1
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Patrahau B, Piejko M, Mayer RJ, Antheaume C, Sangchai T, Ragazzon G, Jayachandran A, Devaux E, Genet C, Moran J, Ebbesen TW. Direct Observation of Polaritonic Chemistry by Nuclear Magnetic Resonance Spectroscopy. Angew Chem Int Ed Engl 2024; 63:e202401368. [PMID: 38584127 DOI: 10.1002/anie.202401368] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 04/01/2024] [Accepted: 04/05/2024] [Indexed: 04/09/2024]
Abstract
Polaritonic chemistry is emerging as a powerful approach to modifying the properties and reactivity of molecules and materials. However, probing how the electronics and dynamics of molecular systems change under strong coupling has been challenging due to the narrow range of spectroscopic techniques that can be applied in situ. Here we develop microfluidic optical cavities for vibrational strong coupling (VSC) that are compatible with nuclear magnetic resonance (NMR) spectroscopy using standard liquid NMR tubes. VSC is shown to influence the equilibrium between two conformations of a molecular balance sensitive to London dispersion forces, revealing an apparent change in the equilibrium constant under VSC. In all compounds studied, VSC does not induce detectable changes in chemical shifts, J-couplings, or spin-lattice relaxation times. This unexpected finding indicates that VSC does not substantially affect molecular electron density distributions, and in turn has profound implications for the possible mechanisms at play in polaritonic chemistry under VSC and suggests that the emergence of collective behavior is critical.
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Affiliation(s)
- B Patrahau
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - M Piejko
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - R J Mayer
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - C Antheaume
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - T Sangchai
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - G Ragazzon
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - A Jayachandran
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - E Devaux
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - C Genet
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - J Moran
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
| | - T W Ebbesen
- University of Strasbourg, CNRS, ISIS & icFRC, 8 allée Gaspard Monge, 67000, Strasbourg, France
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2
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Sidler D, Schnappinger T, Obzhirov A, Ruggenthaler M, Kowalewski M, Rubio A. Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling. J Phys Chem Lett 2024; 15:5208-5214. [PMID: 38717382 PMCID: PMC11103705 DOI: 10.1021/acs.jpclett.4c00913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Revised: 05/01/2024] [Accepted: 05/03/2024] [Indexed: 05/22/2024]
Abstract
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.
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Affiliation(s)
- Dominik Sidler
- Laboratory
for Materials Simulations, Paul Scherrer
Institute, 5232 Villigen PSI, Switzerland
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Thomas Schnappinger
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106
91 Stockholm, Sweden
| | - Anatoly Obzhirov
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael Ruggenthaler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Markus Kowalewski
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106
91 Stockholm, Sweden
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron
Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Nano-Bio
Spectroscopy Group, University of the Basque
Country (UPV/EHU), 20018 San Sebastián, Spain
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3
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Schäfer C, Fojt J, Lindgren E, Erhart P. Machine Learning for Polaritonic Chemistry: Accessing Chemical Kinetics. J Am Chem Soc 2024; 146:5402-5413. [PMID: 38354223 PMCID: PMC10910569 DOI: 10.1021/jacs.3c12829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Revised: 01/23/2024] [Accepted: 01/24/2024] [Indexed: 02/16/2024]
Abstract
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.
