1
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De PK, Jain A. Exciton energy transfer inside cavity-A benchmark study of polaritonic dynamics using the surface hopping method. J Chem Phys 2024; 161:054117. [PMID: 39105549 DOI: 10.1063/5.0216787] [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: 07/22/2024] [Indexed: 08/07/2024] Open
Abstract
Strong coupling between the molecular system and photon inside the cavity generates polaritons, which can alter reaction rates by orders of magnitude. In this work, we benchmark the surface hopping method to simulate non-adiabatic dynamics in a cavity. The comparison is made against a numerically exact method (the hierarchical equations of motion) for a model system investigating excitonic energy transfer for a broad range of parameters. Surface hopping captures the effects of the radiation mode well, both at resonance and off-resonance. We have further investigated parameters that can increase or decrease the rate of population transfer, and we find that surface hopping in general can capture both effects well. Finally, we show that the dipole self-energy term within our parameter regime does not significantly affect the system's dynamics.
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Affiliation(s)
- Priyam Kumar De
- Department of Chemistry, Indian Institute of Technology, Mumbai 400076, India
| | - Amber Jain
- Department of Chemistry, Indian Institute of Technology, Mumbai 400076, India
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2
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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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3
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Huang L, Shi Z, Wang L. Detailed Complementary Consistency: Wave Function Tells Particle How to Hop, Particle Tells Wave Function How to Collapse. J Phys Chem Lett 2024; 15:6771-6781. [PMID: 38912973 DOI: 10.1021/acs.jpclett.4c01313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/25/2024]
Abstract
In mixed quantum-classical dynamics, the quantum subsystem can have both wave function and particle-like descriptions. However, they may yield inconsistent results for the expectation value of the same physical quantity. We here propose a novel detailed complementary consistency (DCC) method based on the principle of detailed internal consistency. Namely, the wave function along each trajectory tells the particle how to hop, while the particle tells the wave function how to collapse based on active states in the trajectory ensemble. As benchmarked in a diverse array of representative models with localized nonadiabatic couplings, DCC not only achieves fully consistent results (i.e., identical populations calculated based on wave functions and active states) but also closely reproduces the exact quantum results. Due to the high performance, our new DCC method has great potential to give a consistent and accurate mixed quantum-classical description of general nonadiabatic dynamics after further development.
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Affiliation(s)
- Lei Huang
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Zhecun Shi
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
| | - Linjun Wang
- Key Laboratory of Excited-State Materials of Zhejiang Province, Department of Chemistry, Zhejiang University, Hangzhou 310058, China
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4
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Liu Z, Hanna G. Population and Energy Transfer Dynamics in an Open Excitonic Quantum Battery. Molecules 2024; 29:889. [PMID: 38398641 PMCID: PMC10892759 DOI: 10.3390/molecules29040889] [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: 12/28/2023] [Revised: 02/07/2024] [Accepted: 02/13/2024] [Indexed: 02/25/2024] Open
Abstract
In a previous study, we proposed an open quantum network model of a quantum battery (QB) that possesses dark states owing to its structural exchange symmetries. While in a dark state, the QB is capable of storing an exciton without any environment-induced population losses. However, when the structural exchange symmetry is broken, the QB begins to discharge the exciton towards its exit site. In this article, we start by demonstrating that this QB is not only loss-free with respect to exciton population during the storage phase, but also with respect to the QB energy. We then explore the exciton population and energy transfer dynamics of the QB during the discharge phase over a wide range of site energies, bath temperatures, and bath reorganization energies. Our results shed light on how to optimize the QB's population and energy transfer dynamics for different purposes.
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Affiliation(s)
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, AB T6G 2G2, Canada;
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5
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Attal L, Falvo C, Calvo F, Parneix P. Modeling the dynamics of quantum systems coupled to large-dimensional baths using effective energy states. J Chem Phys 2024; 160:044107. [PMID: 38270236 DOI: 10.1063/5.0184299] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 12/14/2023] [Indexed: 01/26/2024] Open
Abstract
The quantum dynamics of a low-dimensional system in contact with a large but finite harmonic bath is theoretically investigated by coarse-graining the bath into a reduced set of effective energy states. In this model, the couplings between the system and the bath are obtained from statistically averaging over the discrete, degenerate effective states. Our model is aimed at intermediate bath sizes in which non-Markovian processes and energy transfer between the bath and the main system are important. The method is applied to a model system of a Morse oscillator coupled to 40 harmonic modes. The results are found to be in excellent agreement with the direct quantum dynamics simulations presented in the work of Bouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a much lower computational cost. Extension to larger baths is discussed in comparison to the time-convolutionless method. We also extend this study to the case of a microcanonical bath with finite initial internal energies. The computational efficiency and convergence properties of the effective bath states model with respect to relevant parameters are also discussed.
