1
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Ying W, Mondal ME, Huo P. Theory and quantum dynamics simulations of exciton-polariton motional narrowing. J Chem Phys 2024; 161:064105. [PMID: 39120029 DOI: 10.1063/5.0225387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2024] [Accepted: 07/24/2024] [Indexed: 08/10/2024] Open
Abstract
The motional narrowing effect has been extensively studied for cavity exciton-polariton systems in recent decades both experimentally and theoretically, which is featured by (1) the subaverage behavior and (2) the asymmetric linewidths for the upper polariton and the lower polariton. However, a minimal theoretical model that is clear and adequate to address all these effects as well as the linewidth scaling relations remains missing. In this work, based on the single mode 1D Holstein-Tavis-Cummings (HTC) model, we studied the motional narrowing effect of the polariton linear absorption spectra via both semi-analytic derivations and numerically exact quantum dynamics simulations using the hierarchical equations of motion approach. The results reveal that under collective light-matter coupling between a cavity mode and N molecules, the polariton linewidth scales as 1/N under the slow limit, while scales as 1/N under the fast limit, due to the polaron decoupling effect. Furthermore, by varying the detunings, the polariton linewidths exhibit significant motional narrowing, covering both characters mentioned above. Our analytic linewidth expressions [Eqs. (34) and (35)] agree well with the numerical exact simulations in all the parameter regimes we explored. These results indicate that the physics of motional narrowing is adequately accounted for by the single-mode 1D HTC model. We envision that both the numerical results and the analytic polariton linewidths expression presented in this work will offer great theoretical value for providing a better understanding of the exciton-polariton motional narrowing based on the HTC model.
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Affiliation(s)
- Wenxiang Ying
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - M Elious Mondal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
- The Institute of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, USA
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2
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Borges L, Schnappinger T, Kowalewski M. Extending the Tavis-Cummings model for molecular ensembles-Exploring the effects of dipole self-energies and static dipole moments. J Chem Phys 2024; 161:044119. [PMID: 39072423 PMCID: PMC7616353 DOI: 10.1063/5.0214362] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2024] [Accepted: 06/24/2024] [Indexed: 07/30/2024] Open
Abstract
Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.
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Affiliation(s)
- Lucas Borges
- Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91Stockholm, Sweden
| | - Thomas Schnappinger
- Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91Stockholm, Sweden
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3
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Fábri C, Császár AG, Halász GJ, Cederbaum LS, Vibók Á. Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description. J Chem Phys 2024; 160:214308. [PMID: 38836455 DOI: 10.1063/5.0205048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 05/20/2024] [Indexed: 06/06/2024] Open
Abstract
The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schrödinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work, we compare numerically the Lindblad and Schrödinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schrödinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.
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Affiliation(s)
- Csaba Fábri
- HUN-REN-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Attila G Császár
- HUN-REN-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Gábor J Halász
- Department of Information Technology, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Ágnes Vibók
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
- ELI-ALPS, ELI-HU Non-Profit Ltd., Dugonics tér 13, H-6720 Szeged, Hungary
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4
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Fábri C, Halász GJ, Cederbaum LS, Vibók Á. Impact of Cavity on Molecular Ionization Spectra. J Phys Chem Lett 2024; 15:4655-4661. [PMID: 38647546 DOI: 10.1021/acs.jpclett.4c00247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
Ionization phenomena have been widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of a cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.
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Affiliation(s)
- Csaba Fábri
- HUN-REN-ELTE Complex Chemical Systems Research Group, H-1518 Budapest 112, Hungary
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Gábor J Halász
- Department of Information Technology, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
| | - Lorenz S Cederbaum
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Ágnes Vibók
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
- ELI-ALPS, ELI-HU Non-Profit Ltd, Dugonics tér 13, H-6720 Szeged, Hungary
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5
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Sokolovskii I, Groenhof G. Non-Hermitian molecular dynamics simulations of exciton-polaritons in lossy cavities. J Chem Phys 2024; 160:092501. [PMID: 38426514 DOI: 10.1063/5.0188613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 02/06/2024] [Indexed: 03/02/2024] Open
Abstract
The observation that materials can change their properties when placed inside or near an optical resonator has sparked a fervid interest in understanding the effects of strong light-matter coupling on molecular dynamics, and several approaches have been proposed to extend the methods of computational chemistry into this regime. Whereas the majority of these approaches have focused on modeling a single molecule coupled to a single cavity mode, changes to chemistry have so far only been observed experimentally when very many molecules are coupled collectively to multiple modes with short lifetimes. While atomistic simulations of many molecules coupled to multiple cavity modes have been performed with semi-classical molecular dynamics, an explicit description of cavity losses has so far been restricted to simulations in which only a very few molecular degrees of freedom were considered. Here, we have implemented an effective non-Hermitian Hamiltonian to explicitly treat cavity losses in large-scale semi-classical molecular dynamics simulations of organic polaritons and used it to perform both mean-field and surface hopping simulations of polariton relaxation, propagation, and energy transfer.