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Affiliation(s)
- Christian Schäfer
- Department
of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden
- Department
of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, 412 96, Göteborg, Sweden
| | - Jakub Fojt
- Department
of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden
| | - Eric Lindgren
- Department
of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden
| | - Paul Erhart
- Department
of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden
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4
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Svendsen MK, Thygesen KS, Rubio A, Flick J. Ab Initio Calculations of Quantum Light-Matter Interactions in General Electromagnetic Environments. J Chem Theory Comput 2024; 20:926-936. [PMID: 38189259 PMCID: PMC10809713 DOI: 10.1021/acs.jctc.3c00967] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Revised: 11/17/2023] [Accepted: 12/12/2023] [Indexed: 01/09/2024]
Abstract
The emerging field of strongly coupled light-matter systems has drawn significant attention in recent years because of the prospect of altering both the physical and chemical properties of molecules and materials. Because this emerging field draws on ideas from both condensed-matter physics and quantum optics, it has attracted the attention of theoreticians from both fields. While the former often employ accurate descriptions of the electronic structure of the matter, the description of the electromagnetic environment is often oversimplified. In contrast, the latter often employs sophisticated descriptions of the electromagnetic environment while using oversimplified few-level approximations of the electronic structure. Both approaches are problematic because the oversimplified descriptions of the electronic system are incapable of describing effects such as light-induced structural changes in the electronic system, while the oversimplified descriptions of the electromagnetic environments can lead to unphysical predictions because the light-matter interactions strengths are misrepresented. In this work, we overcome these shortcomings and present the first method which can quantitatively describe both the electronic system and general electromagnetic environments from first principles. We realize this by combining macroscopic QED (MQED) with Quantum Electrodynamical Density-Functional Theory. To exemplify this approach, we consider the example of an absorbing spherical cavity and study the impact of different parameters of both the environment and the electronic system on the transition from weak-to-strong coupling for different aromatic molecules. As part of this work, we also provide an easy-to-use tool to calculate the cavity coupling strengths for simple cavity setups. Our work is a significant step toward parameter-free ab initio calculations for strongly coupled quantum light-matter systems and will help bridge the gap between theoretical methods and experiments in the field.
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Affiliation(s)
- Mark Kamper Svendsen
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- Computational
Atomic scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
- Center
for Computational Quantum Physics, Flatiron
Institute, 10010 New York, New York, United States
| | - Kristian Sommer Thygesen
- Computational
Atomic scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron
Institute, 10010 New York, New York, United States
- Nano-Bio
Spectroscopy Group and European Theoretical Spectroscopy Facility
(ETSF), Universidad del País Vasco
(UPV/EHU), Av. Tolosa
72, 20018 San Sebastian, Spain
| | - Johannes Flick
- Center
for Computational Quantum Physics, Flatiron
Institute, 10010 New York, New York, United States
- Department
of Physics, City College of New York, 10031 New York, New York, United States
- Department
of Physics, The Graduate Center, City University
of New York, 10016 New York, New York, United States
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5
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Schnappinger T, Kowalewski M. Ab Initio Vibro-Polaritonic Spectra in Strongly Coupled Cavity-Molecule Systems. J Chem Theory Comput 2023; 19:9278-9289. [PMID: 38084914 PMCID: PMC10753771 DOI: 10.1021/acs.jctc.3c01135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Revised: 11/23/2023] [Accepted: 11/27/2023] [Indexed: 12/27/2023]
Abstract
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.
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Affiliation(s)
- Thomas Schnappinger
- Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
| | - Markus Kowalewski
- Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
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6
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Sidler D, Ruggenthaler M, Rubio A. Numerically Exact Solution for a Real Polaritonic System under Vibrational Strong Coupling in Thermodynamic Equilibrium: Loss of Light-Matter Entanglement and Enhanced Fluctuations. J Chem Theory Comput 2023; 19:8801-8814. [PMID: 37972347 PMCID: PMC10720342 DOI: 10.1021/acs.jctc.3c00092] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Revised: 10/25/2023] [Accepted: 10/25/2023] [Indexed: 11/19/2023]
Abstract
The first numerically exact simulation of a full ab initio molecular quantum system (HD+) under strong ro-vibrational coupling to a quantized optical cavity mode in thermal equilibrium is presented. Theoretical challenges in describing strongly coupled systems of mixed quantum statistics (bosons and Fermions) are discussed and circumvented by the specific choice of our molecular system. Our numerically exact simulations highlight the absence of zero temperature for the strongly coupled matter and light subsystems, due to cavity-induced noncanonical conditions. Furthermore, we explore the temperature dependency of light-matter quantum entanglement, which emerges for the ground state but is quickly lost already in the deep cryogenic regime. This is in contrast to predictions from the Jaynes-Cummings model, which is the standard starting point to model collective strong-coupling chemistry phenomenologically. Moreover, we find that the fluctuations of matter remain modified by the quantum nature of the thermal and vacuum-field fluctuations for significant temperatures, e.g., at ambient conditions. These observations (loss of entanglement and coupling to quantum fluctuations) have implications for the understanding and control of polaritonic chemistry and materials science, since a semiclassical theoretical description of light-matter interaction becomes reasonable, but the typical (classical) canonical equilibrium assumption for the nuclear subsystem remains violated. This opens the door for quantum fluctuation-induced stochastic resonance phenomena under vibrational strong coupling, which have been suggested as a plausible theoretical mechanism to explain the experimentally observed resonance phenomena in the absence of periodic driving that has not yet been fully understood.
