On the SN2 reactions modified in vibrational strong coupling experiments: reaction mechanisms and vibrational mode assignments

Measuring Kinetics under Vibrational Strong Coupling: Testing for a Change in the Nucleophilicity of Water and Alcohols

Vibrational Strong Coupling (VSC) has been reported to change the rate of organic reactions. However, a lack of convenient and reliable methods to measure reaction kinetics under VSC makes it challenging to obtain mechanistic insight into its influence, hindering progress in the field. Here, we use recently developed fixed-width optical cavities to obtain large kinetic datasets under VSC with small errors (±1-5 %) in an operationally simple manner using UV/Vis spectroscopy. The setup is used to test whether VSC changes a fundamental kinetic property of polar reactions, nucleophilicity, for water and alcohols, species commonly used in VSC-modified chemistry. We determined the rate constants for nucleophilic capture with a library of benzhydrilium ions as reference electrophiles with and without strong coupling of the nucleophile's key vibrations. For all investigated combinations of electrophiles and nucleophiles, only minor changes in the observed rate constants of the reactions were observed independently of the coupled bands. These results indicate that VSC does not substantially alter the nucleophilicity of water and alcohols, suggesting that polar reactions are modified through other, presently unknown mechanisms. Fixed-width cavities allow for convenient and reproducible UV/Vis kinetics, facilitating mechanistic studies of VSC-modified chemistry.

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

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

Theory and modeling of light-matter interactions in chemistry: current and future

Light-matter interaction not only plays an instrumental role in characterizing materials' properties via various spectroscopic techniques but also provides a general strategy to manipulate material properties via the design of novel nanostructures. This perspective summarizes recent theoretical advances in modeling light-matter interactions in chemistry, mainly focusing on plasmon and polariton chemistry. The former utilizes the highly localized photon, plasmonic hot electrons, and local heat to drive chemical reactions. In contrast, polariton chemistry modifies the potential energy curvatures of bare electronic systems, and hence their chemistry, via forming light-matter hybrid states, so-called polaritons. The perspective starts with the basic background of light-matter interactions, molecular quantum electrodynamics theory, and the challenges of modeling light-matter interactions in chemistry. Then, the recent advances in modeling plasmon and polariton chemistry are described, and future directions toward multiscale simulations of light-matter interaction-mediated chemistry are discussed.

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.

Quantum dynamical effects of vibrational strong coupling in chemical reactivity

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

Rovibrational Polaritons in Gas-Phase Methane

Polaritonic states arise when a bright optical transition of a molecular ensemble is resonantly matched to an optical cavity mode frequency. Here, we lay the groundwork to study the behavior of polaritons in clean, isolated systems by establishing a new platform for vibrational strong coupling in gas-phase molecules. We access the strong coupling regime in an intracavity cryogenic buffer gas cell optimized for the preparation of simultaneously cold and dense ensembles and report a proof-of-principle demonstration in gas-phase methane. We strongly cavity-couple individual rovibrational transitions and probe a range of coupling strengths and detunings. We reproduce our findings with classical cavity transmission simulations in the presence of strong intracavity absorbers. This infrastructure will provide a new testbed for benchmark studies of cavity-altered chemistry.

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.

Multidimensional Quantum Dynamical Simulation of Infrared Spectra under Polaritonic Vibrational Strong Coupling

Recent experimental and theoretical studies demonstrate that the chemical reactivity of molecules can be modified inside an optical cavity. Here, we provide a theoretical framework for conducting multidimensional quantum simulations of the infrared (IR) spectra for molecules interacting with cavity modes. A single water molecule under polaritonic vibrational strong coupling serves as an illustrative example. Combined with accurate potential energy and dipole moment surfaces, our cavity vibrational self-consistent field/virtual state configuration interaction (cav-VSCF/VCI) approach can predict the IR spectra when the molecule is inside or outside the cavity. The spectral signatures of Rabi splittings and shifts of certain bands are found to be strongly dependent on the frequency and polarization direction of the cavity modes. Analyses of the simulated spectra show that polaritonic vibrational strong coupling can induce unconventional couplings among the molecule's vibrational modes, suggesting that intramolecular vibrational energy transfer can be significantly accelerated by the cavity.

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.

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.