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Affiliation(s)
- Loïse Attal
- Institut des Sciences Moléculaires d'Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Cyril Falvo
- Institut des Sciences Moléculaires d'Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France
- Université Grenoble-Alpes, CNRS, LiPhy, 38000 Grenoble, France
| | - Florent Calvo
- Université Grenoble-Alpes, CNRS, LiPhy, 38000 Grenoble, France
| | - Pascal Parneix
- Institut des Sciences Moléculaires d'Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France
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6
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Bose A. Quantum correlation functions through tensor network path integral. J Chem Phys 2023; 159:214110. [PMID: 38051096 DOI: 10.1063/5.0174338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Accepted: 11/07/2023] [Indexed: 12/07/2023] Open
Abstract
Tensor networks have historically proven to be of great utility in providing compressed representations of wave functions that can be used for the calculation of eigenstates. Recently, it has been shown that a variety of these networks can be leveraged to make real time non-equilibrium simulations of dynamics involving the Feynman-Vernon influence functional more efficient. In this work, a tensor network is developed for non-perturbatively calculating the equilibrium correlation function for open quantum systems using the path integral methodology. These correlation functions are of fundamental importance in calculations of rates of reactions, simulations of response functions and susceptibilities, spectra of systems, etc. The influence of the solvent on the quantum system is incorporated through an influence functional, whose unconventional structure motivates the design of a new optimal matrix product-like operator that can be applied to the so-called path amplitude matrix product state. This complex-time tensor network path integral approach provides an exceptionally efficient representation of the path integral, enabling simulations for larger systems strongly interacting with baths and at lower temperatures out to longer time. The derivation, design, and implementation of this method are discussed along with a wide range of illustrations ranging from rate theory and symmetrized spin correlation functions to simulation of response of the Fenna-Matthews-Olson complex to light.
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Affiliation(s)
- Amartya Bose
- Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai 400005, India
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7
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He X, Wu B, Shang Y, Li B, Cheng X, Liu J. New phase space formulations and quantum dynamics approaches. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1619] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Xin He
- Beijing National Laboratory for Molecular Sciences Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing China
| | - Baihua Wu
- Beijing National Laboratory for Molecular Sciences Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing China
| | - Youhao Shang
- Beijing National Laboratory for Molecular Sciences Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing China
| | - Bingqi Li
- Beijing National Laboratory for Molecular Sciences Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing China
| | - Xiangsong Cheng
- Beijing National Laboratory for Molecular Sciences Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University Beijing China
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8
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Gardner J, Douglas-Gallardo OA, Stark WG, Westermayr J, Janke SM, Habershon S, Maurer RJ. NQCDynamics.jl: A Julia package for nonadiabatic quantum classical molecular dynamics in the condensed phase. J Chem Phys 2022; 156:174801. [PMID: 35525649 DOI: 10.1063/5.0089436] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the NQCDynamics.jl package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H2 on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.
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Affiliation(s)
- James Gardner
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Oscar A Douglas-Gallardo
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Wojciech G Stark
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Julia Westermayr
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Svenja M Janke
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
| | - Reinhard J Maurer
- Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
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9
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Lindoy LP, Kloss B, Reichman DR. Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator. J Chem Phys 2021; 155:174109. [PMID: 34742222 DOI: 10.1063/5.0070043] [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
The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 106 bath modes and find that for these problems, the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ∼1.3×109 parameters to obtain accurate dynamics.