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Affiliation(s)
- Dominik Sidler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, Hamburg 22761, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, Hamburg 22761, Germany
| | - Michael Ruggenthaler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, Hamburg 22761, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, Hamburg 22761, Germany
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, Hamburg 22761, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, Hamburg 22761, Germany
- Center
for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Nano-Bio
Spectroscopy Group, University of the Basque Country (UPV/EHU), San Sebastián 20018, Spain
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7
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Pavošević F, Smith RL, Rubio A. Cavity Click Chemistry: Cavity-Catalyzed Azide-Alkyne Cycloaddition. J Phys Chem A 2023; 127:10184-10188. [PMID: 37992280 DOI: 10.1021/acs.jpca.3c06285] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2023]
Abstract
Click chemistry, which refers to chemical reactions that are fast and selective with high product yields, has become a powerful approach in organic synthesis and chemical biology. Due to the cytotoxicity of the transition metals employed in click chemistry reactions, a search for novel metal-free alternatives continues. Herein, we demonstrate that an optical cavity can be utilized as a metal-free alternative in the click chemistry cycloaddition reaction between cyanoacetylene and formylazide using the quantum electrodynamics coupled cluster method. We show that by changing the molecular orientation with respect to the polarization of the cavity mode(s), the reaction can be selectively catalyzed to form a major 1,4-disubstituted or 1,5-disubstituted product. This work highlights that a cavity has the same effect on the investigated cycloaddition as the transition metal catalysts traditionally employed in click chemistry reactions. We expect our findings to further stimulate research on cavity-assisted click chemistry reactions.
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Affiliation(s)
- Fabijan Pavošević
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Algorithmiq Ltd, Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Robert L Smith
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Angel Rubio
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761 Hamburg, Germany
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8
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Gudem M, Kowalewski M. Cavity-Modified Chemiluminescent Reaction of Dioxetane. J Phys Chem A 2023; 127:9483-9494. [PMID: 37845803 PMCID: PMC10658626 DOI: 10.1021/acs.jpca.3c05664] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Revised: 09/21/2023] [Indexed: 10/18/2023]
Abstract
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.
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Affiliation(s)
- Mahesh Gudem
- Department of Physics, Stockholm University, Albanova University Centre, SE-106
91 Stockholm, Sweden
| | - Markus Kowalewski
- Department of Physics, Stockholm University, Albanova University Centre, SE-106
91 Stockholm, Sweden
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9
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Rokaj V, Wang J, Sous J, Penz M, Ruggenthaler M, Rubio A. Weakened Topological Protection of the Quantum Hall Effect in a Cavity. PHYSICAL REVIEW LETTERS 2023; 131:196602. [PMID: 38000420 DOI: 10.1103/physrevlett.131.196602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Revised: 08/13/2023] [Accepted: 10/13/2023] [Indexed: 11/26/2023]
Abstract
We study the quantum Hall effect in a two-dimensional homogeneous electron gas coupled to a quantum cavity field. As initially pointed out by Kohn, Galilean invariance for a homogeneous quantum Hall system implies that the electronic center of mass (c.m.) decouples from the electron-electron interaction, and the energy of the c.m. mode, also known as Kohn mode, is equal to the single particle cyclotron transition. In this work, we point out that strong light-matter hybridization between the Kohn mode and the cavity photons gives rise to collective hybrid modes between the Landau levels and the photons. We provide the exact solution for the collective Landau polaritons and we demonstrate the weakening of topological protection at zero temperature due to the existence of the lower polariton mode which is softer than the Kohn mode. This provides an intrinsic mechanism for the recently observed topological breakdown of the quantum Hall effect in a cavity [F. Appugliese et al., Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect, Science 375, 1030 (2022).SCIEAS0036-807510.1126/science.abl5818]. Importantly, our theory predicts the cavity suppression of the thermal activation gap in the quantum Hall transport. Our work paves the way for future developments in cavity control of quantum materials.
