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Sangiogo Gil E, Lauvergnat D, Agostini F. Exact factorization of the photon-electron-nuclear wavefunction: Formulation and coupled-trajectory dynamics. J Chem Phys 2024; 161:084112. [PMID: 39189656 DOI: 10.1063/5.0224779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2024] [Accepted: 07/29/2024] [Indexed: 08/28/2024] Open
Abstract
We employ the exact-factorization formalism to study the coupled dynamics of photons, electrons, and nuclei at the quantum mechanical level, proposing illustrative examples of model situations of nonadiabatic dynamics and spontaneous emission of electron-nuclear systems in the regime of strong light-matter coupling. We make a particular choice of factorization for such a multi-component system, where the full wavefunction is factored as a conditional electronic amplitude and a marginal photon-nuclear amplitude. Then, we apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm to perform trajectory-based simulations, by treating photonic and nuclear degrees of freedom on equal footing in terms of classical-like trajectories. The analysis of the time-dependent potentials of the theory along with the assessment of the performance of CTMQC allows us to point out some limitations of the current approximations used in CTMQC. Meanwhile, comparing CTMQC with other trajectory-based algorithms, namely multi-trajectory Ehrenfest and Tully surface hopping, demonstrates the better quality of CTMQC predictions.
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Affiliation(s)
- Eduarda Sangiogo Gil
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
- Institute of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - David Lauvergnat
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
| | - Federica Agostini
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
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2
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Ke Y, Richardson JO. Quantum nature of reactivity modification in vibrational polariton chemistry. J Chem Phys 2024; 161:054104. [PMID: 39087532 DOI: 10.1063/5.0220908] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2024] [Accepted: 07/14/2024] [Indexed: 08/02/2024] Open
Abstract
In this work, we present a mixed quantum-classical open quantum system dynamics method for studying rate modifications of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. In this approach, the cavity radiation mode is treated classically with a mean-field nuclear force averaging over the remaining degrees of freedom, both within the system and the environment, which are handled quantum mechanically within the hierarchical equations of motion framework. Using this approach, we conduct a comparative analysis by juxtaposing the mixed quantum-classical results with fully quantum-mechanical simulations. After eliminating spurious peaks that can occur when not using the rigorous definition of the rate constant, we confirm the crucial role of the quantum nature of the cavity radiation mode in reproducing the resonant peak observed in the cavity frequency-dependent rate profile. In other words, it appears necessary to explicitly consider the quantized photonic states in studying reactivity modification in vibrational polariton chemistry (at least for the model systems studied in this work), as these phenomena stem from cavity-induced reaction pathways involving resonant energy exchanges between photons and molecular vibrational transitions.
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Affiliation(s)
- Yaling Ke
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
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3
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Anderson MC, Dodin A, Fay TP, Limmer DT. Coherent control from quantum commitment probabilities. J Chem Phys 2024; 161:024115. [PMID: 38995082 DOI: 10.1063/5.0213444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2024] [Accepted: 06/24/2024] [Indexed: 07/13/2024] Open
Abstract
We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail.
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Affiliation(s)
- Michelle C Anderson
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Amro Dodin
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Thomas P Fay
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - David T Limmer
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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4
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Bridge O, Lazzaroni P, Martinazzo R, Rossi M, Althorpe SC, Litman Y. Quantum rates in dissipative systems with spatially varying friction. J Chem Phys 2024; 161:024110. [PMID: 38984959 DOI: 10.1063/5.0216823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2024] [Accepted: 06/20/2024] [Indexed: 07/11/2024] Open
Abstract
We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.
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Affiliation(s)
- Oliver Bridge
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Paolo Lazzaroni
- MPI for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Rocco Martinazzo
- Department of Chemistry, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
| | - Mariana Rossi
- MPI for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Yair Litman
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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5
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Ke Y, Richardson JO. Insights into the mechanisms of optical cavity-modified ground-state chemical reactions. J Chem Phys 2024; 160:224704. [PMID: 38856061 DOI: 10.1063/5.0200410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Accepted: 05/27/2024] [Indexed: 06/11/2024] Open
Abstract
In this work, we systematically investigate the mechanisms underlying the rate modification of ground-state chemical reactions in an optical cavity under vibrational strong-coupling conditions. We employ a symmetric double-well description of the molecular potential energy surface and a numerically exact open quantum system approach-the hierarchical equations of motion in twin space with a matrix product state solver. Our results predict the existence of multiple peaks in the photon frequency-dependent rate profile for a strongly anharmonic molecular system with multiple vibrational transition energies. The emergence of a new peak in the rate profile is attributed to the opening of an intramolecular reaction pathway, energetically fueled by the cavity photon bath through a resonant cavity mode. The peak intensity is determined jointly by kinetic factors. Going beyond the single-molecule limit, we examine the effects of the collective coupling of two molecules to the cavity. We find that when two identical molecules are simultaneously coupled to the same resonant cavity mode, the reaction rate is further increased. This additional increase is associated with the activation of a cavity-induced intermolecular reaction channel. Furthermore, the rate modification due to these cavity-promoted reaction pathways remains unaffected, regardless of whether the molecular dipole moments are aligned in the same or opposite direction as the light polarization.