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Affiliation(s)
- Lachlan P Lindoy
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Benedikt Kloss
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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10
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Yan Y, Ergogo TT, Lü Z, Chen L, Luo J, Zhao Y. Lamb Shift and the Vacuum Rabi Splitting in a Strongly Dissipative Environment. J Phys Chem Lett 2021; 12:9919-9925. [PMID: 34613722 DOI: 10.1021/acs.jpclett.1c02791] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We study the vacuum Rabi splitting of a qubit ultrastrongly coupled to a high-Q cavity mode and a radiation reservoir. Three methods are employed: a numerically exact variational approach with a multiple Davydov ansatz, the rotating-wave approximation (RWA), and the transformed RWA. Agreement between the variational results and the transformed RWA results is found in the regime of validity of the latter, where the RWA breaks down completely. We illustrate that the Lamb shift plays an essential role in modifying the vacuum Rabi splitting in the ultrastrong coupling regime, leading to off-resonant qubit-cavity coupling even though the cavity frequency equals the bare transition frequency of the qubit. Specifically, the emission spectrum exhibits one broad low-frequency peak and one narrow high-frequency peak in the presence of relatively weak cavity-qubit coupling. As the cavity-qubit coupling increases, the low-frequency peak narrows while the high-frequency peak broadens until they have similar widths.
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Affiliation(s)
- Yiying Yan
- Department of Physics, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
| | - Tadele T Ergogo
- Department of Physics, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
| | - Zhiguo Lü
- Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str., 38, 01187 Dresden, Germany
| | - JunYan Luo
- Department of Physics, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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11
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He X, Wu B, Gong Z, Liu J. Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics. J Phys Chem A 2021; 125:6845-6863. [PMID: 34339600 DOI: 10.1021/acs.jpca.1c04429] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
We show that a novel, general phase space mapping Hamiltonian for nonadiabatic systems, which is reminiscent of the renowned Meyer-Miller mapping Hamiltonian, involves a commutator variable matrix rather than the conventional zero-point-energy parameter. In the exact mapping formulation on constraint space for phase space approaches for nonadiabatic dynamics, the general mapping Hamiltonian with commutator variables can be employed to generate approximate trajectory-based dynamics. Various benchmark model tests, which range from gas phase to condensed phase systems, suggest that the overall performance of the general mapping Hamiltonian is better than that of the conventional Meyer-Miller Hamiltonian.
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Affiliation(s)
- Xin He
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Baihua Wu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Zhihao Gong
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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12
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Karmakar A, Gangopadhyay G. Electron-Vibration Entanglement of Resonating Dimers in Quantum Transport. J Phys Chem A 2021; 125:3122-3134. [PMID: 33829793 DOI: 10.1021/acs.jpca.1c00964] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Electron transport in a single molecule resulting from the superposition of its vibronic states depends on the coupling strength with the metallic leads. However, dynamical coherence and Fermionic correlation in molecule-molecule and molecule-lead coupling necessitates a critical approach to treat the current and its noise level, especially in the presence of a variable external bias for temperature-dependent conduction. Primarily, this work is a generalization of the theoretical approach of the atomic dimers to incorporate the effect of vibrational modes in current and conductance characteristics. The variation of current and differential conductance due to the external bias reveals a vibrational Coulomb blockade structure corresponding to the functioning vibrational mode in the system. The numerical demonstration for a diverse class of molecules generically shows that electron-vibration interaction can quantitatively predict the nature of coherent electron transport and current noise. Secondly, an attempt has been made to illustrate the effect of magnitude of coherence-induced noise suppression of current as a signature of electron-vibration entanglement. Finally, temperature-dependent conductance of the molecular junction in dimer structure has been estimated along with the peak shifts due to the applied gate voltage.