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Affiliation(s)
- Vasil Rokaj
- ITAMP, Center for Astrophysics | Harvard & Smithsonian, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Jie Wang
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts 02138, USA
| | - John Sous
- Department of Physics, Stanford University, Stanford, California 93405, USA
- Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA
| | - Markus Penz
- Basic Research Community for Physics, Innsbruck 6020, Austria
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, Germany
- Center for Computational Quantum Physics, Flatiron Institute, New York 10010, USA
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10
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Ruggenthaler M, Sidler D, Rubio A. Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics. Chem Rev 2023; 123:11191-11229. [PMID: 37729114 PMCID: PMC10571044 DOI: 10.1021/acs.chemrev.2c00788] [Citation(s) in RCA: 21] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Indexed: 09/22/2023]
Abstract
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.
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Affiliation(s)
- Michael Ruggenthaler
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Dominik Sidler
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max-Planck-Institut
für Struktur und Dynamik der Materie, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
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11
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Schnappinger T, Sidler D, Ruggenthaler M, Rubio A, Kowalewski M. Cavity Born-Oppenheimer Hartree-Fock Ansatz: Light-Matter Properties of Strongly Coupled Molecular Ensembles. J Phys Chem Lett 2023; 14:8024-8033. [PMID: 37651603 PMCID: PMC10510432 DOI: 10.1021/acs.jpclett.3c01842] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 08/22/2023] [Indexed: 09/02/2023]
Abstract
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.
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Affiliation(s)
- Thomas Schnappinger
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
| | - Dominik Sidler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Michael Ruggenthaler
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter and Center
for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- The
Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics, Flatiron
Institute, 162 Fifth
Avenue, New York, New York 10010, United States
- Nano-Bio
Spectroscopy Group, University of the Basque
Country (UPV/EHU), 20018 San Sebastián, Spain
| | - Markus Kowalewski
- Department
of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden
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12
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Mandal A, Taylor MA, Weight BM, Koessler ER, Li X, Huo P. Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics. Chem Rev 2023; 123:9786-9879. [PMID: 37552606 PMCID: PMC10450711 DOI: 10.1021/acs.chemrev.2c00855] [Citation(s) in RCA: 31] [Impact Index Per Article: 31.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Indexed: 08/10/2023]
Abstract
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.
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Affiliation(s)
- Arkajit Mandal
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Michael A.D. Taylor
- The
Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, United States
| | - Braden M. Weight
- Department
of Physics and Astronomy, University of
Rochester, Rochester, New York 14627, United
States
| | - Eric R. Koessler
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Xinyang Li
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pengfei Huo
- Department
of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
- The
Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, United States
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13
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Pavošević F, Smith RL, Rubio A. Computational study on the catalytic control of endo/exo Diels-Alder reactions by cavity quantum vacuum fluctuations. Nat Commun 2023; 14:2766. [PMID: 37179341 PMCID: PMC10183045 DOI: 10.1038/s41467-023-38474-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 04/28/2023] [Indexed: 05/15/2023] Open
Abstract
Achieving control over chemical reaction's rate and stereoselectivity realizes one of the Holy Grails in chemistry that can revolutionize chemical and pharmaceutical industries. Strong light-matter interaction in optical or nanoplasmonic cavities might provide the knob to reach such control. In this work, we demonstrate the catalytic and selectivity control of an optical cavity for two selected Diels-Alder cycloaddition reactions using the quantum electrodynamics coupled cluster (QED-CC) method. Herein, we find that by changing the molecular orientation with respect to the polarization of the cavity mode the reactions can be significantly inhibited or selectively enhanced to produce major endo or exo products on demand. This work highlights the potential of utilizing quantum vacuum fluctuations of an optical cavity to modulate the rate of Diels-Alder cycloaddition reactions and to achieve stereoselectivity in a practical and non-intrusive way. We expect that the present findings will be applicable to a larger set of relevant reactions, including the click chemical reactions.