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Affiliation(s)
- Ilia Sokolovskii
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
| | - Gerrit Groenhof
- Nanoscience Center and Department of Chemistry, University of Jyväskylä, P.O. Box 35, 40014 Jyväskylä, Finland
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6
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Weight BM, Li X, Zhang Y. Theory and modeling of light-matter interactions in chemistry: current and future. Phys Chem Chem Phys 2023; 25:31554-31577. [PMID: 37842818 DOI: 10.1039/d3cp01415k] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
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.
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Affiliation(s)
- Braden M Weight
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
- Department of Physics and Astronomy, University of Rochester, Rochester, NY, 14627, USA
| | - Xinyang Li
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
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7
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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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8
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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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9
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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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10
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Davidsson E, Kowalewski M. The role of dephasing for dark state coupling in a molecular Tavis-Cummings model. J Chem Phys 2023; 159:044306. [PMID: 37493131 PMCID: PMC7615654 DOI: 10.1063/5.0155302] [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: 04/19/2023] [Accepted: 07/07/2023] [Indexed: 07/27/2023] Open
Abstract
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.
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Affiliation(s)
- Eric Davidsson
- 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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11
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Hu D, Huo P. Ab Initio Molecular Cavity Quantum Electrodynamics Simulations Using Machine Learning Models. J Chem Theory Comput 2023; 19:2353-2368. [PMID: 37000936 PMCID: PMC10134431 DOI: 10.1021/acs.jctc.3c00137] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We present a mixed quantum-classical simulation of polariton dynamics for molecule-cavity hybrid systems. In particular, we treat the coupled electronic-photonic degrees of freedom (DOFs) as the quantum subsystem and the nuclear DOFs as the classical subsystem and use the trajectory surface hopping approach to simulate non-adiabatic dynamics among the polariton states due to the coupled motion of nuclei. We use the accurate nuclear gradient expression derived from the Pauli-Fierz quantum electrodynamics Hamiltonian without making further approximations. The energies, gradients, and derivative couplings of the molecular systems are obtained from the on-the-fly simulations at the level of complete active space self-consistent field (CASSCF), which are used to compute the polariton energies and nuclear gradients. The derivatives of dipoles are also necessary ingredients in the polariton nuclear gradient expression but are often not readily available in electronic structure methods. To address this challenge, we use a machine learning model with the Kernel ridge regression method to construct the dipoles and further obtain their derivatives, at the same level as the CASSCF theory. The cavity loss process is modeled with the Lindblad jump superoperator on the reduced density of the electronic-photonic quantum subsystem. We investigate the azomethane molecule and its photoinduced isomerization dynamics inside the cavity. Our results show the accuracy of the machine-learned dipoles and their usage in simulating polariton dynamics. Our polariton dynamics results also demonstrate the isomerization reaction of azomethane can be effectively tuned by coupling to an optical cavity and by changing the light-matter coupling strength and the cavity loss rate.
