitrary electromagnetic environments, accessing correlated light-matter observables and thereby closing the gap between electronic structure theory, quantum optics, and nanophotonics.

Controlling the Photostability of Pyrrole with Optical Nanocavities

Strong light-matter coupling provides a new strategy to manipulate the non-adiabatic dynamics of molecules by modifying potential energy surfaces. The vacuum field of nanocavities can couple strongly with the molecular degrees of freedom and form hybrid light-matter states, termed as polaritons or dressed states. The photochemistry of molecules possessing intrinsic conical intersections can be significantly altered by introducing cavity couplings to create new conical intersections or avoided crossings. Here, we explore the effects of optical cavities on the photo-induced hydrogen elimination reaction of pyrrole. Wave packet dynamics simulations have been performed on the two-state, two-mode model of pyrrole, combined with the cavity photon mode. Our results show how the optical cavities assist in controlling the photostability of pyrrole and influence the reaction mechanism by providing alternative dissociation pathways. The cavity effects have been found to be intensely dependent on the resonance frequency. We further demonstrate the importance of the vibrational cavity couplings and dipole-self interaction terms in describing the cavity-modified non-adiabatic dynamics.

Challenges in Plasmonic Catalysis

The use of nanoplasmonics to control light and heat close to the thermodynamic limit enables exciting opportunities in the field of plasmonic catalysis. The decay of plasmonic excitations creates highly nonequilibrium distributions of hot carriers that can initiate or catalyze reactions through both thermal and nonthermal pathways. In this Perspective, we present the current understanding in the field of plasmonic catalysis, capturing vibrant debates in the literature, and discuss future avenues of exploration to overcome critical bottlenecks. Our Perspective spans first-principles theory and computation of correlated and far-from-equilibrium light-matter interactions, synthesis of new nanoplasmonic hybrids, and new steady-state and ultrafast spectroscopic probes of interactions in plasmonic catalysis, recognizing the key contributions of each discipline in realizing the promise of plasmonic catalysis. We conclude with our vision for fundamental and technological advances in the field of plasmon-driven chemical reactions in the coming years.

Simulating photodissociation reactions in bad cavities with the Lindblad equation

Optical cavities, e.g., as used in organic polariton experiments, often employ low finesse mirrors or plasmonic structures. The photon lifetime in these setups is comparable to the timescale of the nuclear dynamics governing the photochemistry. This highlights the need for including the effect of dissipation in the molecular simulations. In this study, we perform wave packet dynamics with the Lindblad master equation to study the effect of a finite photon lifetime on the dissociation of the MgH⁺ molecule model system. Photon lifetimes of several different orders of magnitude are considered to encompass an ample range of effects inherent to lossy cavities.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Role of Cavity Losses on Nonadiabatic Couplings and Dynamics in Polaritonic Chemistry

We present a non-Hermitian formulation of the polaritonic structure of azobenzene strongly coupled to a photonic mode that explicitly accounts for the fleeting nature of the photon-molecule interaction. This formalism reveals that the polaritonic nonadiabatic couplings that facilitate cis-trans isomerization can be dramatically modified by photonic dissipation. We perform Fewest-Switches Surface Hopping dynamics on the surfaces that derive from our non-Hermitian formalism and find that the polaritonic isomerization yields are strongly suppressed for moderate dissipation rates and that cavity-free isomerization dynamics are recovered under large dissipation rates. These findings highlight the important role that the finite lifetime of photonic degrees of freedom play in polaritonic chemistry.