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Affiliation(s)
- Fabijan Pavošević
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Ave., New York, 10010, NY, USA.
| | - Robert L Smith
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Ave., New York, 10010, NY, USA
- Department of Chemistry, Virginia Tech, Blacksburg, VA, 24061, USA
| | - Angel Rubio
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Ave., New York, 10010, NY, USA.
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, 22761, Hamburg, Germany.
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility (ETSF), Universidad del País Vasco (UPV/EHU), Av. Tolosa 72, 20018, San Sebastian, Spain.
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14
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Schäfer C, Baranov DG. Chiral Polaritonics: Analytical Solutions, Intuition, and Use. J Phys Chem Lett 2023; 14:3777-3784. [PMID: 37052302 PMCID: PMC10123817 DOI: 10.1021/acs.jpclett.3c00286] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 03/22/2023] [Indexed: 06/19/2023]
Abstract
Preferential selection of a given enantiomer over its chiral counterpart has become increasingly relevant in the advent of the next era of medical drug design. In parallel, cavity quantum electrodynamics has grown into a solid framework to control energy transfer and chemical reactivity, the latter requiring strong coupling. In this work, we derive an analytical solution to a system of many chiral emitters interacting with a chiral cavity similar to the widely used Tavis-Cummings and Hopfield models of quantum optics. We are able to estimate the discriminating strength of chiral polaritonics, discuss possible future development directions and exciting applications such as elucidating homochirality, and deliver much needed intuition to foster the newly flourishing field of chiral polaritonics.
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Affiliation(s)
- Christian Schäfer
- MC2
Department, Chalmers University of Technology, 41258 Gothenburg, Sweden
| | - Denis G. Baranov
- Center
for Photonics and 2D Materials, Moscow Institute
of Physics and Technology, Dolgoprudny 141700, Russia
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15
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Mondal S, Wang DS, Keshavamurthy S. Dissociation dynamics of a diatomic molecule in an optical cavity. J Chem Phys 2022; 157:244109. [PMID: 36586980 DOI: 10.1063/5.0124085] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
We study the dissociation dynamics of a diatomic molecule, modeled as a Morse oscillator, coupled to an optical cavity. A marked suppression of the dissociation probability, both classical and quantum, is observed for cavity frequencies significantly below the fundamental transition frequency of the molecule. We show that the suppression in the probability is due to the nonlinearity of the dipole function. The effect can be rationalized entirely in terms of the structures in the classical phase space of the model system.
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Affiliation(s)
- Subhadip Mondal
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208 016, India
| | - Derek S Wang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208 016, India
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16
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Schäfer C, Flick J, Ronca E, Narang P, Rubio A. Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity. Nat Commun 2022; 13:7817. [PMID: 36535939 PMCID: PMC9763331 DOI: 10.1038/s41467-022-35363-6] [Citation(s) in RCA: 41] [Impact Index Per Article: 20.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2022] [Accepted: 11/28/2022] [Indexed: 12/24/2022] Open
Abstract
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.
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Affiliation(s)
- Christian Schäfer
- grid.469852.40000 0004 1796 3508Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Hamburg, Germany ,The Hamburg Center for Ultrafast Imaging, Hamburg, Germany ,grid.5371.00000 0001 0775 6028Department of Physics, Chalmers University of Technology, Göteborg, Sweden ,grid.5371.00000 0001 0775 6028Department of Microtechnology and Nanoscience, MC2, Chalmers University of Technology, Göteborg, Sweden
| | - Johannes Flick
- grid.430264.70000 0004 4648 6763Center for Computational Quantum Physics, Flatiron Institute, New York, NY USA ,grid.38142.3c000000041936754XJohn A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA USA ,grid.254250.40000 0001 2264 7145Department of Physics, City College of New York, New York, NY USA ,grid.212340.60000000122985718Department of Physics, The Graduate Center, City University of New York, New York, NY USA
| | - Enrico Ronca
- Istituto per i Processi Chimico Fisici del CNR (IPCF-CNR), Pisa, Italy
| | - Prineha Narang
- grid.38142.3c000000041936754XJohn A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA USA ,grid.19006.3e0000 0000 9632 6718Physical Sciences, College of Letters and Science, University of California, Los Angeles, Los Angeles, CA USA
| | - Angel Rubio
- grid.469852.40000 0004 1796 3508Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Hamburg, Germany ,The Hamburg Center for Ultrafast Imaging, Hamburg, Germany ,grid.430264.70000 0004 4648 6763Center for Computational Quantum Physics, Flatiron Institute, New York, NY USA
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17
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Schäfer C. Polaritonic Chemistry from First Principles via Embedding Radiation Reaction. J Phys Chem Lett 2022; 13:6905-6911. [PMID: 35866694 PMCID: PMC9358701 DOI: 10.1021/acs.jpclett.2c01169] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
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.