Suppression and Enhancement of Thermal Chemical Rates in a Cavity

The observed modification of thermal chemical rates in Fabry-Perot cavities remains a poorly understood effect theoretically. Recent breakthroughs explain some of the observations through the Grote-Hynes theory, where the cavity introduces friction with the reaction coordinate, thus reducing the transmission coefficient and the rate. The regime of rate enhancement, the observed sharp resonances at varying cavity frequencies, and the survival of these effects in the collective regime remain mostly unexplained. In this Letter, we consider the cis-trans isomerization of HONO atomistically using an ab initio potential energy surface. We evaluate the transmission coefficient using the reactive flux method and identify the conditions for rate acceleration. In the underdamped, low-friction regime of the reaction coordinate, the cavity coupling enhances the rate with increasing coupling strength until reaching the Kramers turnover point. Sharp resonances in this regime are related to cavity-enabled energy redistribution channels.

A Multi-Scale Approach for Modeling the Optical Response of Molecular Materials Inside Cavities

The recent fabrication advances in nanoscience and molecular materials point toward a new era where material properties are tailored in silico for target applications. To fully realize this potential, accurate and computationally efficient theoretical models are needed for: a) the computer-aided design and optimization of new materials before their fabrication; and b) the accurate interpretation of experiments. The development of such theoretical models is a challenging multi-disciplinary problem where physics, chemistry, and material science are intertwined across spatial scales ranging from the molecular to the device level, that is, from ångströms to millimeters. In photonic applications, molecular materials are often placed inside optical cavities. Together with the sought-after enhancement of light-molecule interactions, the cavities bring additional complexity to the modeling of such devices. Here, a multi-scale approach that, starting from ab initio quantum mechanical molecular simulations, can compute the electromagnetic response of macroscopic devices such as cavities containing molecular materials is presented. Molecular time-dependent density-functional theory calculations are combined with the efficient transition matrix based solution of Maxwell's equations. Some of the capabilities of the approach are demonstrated by simulating surface metal-organic frameworks -in-cavity and J-aggregates-in-cavity systems that have been recently investigated experimentally, and providing a refined understanding of the experimental results.

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.

Polariton relaxation under vibrational strong coupling: Comparing cavity molecular dynamics simulations against Fermi's golden rule rate

Under vibrational strong coupling (VSC), the formation of molecular polaritons may significantly modify the photo-induced or thermal properties of molecules. In an effort to understand these intriguing modifications, both experimental and theoretical studies have focused on the ultrafast dynamics of vibrational polaritons. Here, following our recent work [Li et al., J. Chem. Phys. 154, 094124 (2021)], we systematically study the mechanism of polariton relaxation for liquid CO₂ under a weak external pumping. Classical cavity molecular dynamics (CavMD) simulations confirm that polariton relaxation results from the combined effects of (i) cavity loss through the photonic component and (ii) dephasing of the bright-mode component to vibrational dark modes as mediated by intermolecular interactions. The latter polaritonic dephasing rate is proportional to the product of the weight of the bright mode in the polariton wave function and the spectral overlap between the polariton and dark modes. Both these factors are sensitive to parameters such as the Rabi splitting and cavity mode detuning. Compared to a Fermi's golden rule calculation based on a tight-binding harmonic model, CavMD yields a similar parameter dependence for the upper polariton relaxation lifetime but sometimes a modest disagreement for the lower polariton. We suggest that this disagreement results from polariton-enhanced molecular nonlinear absorption due to molecular anharmonicity, which is not included in our analytical model. We also summarize recent progress on probing nonreactive VSC dynamics with CavMD.

Molecular orbital theory in cavity QED environments

Coupling between molecules and vacuum photon fields inside an optical cavity has proven to be an effective way to engineer molecular properties, in particular reactivity. To ease the rationalization of cavity induced effects we introduce an ab initio method leading to the first fully consistent molecular orbital theory for quantum electrodynamics environments. Our framework is non-perturbative and explains modifications of the electronic structure due to the interaction with the photon field. In this work, we show that the newly developed orbital theory can be used to predict cavity induced modifications of molecular reactivity and pinpoint classes of systems with significant cavity effects. We also investigate electronic cavity-induced modifications of reaction mechanisms in vibrational strong coupling regimes.

Vibration-Cavity Polariton Chemistry and Dynamics

Molecular polaritons result from light-matter coupling between optical resonances and molecular electronic or vibrational transitions. When the coupling is strong enough, new hybridized states with mixed photon-material character are observed spectroscopically, with resonances shifted above and below the uncoupled frequency. These new modes have unique optical properties and can be exploited to promote or inhibit physical and chemical processes. One remarkable result is that vibrational strong coupling to cavities can alter reaction rates and product branching ratios with no optical excitation whatsoever. In this work we review the ability of vibration-cavity polaritons to modify chemical and physical processes including chemical reactivity, as well as steady-state and transient spectroscopy. We discuss the larger context of these works and highlight their most important contributions and implications. Our goal is to provide insight for systematically manipulating molecular polaritons in photonic and chemical applications. 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.