Ab initio polaritonic potential-energy surfaces for excited-state nanophotonics and polaritonic chemistry

Advances in nanophotonics, quantum optics, and low-dimensional materials have enabled precise control of light-matter interactions down to the nanoscale. Combining concepts from each of these fields, there is now an opportunity to create and manipulate photonic matter via strong coupling of molecules to the electromagnetic field. Toward this goal, here we demonstrate a first principles framework to calculate polaritonic excited-state potential-energy surfaces, transition dipole moments, and transition densities for strongly coupled light-matter systems. In particular, we demonstrate the applicability of our methodology by calculating the polaritonic excited-state manifold of a formaldehyde molecule strongly coupled to an optical cavity. This proof-of-concept calculation shows how strong coupling can be exploited to alter photochemical reaction pathways by influencing avoided crossings with tuning of the cavity frequency and coupling strength. Therefore, by introducing an ab initio method to calculate excited-state potential-energy surfaces, our work opens a new avenue for the field of polaritonic chemistry.

Photochemistry in the strong coupling regime: A trajectory surface hopping scheme

The strong coupling regime between confined light and organic molecules turned out to be promising in modifying both the ground state and the excited states properties. Under this peculiar condition, the electronic states of the molecule are mixed with the quantum states of light. The dynamical processes occurring on such hybrid states undergo several modifications accordingly. Hence, the dynamical description of chemical reactivity in polaritonic systems needs to explicitly take into account the photon degrees of freedom and nonadiabatic events. With the aim of describing photochemical polaritonic processes, in the present work, we extend the direct trajectory surface hopping scheme to investigate photochemistry under strong coupling between light and matter.

Cooperative Conical Intersection Dynamics of Two Pyrazine Molecules in an Optical Cavity

Hybrid light-matter states in optical cavities, known as polaritons, offer a novel means of manipulating and controlling photochemical processes. We investigate the cooperative cavity photochemistry of two pyrazine molecules undergoing conical intersection dynamics and interacting with a single cavity photon mode by exact quantum dynamics. When the cavity mode is coupled to the electronic transition between the ground and excited states, we find an enhanced polaritonic splitting and collective dark states. These features dominate the cooperative polariton dynamics and can be observed in the transient absorption spectrum.

Exciton-phonon polaritons in organic microcavities: Testing a simple ansatz for treating a large number of chromophores

Polaritons in an ensemble of permutationally symmetric chromophores confined to an optical microcavity are investigated numerically. The analysis is based on the Holstein-Tavis-Cummings Hamiltonian which accounts for the coupling between an electronic excitation on each chromophore and a single cavity mode, as well as the coupling between the electronic and nuclear degrees of freedom on each chromophore. A straightforward ensemble partitioning scheme is introduced, which, along with an intuitive ansatz, allows one to obtain accurate evaluations of the lowest-energy polaritons using a subset of collective states. The polaritons include all three degrees of freedom-electronic, vibronic, and photonic-and can therefore be described as exciton-phonon polaritons. Applications focus on the limiting regimes where the Rabi frequency is small or large compared to the nuclear relaxation energy subsequent to optical excitation, with relaxation occurring mainly along the vinyl stretching coordinate in conjugated organic chromophores. Comparisons are also made to the more conventional vibronic polariton approach, which does not take into account two-particle excitations and vibration-photon states.

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

Polariton Assisted Down-Conversion of Photons via Nonadiabatic Molecular Dynamics: A Molecular Dynamical Casimir Effect

Quantum dynamics of the photoisomerization of a single 3,3'-diethyl-2,2'-thiacynine iodide molecule embedded in an optical microcavity was theoretically studied. The molecular model consisting of two electronic states and the reaction coordinate was coupled to a single cavity mode via the quantum Rabi Hamiltonian, and the corresponding time-dependent Schrödinger equation starting with a purely molecular excitation was solved using the Multiconfigurational Time-Dependent Hartree Method (MCTDH). We show that, for single-molecule strong coupling with the photon mode, nonadiabatic molecular dynamics produces mixing of polariton manifolds with differing number of excitations, without the need of counter-rotating light-matter coupling terms. Therefore, an electronic excitation of the molecule at the cis configuration is followed by the generation of two photons in the trans configuration upon isomerization. Conditions for this phenomenon to be operating in the collective strong light-matter coupling regime are discussed and found to be unfeasible for the present system, based on simulations of two molecules inside the microcavity. Yet, our finding suggests a new mechanism that, without ultrastrong coupling, achieves photon down-conversion by exploiting the emergent molecular dynamics arising in polaritonic architectures.