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Affiliation(s)
- Anirban Karmakar
- Department of Chemistry, Bankim Sardar College, Tangrakhali, Taldi, South 24 Parganas, West Bengal Pin-743329, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake City, Kolkata 700 106, India
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13
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Carpio-Martínez P, Hanna G. Quantum bath effects on nonequilibrium heat transport in model molecular junctions. J Chem Phys 2021; 154:094108. [PMID: 33685175 DOI: 10.1063/5.0040752] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum-classical dynamics simulations enable the study of nonequilibrium heat transport in realistic models of molecules coupled to thermal baths. In these simulations, the initial conditions of the bath degrees of freedom are typically sampled from classical distributions. Herein, we investigate the effects of sampling the initial conditions of the thermal baths from quantum and classical distributions on the steady-state heat current in the nonequilibrium spin-boson model-a prototypical model of a single-molecule junction-in different parameter regimes. For a broad range of parameter regimes considered, we find that the steady-state heat currents are ∼1.3-4.5 times larger with the classical bath sampling than with the quantum bath sampling. Using both types of sampling, the steady-state heat currents exhibit turnovers as a function of the bath reorganization energy, with sharper turnovers in the classical case than in the quantum case and different temperature dependencies of the turnover maxima. As the temperature gap between the hot and cold baths increases, we observe an increasing difference in the steady-state heat currents obtained with the classical and quantum bath sampling. In general, as the bath temperatures are increased, the differences between the results of the classical and quantum bath sampling decrease but remain non-negligible at the high bath temperatures. The differences are attributed to the more pronounced temperature dependence of the classical distribution compared to the quantum one. Moreover, we find that the steady-state fluctuation theorem only holds for this model in the Markovian regime when quantum bath sampling is used. Altogether, our results highlight the importance of quantum bath sampling in quantum-classical dynamics simulations of quantum heat transport.
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Affiliation(s)
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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14
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Wang H, Meyer HD. Importance of Appropriately Regularizing the ML-MCTDH Equations of Motion. J Phys Chem A 2021; 125:3077-3087. [DOI: 10.1021/acs.jpca.0c11221] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
| | - Hans-Dieter Meyer
- Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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15
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Sathyamurthy N, Mahapatra S. Time-dependent quantum mechanical wave packet dynamics. Phys Chem Chem Phys 2020; 23:7586-7614. [PMID: 33306771 DOI: 10.1039/d0cp03929b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Starting from a model study of the collinear (H, H2) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH4. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H2) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.
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16
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Zhang HD, Cui L, Gong H, Xu RX, Zheng X, Yan Y. Hierarchical equations of motion method based on Fano spectrum decomposition for low temperature environments. J Chem Phys 2020; 152:064107. [PMID: 32061227 DOI: 10.1063/1.5136093] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The hierarchical equations of motion (HEOM) method has become one of the most popular methods for the studies of the open quantum system. However, its applicability to systems at ultra-low temperatures is largely restrained by the enormous computational cost, which is caused by the numerous exponential functions required to accurately characterize the non-Markovian memory of the reservoir environment. To overcome this problem, a Fano spectrum decomposition (FSD) scheme has been proposed recently [Cui et al., J. Chem. Phys. 151, 024110 (2019)], which expands the reservoir correlation functions using polynomial-exponential functions and hence greatly reduces the size of the memory basis set. In this work, we explicitly establish the FSD-based HEOM formalisms for both bosonic and fermionic environments. The accuracy and efficiency of the FSD-based HEOM are exemplified by the calculated low-temperature dissipative dynamics of a spin-boson model and the dynamic and static properties of a single-orbital Anderson impurity model in the Kondo regime. The encouraging numerical results highlight the practicality and usefulness of the FSD-based HEOM method for general open systems at ultra-low temperatures.
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Affiliation(s)
- Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lei Cui
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Hong Gong
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale, iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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17
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Saller MAC, Kelly A, Richardson JO. Improved population operators for multi-state nonadiabatic dynamics with the mixed quantum-classical mapping approach. Faraday Discuss 2020; 221:150-167. [DOI: 10.1039/c9fd00050j] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Application to the 7-state Frenkel-exciton Hamiltonian for the Fenna–Matthews–Olson complex shows that using a different representation of the electronic population operators can drastically improve the accuracy of the quasiclassical mapping approach without increasing the computational effort.