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12
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Schnappinger T, Kowalewski M. Nonadiabatic Wave Packet Dynamics with Ab Initio Cavity-Born-Oppenheimer Potential Energy Surfaces. J Chem Theory Comput 2023; 19:460-471. [PMID: 36625723 PMCID: PMC9878721 DOI: 10.1021/acs.jctc.2c01154] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Indexed: 01/11/2023]
Abstract
Strong coupling of molecules with quantized electromagnetic fields can reshape their potential energy surfaces by forming dressed states. In such a scenario, it is possible to manipulate the dynamics of the molecule and open new photochemical reaction pathways. A theoretical approach to describe such coupled molecular-photon systems is the Cavity-Born-Oppenheimer (CBO) approximation. Similarly to the standard Born-Oppenheimer (BO) approximation, the system is partitioned and the electronic part of the system is treated quantum mechanically. This separation leads to CBO surfaces that depend on both nuclear and photonic coordinates. In this work, we demonstrated, for two molecular examples, how the concept of the CBO approximation can be used to perform nonadiabatic wave packet dynamics of a coupled molecular-cavity system. The light-matter interaction is incorporated in the CBO surfaces and the associated nonadiabatic coupling elements. We show that molecular and cavity contributions can be treated on the same numerical footing. This approach gives a new perspective on the description of light-matter coupling in molecular systems.
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Affiliation(s)
- Thomas Schnappinger
- Department of Physics, Stockholm University, AlbaNova University Center, SE-106
91Stockholm, Sweden
| | - Markus Kowalewski
- Department of Physics, Stockholm University, AlbaNova University Center, SE-106
91Stockholm, Sweden
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13
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Ochoa MA. Quantum thermodynamics of periodically driven polaritonic systems. Phys Rev E 2022; 106:064113. [PMID: 36671137 DOI: 10.1103/physreve.106.064113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 11/16/2022] [Indexed: 06/17/2023]
Abstract
We investigate the energy distribution and quantum thermodynamics in periodically-driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and quantify the energy reorganization between these two systems and their interaction as a function of coupling strength, driving force, and detuning. After deriving the quantum master equation for the polariton density matrix with weak environment interactions, we obtain the dissipative time propagator and the long-time evolution of an equilibrium initial state. This approach provides direct access to the stationary state and overcomes the difficulties found in the numerical evolution of weakly damped quantum systems near resonance, also providing maps on the polariton lineshape. Then, we compute the thermodynamic performance during harmonic modulation and demonstrate that maximum efficiency occurs at resonance. We also provide an expression for the irreversible heat rate and numerically demonstrate that this agrees with the thermodynamic laws.
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Affiliation(s)
- Maicol A Ochoa
- Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland, USA
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14
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Schnappinger T, Jadoun D, Gudem M, Kowalewski M. Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry. Chem Commun (Camb) 2022; 58:12763-12781. [PMID: 36317595 PMCID: PMC9671098 DOI: 10.1039/d2cc04875b] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 10/21/2022] [Indexed: 11/03/2023]
Abstract
The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.
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Affiliation(s)
- Thomas Schnappinger
- Department of Physics, Stockholm University, Albanova University Centre, SE-106 91 Stockholm, Sweden.
| | - Deependra Jadoun
- Department of Physics, Stockholm University, Albanova University Centre, SE-106 91 Stockholm, Sweden.
| | - 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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15
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Couto RC, Kowalewski M. Suppressing non-radiative decay of photochromic organic molecular systems in the strong coupling regime. Phys Chem Chem Phys 2022; 24:19199-19208. [PMID: 35861014 PMCID: PMC9382694 DOI: 10.1039/d2cp00774f] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 07/10/2022] [Indexed: 11/21/2022]
Abstract
The lifetimes of electronic excited states have a strong influence on the efficiency of organic solar cells. However, in some molecular systems a given excited state lifetime is reduced due to the non-radiative decay through conical intersections. Several strategies may be used to suppress this decay channel. The use of the strong light-matter coupling provided in optical nano-cavities is the focus of this paper. Here, we consider the meso-tert-butyl-4,4-difluoro-4-bora-3a,4a-diaza-s-indacene molecule (meso-tert-butyl-BODIPY) as a showcase of how strong and ultrastrong coupling might help in the development of organic solar cells. The meso-tert-butyl-BODIPY is known for its low fluorescence yield caused by the non-radiative decay through a conical intersection. However, we show here that, by considering this system within a cavity, the strong coupling can lead to significant changes in the multidimensional landscape of the potential energy surfaces of meso-tert-butyl-BODIPY, suppressing almost completely the decay of the excited state wave packet back to the ground state. By means of multi configuration electronic structure calculations and nuclear wave packet dynamics, the coupling with the cavity is analyzed in-depth to provide further insight of the interaction. By fine-tuning the cavity field strength and resonance frequency, we show that one can change the nuclear dynamics in the excited state, and control the non-radiative decay. This may lead to a faster and more efficient population transfer or the suppression of it.