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Affiliation(s)
- Yaling Ke
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
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6
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Yu Q, Bowman JM. Fully Quantum Simulation of Polaritonic Vibrational Spectra of Large Cavity-Molecule System. J Chem Theory Comput 2024; 20:4278-4287. [PMID: 38717309 DOI: 10.1021/acs.jctc.4c00129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
The formation of molecular vibrational polaritons, arising from the interplay between molecular vibrations and infrared cavity modes, is a quantum phenomenon necessitating accurate quantum dynamical simulations. Here, we introduce the cavity vibrational self-consistent field/virtual state configuration interaction method, enabling quantum simulation of the vibrational spectra of many-molecule systems within the optical cavity. Focusing on the representative (H2O)21 system, we showcase this parameter-free quantum approach's ability to capture both linear and nonlinear vibrational spectral features. Our findings highlight the growing prominence of molecular couplings among OH stretches and bending excited bands with increased light-matter interaction, revealing distinctive nonlinear spectral features induced by vibrational strong coupling.
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Affiliation(s)
- Qi Yu
- Department of Chemistry, Fudan University, Shanghai 200438, P. R. China
| | - Joel M Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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Phuc NT. Semiclassical Truncated-Wigner-Approximation Theory of Molecular Vibration-Polariton Dynamics in Optical Cavities. J Chem Theory Comput 2024; 20:3019-3027. [PMID: 38608260 DOI: 10.1021/acs.jctc.4c00078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2024]
Abstract
It has been experimentally demonstrated that molecular-vibration polaritons formed by strong coupling of a molecular vibration to an infrared cavity mode can significantly modify the physical properties and chemical reactivities of various molecular systems. However, a complete theoretical understanding of the underlying mechanisms of the modifications remains elusive due to the complexity of the hybrid system, especially the collective nature of polaritonic states in systems containing many molecules. We develop here the semiclassical theory of molecular vibration-polariton dynamics based on the truncated Wigner approximation (TWA) that is tractable in large molecular systems and simultaneously captures the quantum character of photons in the optical cavity. The theory is then applied to investigate the nuclear quantum dynamics of a system of identical diatomic molecules having the ground-state Morse potential and being strongly coupled to an infrared cavity mode in the ultrastrong coupling regime. The validity of TWA is examined by comparing it with the full quantum dynamics of a single-molecule system for two different initial states in the dipole and Coulomb gauges. For the initial tensor-product ground state in the dipole gauge, which corresponds to a light-matter entangled state in the Coulomb gauge, the collective and resonance effects of molecular vibration-polariton formation on the nuclear dynamics are observed in a system of many molecules.
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Affiliation(s)
- Nguyen Thanh Phuc
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
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8
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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: 3] [Impact Index Per Article: 3.0] [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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9
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Hu D, Ying W, Huo P. Resonance Enhancement of Vibrational Polariton Chemistry Obtained from the Mixed Quantum-Classical Dynamics Simulations. J Phys Chem Lett 2023; 14:11208-11216. [PMID: 38055902 PMCID: PMC10726371 DOI: 10.1021/acs.jpclett.3c02985] [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: 10/25/2023] [Revised: 11/21/2023] [Accepted: 12/01/2023] [Indexed: 12/08/2023]
Abstract
We applied a variety of mixed quantum-classical (MQC) approaches to simulate the VSC-influenced reaction rate constant. All of these MQC simulations treat the key vibrational levels associated with the reaction coordinate in the quantum subsystem (as quantum states), whereas all other degrees of freedom (DOFs) are treated inside the classical subsystem. We find that, as long as we have the quantum state descriptions for the vibrational DOFs, one can correctly describe the VSC resonance condition when the cavity frequency matches the bond vibrational frequency. This correct resonance behavior can be obtained regardless of the detailed MQC methods that one uses. The results suggest that the MQC approaches can generate semiquantitative agreement with the exact results for rate constant changes when changing the cavity frequency, the light-matter coupling strength, or the cavity lifetime. The finding of this work suggests that one can use computationally economic MQC approaches to explore the collective coupling scenario when many molecules are collectively coupled to many cavity modes in the future.
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Affiliation(s)
- Deping Hu
- Center
for Advanced Materials Research, Beijing
Normal University, Zhuhai 519087, China
| | - Wenxiang Ying
- Department
of Chemistry, University of Rochester, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department
of Chemistry, University of Rochester, Rochester, New York 14627, United States
- Institute
of Optics, Hajim School of Engineering, University of Rochester, Rochester, New York 14627, United States
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