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Affiliation(s)
| | - Aaron Kelly
- Department of Chemistry
- Dalhousie University
- Halifax
- Canada
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18
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Mangaud E, Lasorne B, Atabek O, Desouter-Lecomte M. Statistical distributions of the tuning and coupling collective modes at a conical intersection using the hierarchical equations of motion. J Chem Phys 2019; 151:244102. [DOI: 10.1063/1.5128852] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Etienne Mangaud
- Physicochimie des Electrolytes et des Nanosystèmes Interfaciaux-UMR 8234 Sorbonne Université, F-75252 Paris, France and Laboratoire Collisions Agrégats Réactivité (IRSAMC), Université Toulouse III Paul Sabatier, UMR 5589, F-31062 Toulouse, France
| | - Benjamin Lasorne
- Institut Charles Gerhardt Montpellier (ICGM), Université de Montpellier, CNRS, ENSCM, F-34095 Montpellier, France
| | - Osman Atabek
- Institut des Sciences Moléculaires d’Orsay (ISMO), Université Paris-Saclay, CNRS, F-91405 Orsay, France
| | - Michèle Desouter-Lecomte
- Institut de Chimie Physique (ICP), Université Paris-Saclay, CNRS, F-91405 Orsay, France and Département de Chimie, Université de Liège, Sart Tilman, B6, B-4000 Liège, Belgium
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19
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Carpio-Martínez P, Hanna G. Nonequilibrium heat transport in a molecular junction: A mixed quantum-classical approach. J Chem Phys 2019; 151:074112. [PMID: 31438711 DOI: 10.1063/1.5113599] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In a recent study [J. Liu et al., J. Chem. Phys. 149, 224104 (2018)], we developed a general mixed quantum-classical framework for studying heat transport through molecular junctions, in which the junction molecule is treated quantum mechanically and the thermal reservoirs to which the molecule is coupled are treated classically. This framework yields expressions for the transferred heat and steady-state heat current, which could be calculated using a variety of mixed quantum-classical dynamics methods. In this work, we use the recently developed "Deterministic Evolution of Coordinates with Initial Decoupled Equations" (DECIDE) method for calculating the steady-state heat current in the nonequilibrium spin-boson model in a variety of parameter regimes. Our results are compared and contrasted with those obtained using the numerically exact multilayer multiconfiguration time-dependent Hartree approach, and using approximate methods, including mean field theory, Redfield theory, and adiabatic mixed quantum-classical dynamics. Despite some quantitative differences, the DECIDE method performs quite well, is capable of capturing the expected trends in the steady-state heat current, and, overall, outperforms the approximate methods. These results hold promise for DECIDE simulations of nonequilibrium heat transport in realistic models of nanoscale systems.
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Affiliation(s)
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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20
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Liu J, Segal D. Interplay of Direct and Indirect Charge-Transfer Pathways in Donor–Bridge–Acceptor Systems. J Phys Chem B 2019; 123:6099-6110. [DOI: 10.1021/acs.jpcb.9b04958] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Junjie Liu
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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21
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He X, Liu J. A new perspective for nonadiabatic dynamics with phase space mapping models. J Chem Phys 2019; 151:024105. [DOI: 10.1063/1.5108736] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xin He
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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22
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Hartmann R, Werther M, Grossmann F, Strunz WT. Exact open quantum system dynamics: Optimal frequency vs time representation of bath correlations. J Chem Phys 2019; 150:234105. [PMID: 31228905 DOI: 10.1063/1.5097158] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Richard Hartmann
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
| | - Michael Werther
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
| | - Frank Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
| | - Walter T. Strunz
- Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
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23
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Teh HH, Jin BY, Cheng YC. Frozen-mode small polaron quantum master equation with variational bound for excitation energy transfer in molecular aggregates. J Chem Phys 2019; 150:224110. [DOI: 10.1063/1.5096287] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hung-Hsuan Teh
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Bih-Yaw Jin
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Yuan-Chung Cheng
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
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24
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Wang Q, Gong Z, Duan C, Tang Z, Wu J. Dynamical scaling in the Ohmic spin-boson model studied by extended hierarchical equations of motion. J Chem Phys 2019; 150:084114. [PMID: 30823766 DOI: 10.1063/1.5085871] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Through a decomposition of the bath correlation function, the hierarchical equations of motion are extended to the Ohmic spin-boson model at zero temperature. For two typical cutoff functions of the bath spectral density, the rate kernel of spin dynamics is numerically extracted by a time-convolution equation of the average magnetic moment. A characteristic time is defined accordingly as the inverse of the zeroth-order moment of the rate kernel. For a given Kondo parameter in the incoherent regime, the time evolution of average magnetic moments gradually collapses onto a master curve after rescaling the time variable with the characteristic time. The rescaled spin dynamics is nearly independent of the cutoff frequency and the form of cutoff functions. For a given cutoff frequency, the characteristic time with the change of the Kondo parameter is fitted excellently as a function of the renormalized tunneling amplitude. Despite a significant difference in definition, our result is in good agreement with the characteristic time of the noninteracting blip approximation.