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Affiliation(s)
- Rafael C Couto
- 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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16
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Abstract
Triplet-triplet annihilation (TTA) is a spin-allowed conversion of two triplet states into one singlet excited state, which provides an efficient route to generate a photon of higher frequency than the incident light. Multiple energy transfer steps between absorbing (sensitizer) and emitting (annihilator) molecular species are involved in the TTA based photon upconversion process. TTA compounds have recently been studied for solar energy applications, even though the maximum upconversion efficiency of 50 % is yet to be achieved. With the aid of quantum calculations and based on a few key requirements, several design principles have been established to develop the well-functioning annihilators. However, a complete molecular level understanding of triplet fusion dynamics is still missing. In this work, we have employed multi-reference electronic structure methods along with quantum dynamics to obtain a detailed and fundamental understanding of TTA mechanism in naphthalene. Our results suggest that the TTA process in naphthalene is mediated by conical intersections. In addition, we have explored the triplet fusion dynamics under the influence of strong light-matter coupling and found an increase of the TTA based upconversion efficiency.
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Affiliation(s)
- Mahesh Gudem
- Department of PhysicsStockholm UniversityAlbanova University CentreSE-106 91StockholmSweden
| | - Markus Kowalewski
- Department of PhysicsStockholm UniversityAlbanova University CentreSE-106 91StockholmSweden
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17
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Koessler ER, Mandal A, Huo P. Incorporating Lindblad Decay Dynamics into Mixed Quantum-Classical Simulations. J Chem Phys 2022; 157:064101. [DOI: 10.1063/5.0099922] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We derive the $\mathcal{L}$-MFE method to incorporate Lindblad jump operator dynamics into the mean-field Ehrenfest (MFE) approach. We map the density matrix evolution of Lindblad dynamics onto pure state coefficients using trajectory averages. We use simple assumptions to construct the $\mathcal{L}$-MFE method that satisfies this exact mapping. This establishes a method that uses independent trajectories which exactly reproduces Lindblad decay dynamics using a wavefunction description, with deterministic changes of the magnitudes of the quantum expansion coefficients, while only adding on a stochastic phase. We further demonstrate that when including nuclei in the Ehrenfest dynamics, the $\mathcal{L}$-MFE method gives semi-quantitatively accurate results, with the accuracy limited by the accuracy of the approximations present in the semiclassical MFE approach. This work provides a general framework to incorporate Lindblad dynamics into semiclassical or mixed quantum-classical simulations.
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Affiliation(s)
- Eric R Koessler
- Chemistry, University of Rochester, United States of America
| | | | - Pengfei Huo
- Department of Chemsitry, University of Rochester Department of Chemistry, United States of America
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18
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Fregoni J, Garcia-Vidal FJ, Feist J. Theoretical Challenges in Polaritonic Chemistry. ACS PHOTONICS 2022; 9:1096-1107. [PMID: 35480492 PMCID: PMC9026242 DOI: 10.1021/acsphotonics.1c01749] [Citation(s) in RCA: 42] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 02/01/2022] [Accepted: 02/02/2022] [Indexed: 06/14/2023]
Abstract
Polaritonic chemistry exploits strong light-matter coupling between molecules and confined electromagnetic field modes to enable new chemical reactivities. In systems displaying this functionality, the choice of the cavity determines both the confinement of the electromagnetic field and the number of molecules that are involved in the process. While in wavelength-scale optical cavities the light-matter interaction is ruled by collective effects, plasmonic subwavelength nanocavities allow even single molecules to reach strong coupling. Due to these very distinct situations, a multiscale theoretical toolbox is then required to explore the rich phenomenology of polaritonic chemistry. Within this framework, each component of the system (molecules and electromagnetic modes) needs to be treated in sufficient detail to obtain reliable results. Starting from the very general aspects of light-molecule interactions in typical experimental setups, we underline the basic concepts that should be taken into account when operating in this new area of research. Building on these considerations, we then provide a map of the theoretical tools already available to tackle chemical applications of molecular polaritons at different scales. Throughout the discussion, we draw attention to both the successes and the challenges still ahead in the theoretical description of polaritonic chemistry.