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18
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Welakuh DM, Flick J, Ruggenthaler M, Appel H, Rubio A. Frequency-Dependent Sternheimer Linear-Response Formalism for Strongly Coupled Light-Matter Systems. J Chem Theory Comput 2022; 18:4354-4365. [PMID: 35675628 PMCID: PMC9281401 DOI: 10.1021/acs.jctc.2c00076] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Davis M Welakuh
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, Hamburg 22761, Germany.,Harvard John A. Paulson School Of Engineering And Applied Sciences, Harvard University, Cambridge 02138, Massachusetts, United States
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York 10010, New York, United States
| | - Michael Ruggenthaler
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, Hamburg 22761, Germany
| | - Heiko Appel
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, Hamburg 22761, Germany
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science & Department of Physics, Luruper Chaussee 149, Hamburg 22761, Germany.,Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York 10010, New York, United States
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19
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Pavosevic F, Rubio A. Wavefunction embedding for molecular polaritons. J Chem Phys 2022; 157:094101. [DOI: 10.1063/5.0095552] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Polaritonic chemistry relies on the strong light-matter interaction phenomena for altering the chemical reaction rates inside optical cavities. To explain and to understand these processes, the development of reliable theoretical models is essential. While computationally efficient quantum electrodynamics self-consistent field (QED-SCF) methods, such as quantum electrodynamics density functional theory (QEDFT) needs accurate functionals, quantum electrodynamics coupled cluster (QED-CC) methods provide a systematic increase in accuracy but at much greater cost. To overcome this computational bottleneck, herein we introduce and develop the QED-CC-in-QED-SCF projection-based embedding method that inherits all the favorable properties from the two worlds, computational efficiency and accuracy. The performance of the embedding method is assessed by studying some prototypical but relevant reactions, such as methyl transfer reaction, proton transfer reaction, as well as protonation reaction in a complex environment. The results obtained with the new embedding method are in excellent agreement with more expensive QED-CC results. The analysis performed on these reactions indicate that the electron-photon correlation effects are local in nature and that only a small region should be treated at the QED-CC level for capturing important effects due to cavity. This work sets the stage for future developments of polaritonic quantum chemistry methods and it will serve as a guideline for development of other polaritonic embedding models.
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Affiliation(s)
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Germany
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20
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Fukushima T, Yoshimitsu S, Murakoshi K. Inherent Promotion of Ionic Conductivity via Collective Vibrational Strong Coupling of Water with the Vacuum Electromagnetic Field. J Am Chem Soc 2022; 144:12177-12183. [PMID: 35737737 DOI: 10.1021/jacs.2c02991] [Citation(s) in RCA: 23] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
Hydrogen bonding interactions among water molecules play a critical role in chemical reactivity, dynamic proton mobility, static dielectric behavior, and the thermodynamic properties of water. In this study, we demonstrate the modification of ionic conductivity of water through hybridization with a vacuum electromagnetic field by strongly coupling the O─H stretching mode of H2O to a Fabry-Perot cavity mode. The hybridization generates collective vibro-polaritonic states, thereby enhancing the proton conductivity by an order of magnitude at resonance. In addition, the dielectric constants increase at resonance in the coupled state. The findings presented herein reveal how a vacuum electromagnetic environment can be engineered to control the ground-state properties of water.
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Affiliation(s)
- Tomohiro Fukushima
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
| | - Soushi Yoshimitsu
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
| | - Kei Murakoshi
- Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
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