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Affiliation(s)
- Qianlong Wang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Zhihao Gong
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Chenru Duan
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Zhoufei Tang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
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25
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Computational study on the removal of photolabile protecting groups by photochemical reactions. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.01.016] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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26
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Saller MAC, Kelly A, Richardson JO. On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics. J Chem Phys 2019; 150:071101. [DOI: 10.1063/1.5082596] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Aaron Kelly
- Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada
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27
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Wang H, Shao J. Quantum Phase Transition in the Spin-Boson Model: A Multilayer Multiconfiguration Time-Dependent Hartree Study. J Phys Chem A 2019; 123:1882-1893. [DOI: 10.1021/acs.jpca.8b11136] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
- Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Jiushu Shao
- College of Chemistry and Center for Advanced Quantum Studies and Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China
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28
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Liu J, Hsieh CY, Segal D, Hanna G. Heat transfer statistics in mixed quantum-classical systems. J Chem Phys 2018; 149:224104. [PMID: 30553258 DOI: 10.1063/1.5066025] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
The modelling of quantum heat transfer processes at the nanoscale is crucial for the development of energy harvesting and molecular electronic devices. Herein, we adopt a mixed quantum-classical description of a device, in which the open subsystem of interest is treated quantum mechanically and the surrounding heat baths are treated in a classical-like fashion. By introducing such a mixed quantum-classical description of the composite system, one is able to study the heat transfer between the subsystem and bath from a closed system point of view, thereby avoiding simplifying assumptions related to the bath time scale and subsystem-bath coupling strength. In particular, we adopt the full counting statistics approach to derive a general expression for the moment generating function of heat in systems whose dynamics are described by the quantum-classical Liouville equation (QCLE). From this expression, one can deduce expressions for the dynamics of the average heat and heat current, which may be evaluated using numerical simulations. Due to the approximate nature of the QCLE, we also find that the steady state fluctuation symmetry holds up to order ℏ for systems whose subsystem-bath couplings and baths go beyond bilinear and harmonic, respectively. To demonstrate the approach, we consider the nonequilibrium spin boson model and simulate its time-dependent average heat and heat current under various conditions.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
| | - Chang-Yu Hsieh
- Singapore-MIT Alliance for Research and Technology (SMART) Center, 1 Create Way, Singapore 138602, Singapore
| | - Dvira Segal
- Department of Chemistry and Centre for Quantum Information and Quantum Control, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6, Canada
| | - Gabriel Hanna
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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29
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30
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Wang H, Liu X, Liu J. Accurate calculation of equilibrium reduced density matrix for the system-bath model: A multilayer multiconfiguration time-dependent Hartree approach and its comparison to a multi-electronic-state path integral molecular dynamics approach. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1805122] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver CO 80217-3364, USA
| | - Xinzijian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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31
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Liu YY, Yan YM, Xu M, Song K, Shi Q. Exact generator and its high order expansions in time-convolutionless generalized master equation: Applications to spin-boson model and excitation energy transfer. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806146] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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32
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Hans-Dieter Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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33
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Liu J, Hanna G. Efficient and Deterministic Propagation of Mixed Quantum-Classical Liouville Dynamics. J Phys Chem Lett 2018; 9:3928-3933. [PMID: 29947224 DOI: 10.1021/acs.jpclett.8b01619] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We propose a highly efficient mixed quantum-classical molecular dynamics scheme based on a solution of the quantum-classical Liouville equation (QCLE). By casting the equations of motion for the quantum subsystem and classical bath degrees of freedom onto an approximate set of coupled first-order differential equations for c-numbers, this scheme propagates the composite system in time deterministically in terms of independent classical-like trajectories. To demonstrate its performance, we apply the method to the spin-boson model, a photoinduced electron transfer model, and a Fenna-Matthews-Olsen complex model, and find excellent agreement out to long times with the numerically exact results, using several orders of magnitude fewer trajectories than surface-hopping solutions of the QCLE. Owing to its accuracy and efficiency, this method promises to be very useful for studying the dynamics of mixed quantum-classical systems.