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19
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Climent C, Casanova D, Feist J, Garcia-Vidal FJ. Not dark yet for strong light-matter coupling to accelerate singlet fission dynamics. CELL REPORTS. PHYSICAL SCIENCE 2022; 3:100841. [PMID: 35620360 PMCID: PMC9022090 DOI: 10.1016/j.xcrp.2022.100841] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 02/25/2022] [Accepted: 03/14/2022] [Indexed: 06/14/2023]
Abstract
Polaritons are unique hybrid light-matter states that offer an alternative way to manipulate chemical processes. In this work, we show that singlet fission dynamics can be accelerated under strong light-matter coupling. For superexchange-mediated singlet fission, state mixing speeds up the dynamics in cavities when the lower polariton is close in energy to the multiexcitonic state. This effect is more pronounced in non-conventional singlet fission materials in which the energy gap between the bright singlet exciton and the multiexcitonic state is large ( > 0.1 eV). In this case, the dynamics is dominated by the polaritonic modes and not by the bare-molecule-like dark states, and, additionally, the resonant enhancement due to strong coupling is robust even for energetically broad molecular states. The present results provide a new strategy to expand the range of suitable materials for efficient singlet fission by making use of strong light-matter coupling.
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Affiliation(s)
- Clàudia Climent
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - David Casanova
- Donostia International Physics Centre (DIPC), 20018 Donostia, Euskadi, Spain
- IKERBASQUE, Basque Foundation for Science, 48009 Bilbao, Euskadi, Spain
| | - Johannes Feist
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
| | - Francisco J. Garcia-Vidal
- Departamento de Física Teórica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, 28049 Madrid, Spain
- Institute of High Performance Computing, Agency for Science, Technology, and Research (A∗STAR), Connexis, 138632, Singapore
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20
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McTague J, Foley J. Non-Hermitian Cavity Quantum Electrodynamics - Configuration Interaction Singles Approach for Polaritonic Structure with ab initio Molecular Hamiltonians. J Chem Phys 2022; 156:154103. [DOI: 10.1063/5.0091953] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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.
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Affiliation(s)
- Jonathan McTague
- William Paterson University College of Science and Health, United States of America
| | - Jonathan Foley
- Chemistry, William Paterson University College of Science and Health, United States of America
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21
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Fábri C, Halász GJ, Vibók Á. Probing Light-Induced Conical Intersections by Monitoring Multidimensional Polaritonic Surfaces. J Phys Chem Lett 2022; 13:1172-1179. [PMID: 35084197 DOI: 10.1021/acs.jpclett.1c03465] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.
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Affiliation(s)
- Csaba Fábri
- MTA-ELTE Complex Chemical Systems Research Group, P.O. Box 32, Budapest 112, H-1518, Hungary
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, Debrecen, H-4002, Hungary
| | - Gábor J Halász
- Department of Information Technology, University of Debrecen, P.O. Box 400, Debrecen, H-4002, Hungary
| | - Ágnes Vibók
- Department of Theoretical Physics, University of Debrecen, P.O. Box 400, Debrecen, H-4002, Hungary
- ELI-ALPS, ELI-HU Non-Profit Ltd., Dugonics tér 13, Szeged, H-6720, Hungary
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22
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Rosenzweig B, Hoffmann NM, Lacombe L, Maitra NT. Analysis of the classical trajectory treatment of photon dynamics for polaritonic phenomena. J Chem Phys 2022; 156:054101. [DOI: 10.1063/5.0079379] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Bart Rosenzweig
- Department of Mathematics and Statistics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Norah M. Hoffmann
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Lionel Lacombe
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Neepa T. Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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23
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Yuen-Zhou J, Xiong W, Shegai T. Polariton chemistry: Molecules in cavities and plasmonic media. J Chem Phys 2022; 156:030401. [DOI: 10.1063/5.0080134] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
- Joel Yuen-Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Wei Xiong
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Timur Shegai
- Department of Physics, Chalmers University of Technology, Gothenburg 41296, Sweden
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24
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Wang S, Chuang YT, Hsu LY. Simple but accurate estimation of light-matter coupling strength and optical loss for a molecular emitter coupled with photonic modes. J Chem Phys 2021; 155:134117. [PMID: 34624977 DOI: 10.1063/5.0060171] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Light-matter coupling strength and optical loss are two key physical quantities in cavity quantum electrodynamics (CQED), and their interplay determines whether light-matter hybrid states can be formed or not in chemical systems. In this study, by using macroscopic quantum electrodynamics (MQED) combined with a pseudomode approach, we present a simple but accurate method, which allows us to quickly estimate the light-matter coupling strength and optical loss without free parameters. Moreover, for a molecular emitter coupled with photonic modes (including cavity modes and plasmon polariton modes), we analytically and numerically prove that the dynamics derived from the MQED-based wavefunction approach is mathematically equivalent to the dynamics governed by the CQED-based Lindblad master equation when the Purcell factor behaves like Lorentzian functions.