Theory of vibrational polariton chemistry in the collective coupling regime

We theoretically demonstrate that the chemical reaction rate constant can be significantly suppressed by coupling molecular vibrations with an optical cavity, exhibiting both the collective coupling effect and the cavity frequency modification of the rate constant. When a reaction coordinate is strongly coupled to the solvent molecules, the reaction rate constant is reduced due to the dynamical caging effect. We demonstrate that collectively coupling the solvent to the cavity can further enhance this dynamical caging effect, leading to additional suppression of the chemical kinetics. This effect is further amplified when cavity loss is considered.

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.

High-Level Systematic Ab Initio Comparison of Carbon- and Silicon-Centered SN2 Reactions

We characterize the stationary points along the Walden inversion, front-side attack, and double-inversion pathways of the X^– + CH₃Y and X^– + SiH₃Y [X, Y = F, Cl, Br, I] S_N2 reactions using chemically accurate CCSD(T)-F12b/aug-cc-pVnZ [n = D, T, Q] levels of theory. At the carbon center, Walden inversion dominates and proceeds via prereaction (X^–···H₃CY) and postreaction (XCH₃···Y^–) ion-dipole wells separated by a usually submerged transition state (X–H₃C–Y)⁻, front-side attack occurs over high barriers, double inversion is the lowest-energy retention pathway for X = F, and hydrogen- (F^–···HCH₂Y) and halogen-bonded (X^–···YCH₃) complexes exist in the entrance channel. At the silicon center, Walden inversion proceeds through a single minimum (X–SiH₃–Y)⁻, the front-side attack is competitive via a usually submerged transition state separating pre- and postreaction minima having X–Si–Y angles close to 90°, double inversion occurs over positive, often high barriers, and hydrogen- and halogen-bonded complexes are not found. In addition to the S_N2 channels (Y^– + CH₃X/SiH₃X), we report reaction enthalpies for proton abstraction (HX + CH₂Y^–/SiH₂Y^–), hydride substitution (H^– + CH₂XY/SiH₂XY), XH···Y^– complex formation (XH···Y^– + ¹CH₂/¹SiH₂), and halogen abstraction (XY + CH₃^–/SiH₃^– and XY^– + CH₃/SiH₃).

Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light-matter coupling

Strong light-matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light-matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density-type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

Theory of Mode-Selective Chemistry through Polaritonic Vibrational Strong Coupling

Recent experiments have demonstrated remarkable mode-selective reactivities by coupling molecular vibrations with a quantized radiation field inside an optical cavity. The fundamental mechanism behind such effects, on the other hand, remains elusive. In this work, we provide a theoretical explanation of the basic principle of how cavity frequency can be tuned to achieve mode-selective reactivities. We find that the dynamics of the radiation mode leads to a cavity frequency-dependent dynamical caging effect of a reaction coordinate, resulting in suppression of the rate constant. In the presence of competitive reactions, it is possible to preferentially cage a reaction coordinate when the barrier frequencies of competing reactions are different, resulting in a selective slow down of a given reaction. Our theoretical results illustrate the cavity-induced mode-selective chemistry through polaritonic vibrational strong couplings, revealing the fundamental mechanism for changing chemical selectivities through cavity quantum electrodynamics.

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

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

Cavity frequency-dependent theory for vibrational polariton chemistry

Recent experiments demonstrate the control of chemical reactivities by coupling molecules inside an optical microcavity. In contrast, transition state theory predicts no change of the reaction barrier height during this process. Here, we present a theoretical explanation of the cavity modification of the ground state reactivity in the vibrational strong coupling (VSC) regime in polariton chemistry. Our theoretical results suggest that the VSC kinetics modification is originated from the non-Markovian dynamics of the cavity radiation mode that couples to the molecule, leading to the dynamical caging effect of the reaction coordinate and the suppression of reaction rate constant for a specific range of photon frequency close to the barrier frequency. We use a simple analytical non-Markovian rate theory to describe a single molecular system coupled to a cavity mode. We demonstrate the accuracy of the rate theory by performing direct numerical calculations of the transmission coefficients with the same model of the molecule-cavity hybrid system. Our simulations and analytical theory provide a plausible explanation of the photon frequency dependent modification of the chemical reactivities in the VSC polariton chemistry.