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Affiliation(s)
- Junjie Liu
- Department of Chemistry , University of Alberta , Edmonton , Alberta T6G 2G2 , Canada
| | - Gabriel Hanna
- Department of Chemistry , University of Alberta , Edmonton , Alberta T6G 2G2 , Canada
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34
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Wang L, Fujihashi Y, Chen L, Zhao Y. Finite-temperature time-dependent variation with multiple Davydov states. J Chem Phys 2018; 146:124127. [PMID: 28388128 DOI: 10.1063/1.4979017] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.
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Affiliation(s)
- Lu Wang
- Department of Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
| | - Yuta Fujihashi
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Lipeng Chen
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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35
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Wang H, Thoss M. A multilayer multiconfiguration time-dependent Hartree study of the nonequilibrium Anderson impurity model at zero temperature. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.03.021] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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36
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Shi Q, Xu Y, Yan Y, Xu M. Efficient propagation of the hierarchical equations of motion using the matrix product state method. J Chem Phys 2018; 148:174102. [DOI: 10.1063/1.5026753] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yang Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Meng Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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37
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Affiliation(s)
- Hans-Dieter Meyer
- Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
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38
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Tempelaar R, Reichman DR. Generalization of fewest-switches surface hopping for coherences. J Chem Phys 2018; 148:102309. [DOI: 10.1063/1.5000843] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roel Tempelaar
- Department of Chemistry, Columbia University, 3000 Broadway,
New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway,
New York, New York 10027, USA
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39
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Cerezo J, Liu Y, Lin N, Zhao X, Improta R, Santoro F. Mixed Quantum/Classical Method for Nonadiabatic Quantum Dynamics in Explicit Solvent Models: The ππ*/nπ* Decay of Thymine in Water as a Test Case. J Chem Theory Comput 2018; 14:820-832. [PMID: 29207245 DOI: 10.1021/acs.jctc.7b01015] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a novel mixed quantum classical dynamical method to include solvent effects on internal conversion (IC) processes. All the solute degrees of freedom are represented by a wavepacket moving according to nonadiabatic quantum dynamics, while the motion of an explicit solvent model is described by an ensemble of classical trajectories. The mutual coupling of the solute and solvent dynamics is included within a mean-field framework and the quantum and classical equations of motions are solved simultaneously. As a test case we apply our method to the ultrafast ππ* → nπ* decay of thymine in water. Solvent dynamical response modifies IC yield already on the 50 fs time scale. This effect is due to water librational motions that stabilize the most populated state. Pure static disorder, that is, the existence of different solvent configurations when photoexcitation takes place, also has a remarkable impact on the dynamics.
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Affiliation(s)
- Javier Cerezo
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR) , SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy.,Departamento de Química Física, Universidad de Murcia , 30100 Murcia, Spain
| | - Yanli Liu
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR) , SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy.,School of Physics and Optoelectronics Engineering, Ludong University , 264025 Yantai, P. R. China
| | - Na Lin
- State Key Laboratory of Crystal Materials, Shandong University , 250100 Jinan, Shandong, P. R. China
| | - Xian Zhao
- State Key Laboratory of Crystal Materials, Shandong University , 250100 Jinan, Shandong, P. R. China
| | - Roberto Improta
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR) , via Mezzocannone 16, I-80136 Napoli, Italy.,LIDYL, CEA, CNRS, Université Paris-Saclay , F-91191 Gif-sur-Yvette, France
| | - Fabrizio Santoro
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organo Metallici (ICCOM-CNR) , SS di Pisa, Area della Ricerca, via G. Moruzzi 1, I-56124 Pisa, Italy
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40
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Gong Z, Tang Z, Wang H, Wu J. Quantum kinetic expansion in the spin-boson model: Matrix formulation and system-bath factorized initial state. J Chem Phys 2017; 147:244112. [PMID: 29289122 DOI: 10.1063/1.4998784] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within the framework of the hierarchy equation of motion (HEOM), the quantum kinetic expansion (QKE) method of the spin-boson model is reformulated in the matrix representation. The equivalence between the two formulations (HEOM matrices and quantum operators) is numerically verified from the calculation of the time-integrated QKE rates. The matrix formulation of the QKE is extended to the system-bath factorized initial state. Following a one-to-one mapping between HEOM matrices and quantum operators, a quantum kinetic equation is rederived. The rate kernel is modified by an extra term following a systematic expansion over the site-site coupling. This modified QKE is numerically tested for its reliability by calculating the time-integrated rate and non-Markovian population kinetics. For an intermediate-to-strong dissipation strength and a large site-site coupling, the population transfer is found to be significantly different when the initial condition is changed from the local equilibrium to system-bath factorized state.