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Affiliation(s)
- Siwei Wang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Yi-Ting Chuang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Liang-Yan Hsu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
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25
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Ye C, Mallick S, Hertzog M, Kowalewski M, Börjesson K. Direct Transition from Triplet Excitons to Hybrid Light-Matter States via Triplet-Triplet Annihilation. J Am Chem Soc 2021; 143:7501-7508. [PMID: 33973463 PMCID: PMC8154526 DOI: 10.1021/jacs.1c02306] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
![]()
Strong light–matter
coupling generates hybrid states that
inherit properties of both light and matter, effectively allowing
the modification of the molecular potential energy landscape. This
phenomenon opens up a plethora of options for manipulating the properties
of molecules, with a broad range of applications in photochemistry
and photophysics. In this article, we use strong light–matter
coupling to transform an endothermic triplet–triplet annihilation
process into an exothermic one. The resulting gradual on–off
photon upconversion experiment demonstrates a direct conversion between
molecular states and hybrid light–matter states. Our study
provides a direct evidence that energy can relax from nonresonant
low energy molecular states directly into hybrid light–matter
states and lays the groundwork for tunable photon upconversion systems
that modify molecular properties in situ by optical cavities rather
than with chemical modifications.
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Affiliation(s)
- Chen Ye
- Department of Chemistry and Molecular Biology, University of Gothenburg, Kemigården 4, 412 96 Gothenburg, Sweden
| | - Suman Mallick
- Department of Chemistry and Molecular Biology, University of Gothenburg, Kemigården 4, 412 96 Gothenburg, Sweden
| | - Manuel Hertzog
- Department of Chemistry and Molecular Biology, University of Gothenburg, Kemigården 4, 412 96 Gothenburg, Sweden
| | - Markus Kowalewski
- Department of Physics, Stockholm University, Albanova University Centre, 106 91 Stockholm, Sweden
| | - Karl Börjesson
- Department of Chemistry and Molecular Biology, University of Gothenburg, Kemigården 4, 412 96 Gothenburg, Sweden
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26
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Du M, Campos-Gonzalez-Angulo JA, Yuen-Zhou J. Nonequilibrium effects of cavity leakage and vibrational dissipation in thermally activated polariton chemistry. J Chem Phys 2021; 154:084108. [PMID: 33639750 DOI: 10.1063/5.0037905] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
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.
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Affiliation(s)
- Matthew Du
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | | | - Joel Yuen-Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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27
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Gudem M, Kowalewski M. Controlling the Photostability of Pyrrole with Optical Nanocavities. J Phys Chem A 2021; 125:1142-1151. [PMID: 33464084 PMCID: PMC7883346 DOI: 10.1021/acs.jpca.0c09252] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Revised: 12/15/2020] [Indexed: 11/28/2022]
Abstract
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.
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Affiliation(s)
- Mahesh Gudem
- Department of Physics, Albanova University
Centre, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Markus Kowalewski
- Department of Physics, Albanova University
Centre, Stockholm University, SE-106 91 Stockholm, Sweden
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28
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Wellnitz D, Pupillo G, Schachenmayer J. A quantum optics approach to photoinduced electron transfer in cavities. J Chem Phys 2021; 154:054104. [DOI: 10.1063/5.0037412] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- D. Wellnitz
- ISIS (UMR 7006), University of Strasbourg and CNRS, and icFRC, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
| | - G. Pupillo
- ISIS (UMR 7006), University of Strasbourg and CNRS, and icFRC, 67000 Strasbourg, France
| | - J. Schachenmayer
- ISIS (UMR 7006), University of Strasbourg and CNRS, and icFRC, 67000 Strasbourg, France
- IPCMS (UMR 7504), CNRS, 67000 Strasbourg, France
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