Manipulating nonadiabatic conical intersection dynamics by optical cavities

Optical cavities hold great promise to manipulate and control the photochemistry of molecules. We demonstrate how molecular photochemical processes can be manipulated by strong light-matter coupling. For a molecule with an inherent conical intersection, optical cavities can induce significant changes in the nonadiabatic dynamics by either splitting the pristine conical intersections into two novel polaritonic conical intersections or by creating light-induced avoided crossings in the polaritonic surfaces. This is demonstrated by exact real-time quantum dynamics simulations of a three-state two-mode model of pyrazine strongly coupled to a single cavity photon mode. We further explore the effects of external environments through dissipative polaritonic dynamics computed using the hierarchical equation of motion method. We find that cavity-controlled photochemistry can be immune to external environments. We also demonstrate that the polariton-induced changes in the dynamics can be monitored by transient absorption spectroscopy.

Light-Matter Response in Nonrelativistic Quantum Electrodynamics

We derive the full linear-response theory for nonrelativistic quantum electrodynamics in the long wavelength limit and provide a practical framework to solve the resulting equations by using quantum-electrodynamical density-functional theory. We highlight how the coupling between quantized light and matter changes the usual response functions and introduces cross-correlated light-matter response functions. These cross-correlation responses lead to measurable changes in Maxwell's equations due to the quantum-matter-mediated photon-photon interactions. Key features of treating the combined matter-photon response are that natural lifetimes of excitations become directly accessible from first-principles, changes in the electronic structure due to strong light-matter coupling are treated fully nonperturbatively, and self-consistent solutions of the back-reaction of matter onto the photon vacuum and vice versa are accounted for. By introducing a straightforward extension of the random-phase approximation for the coupled matter-photon problem, we calculate the ab initio spectra for a real molecular system that is coupled to the quantized electromagnetic field. Our approach can be solved numerically very efficiently. The presented framework leads to a shift in paradigm by highlighting how electronically excited states arise as a modification of the photon field and that experimentally observed effects are always due to a complex interplay between light and matter. At the same time the findings provide a route to analyze as well as propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics.

Time propagation of the coupled Maxwell and Kohn-Sham equations using the Riemann-Silberstein formalism

The coupled Maxwell and time-dependent Kohn-Sham equations are solved using the Riemann-Silberstein vectors to represent the electromagnetic fields. Momentum-space time propagation of the Riemann-Silberstein vectors are proposed and test calculations are presented to show the accuracy of the approach.

Investigating New Reactivities Enabled by Polariton Photochemistry

We perform quantum dynamics simulations to investigate new chemical reactivities enabled by cavity quantum electrodynamics. The quantum light-matter interactions between the molecule and the quantized radiation mode inside an optical cavity create a set of hybridized electronic-photonic states, so-called polaritons. The polaritonic states adapt the curvatures from both the ground and the excited electronic states, opening up new possibilities to control photochemical reactions by exploiting intrinsic quantum behaviors of light-matter interactions. With quantum dynamics simulations, we demonstrate that the selectivity of a model photoisomerization reaction can be controlled by tuning the photon frequency of the cavity mode or the light-matter coupling strength, providing new ways to manipulate chemical reactions via the light-matter interaction. We further investigate collective quantum effects enabled by coupling the quantized radiation mode to multiple molecules. Our results suggest that in the resonance case, a photon is recycled among molecules to enable multiple excited state reactions, thus effectively functioning as a catalyst. In the nonresonance case, molecules emit and absorb virtual photons to initiate excited state reactions through fundamental quantum electrodynamics processes. These results from quantum dynamics simulations reveal basic principles of polariton photochemistry as well as promising reactivities that take advantage of intrinsic quantum behaviors of photons.