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Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Zhoufei Tang
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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41
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Chen L, Borrelli R, Zhao Y. Dynamics of Coupled Electron–Boson Systems with the Multiple Davydov D1 Ansatz and the Generalized Coherent State. J Phys Chem A 2017; 121:8757-8770. [DOI: 10.1021/acs.jpca.7b07069] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lipeng Chen
- Division
of Materials Science, Nanyang Technological University, 639798, Singapore
| | - Raffaele Borrelli
- Department
of Agricultural, Forestry and Food Science, Universitá di Torino, I-10095 Grugliasco, Turin, Italy
| | - Yang Zhao
- Division
of Materials Science, Nanyang Technological University, 639798, Singapore
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42
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Hait D, Mavros MG, Van Voorhis T. A hybrid memory kernel approach for condensed phase non-adiabatic dynamics. J Chem Phys 2017; 147:014108. [PMID: 28688393 DOI: 10.1063/1.4990739] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow-bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular non-interacting blip approximation (NIBA) method to generate a memory kernel that is formally exact to second-order in the diabatic coupling but also contains higher-order contributions approximated from the second-order term alone. This kernel has the same computational complexity as the NIBA, but is found to yield dramatically superior dynamics in regimes where the NIBA breaks down-such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher-order effects into second-order methods and could potentially be generalized to develop alternate kernel resummation schemes.
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Affiliation(s)
- Diptarka Hait
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Michael G Mavros
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
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43
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Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
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Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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Song K, Shi Q. Theoretical study of photoinduced proton coupled electron transfer reaction using the non-perturbative hierarchical equations of motion method. J Chem Phys 2017. [DOI: 10.1063/1.4982928] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Kai Song
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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45
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Wang H, Thoss M. A multilayer multiconfiguration time-dependent Hartree simulation of the reaction-coordinate spin-boson model employing an interaction picture. J Chem Phys 2017; 146:124112. [PMID: 28388113 DOI: 10.1063/1.4978901] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The multilayer multiconfiguration time-dependent Hartree method is applied in an interaction picture to simulate dynamics of the spin-boson model in the reaction-coordinate representation. The use of the interaction picture allows a more effective description of correlation effects, especially when the coupling strength between the reaction coordinate and the bath is very strong. Examples show that in most physical regimes the efficiency is improved significantly, in some cases up to several orders of magnitude. This opens up new avenues for studying quantum dynamical problems.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No.10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, Erlangen D-91058, Germany
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Chen HT, Cohen G, Reichman DR. Inchworm Monte Carlo for exact non-adiabatic dynamics. II. Benchmarks and comparison with established methods. J Chem Phys 2017; 146:054106. [DOI: 10.1063/1.4974329] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Guy Cohen
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Chen HT, Cohen G, Reichman DR. Inchworm Monte Carlo for exact non-adiabatic dynamics. I. Theory and algorithms. J Chem Phys 2017; 146:054105. [DOI: 10.1063/1.4974328] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Guy Cohen
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Montoya-Castillo A, Reichman DR. Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths. J Chem Phys 2017; 146:024107. [DOI: 10.1063/1.4973646] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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49
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Mavros MG, Hait D, Van Voorhis T. Condensed phase electron transfer beyond the Condon approximation. J Chem Phys 2016; 145:214105. [DOI: 10.1063/1.4971166] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael G. Mavros
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Diptarka Hait
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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Wang H, Thoss M. Employing an interaction picture to remove artificial correlations in multilayer multiconfiguration time-dependent Hartree simulations. J Chem Phys 2016; 145:164105. [DOI: 10.1063/1.4965712] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058, Germany
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