1
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Liu Z, Lyu N, Hu Z, Zeng H, Batista VS, Sun X. Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics. J Chem Phys 2024; 161:024102. [PMID: 38980091 DOI: 10.1063/5.0208708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2024] [Accepted: 06/20/2024] [Indexed: 07/10/2024] Open
Abstract
Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.
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Affiliation(s)
- Zengkui Liu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Ningyi Lyu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Zhubin Hu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Hao Zeng
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
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2
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Sayer T, Montoya-Castillo A. Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions. J Chem Phys 2024; 161:011101. [PMID: 38949578 DOI: 10.1063/5.0219205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2024] [Accepted: 06/12/2024] [Indexed: 07/02/2024] Open
Abstract
Multitime quantum correlation functions are central objects in physical science, offering a direct link between the experimental observables and the dynamics of an underlying model. While experiments such as 2D spectroscopy and quantum control can now measure such quantities, the accurate simulation of such responses remains computationally expensive and sometimes impossible, depending on the system's complexity. A natural tool to employ is the generalized quantum master equation (GQME), which can offer computational savings by extending reference dynamics at a comparatively trivial cost. However, dynamical methods that can tackle chemical systems with atomistic resolution, such as those in the semiclassical hierarchy, often suffer from poor accuracy, limiting the credence one might lend to their results. By combining work on the accuracy-boosting formulation of semiclassical memory kernels with recent work on the multitime GQME, here we show for the first time that one can exploit a multitime semiclassical GQME to dramatically improve both the accuracy of coarse mean-field Ehrenfest dynamics and obtain orders of magnitude efficiency gains.
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Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
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3
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Lawrence JE, Mannouch JR, Richardson JO. A size-consistent multi-state mapping approach to surface hopping. J Chem Phys 2024; 160:244112. [PMID: 38940540 DOI: 10.1063/5.0208575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 06/05/2024] [Indexed: 06/29/2024] Open
Abstract
We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.
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Affiliation(s)
- Joseph E Lawrence
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
- Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, USA
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Jonathan R Mannouch
- Hamburg Center for Ultrafast Imaging, Universität Hamburg and the Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zurich, 8093 Zurich, Switzerland
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4
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Kang M, Nuomin H, Chowdhury SN, Yuly JL, Sun K, Whitlow J, Valdiviezo J, Zhang Z, Zhang P, Beratan DN, Brown KR. Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics. Nat Rev Chem 2024; 8:340-358. [PMID: 38641733 DOI: 10.1038/s41570-024-00595-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/07/2024] [Indexed: 04/21/2024]
Abstract
Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.
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Affiliation(s)
- Mingyu Kang
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
| | - Hanggai Nuomin
- Department of Chemistry, Duke University, Durham, NC, USA
| | | | - Jonathon L Yuly
- Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA
| | - Ke Sun
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Physics, Duke University, Durham, NC, USA
| | - Jacob Whitlow
- Duke Quantum Center, Duke University, Durham, NC, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA
| | - Jesús Valdiviezo
- Kenneth S. Pitzer Theory Center, University of California, Berkeley, CA, USA
- Department of Chemistry, University of California, Berkeley, CA, USA
- Departamento de Ciencias, Sección Química, Pontificia Universidad Católica del Perú, Lima, Peru
| | - Zhendian Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - Peng Zhang
- Department of Chemistry, Duke University, Durham, NC, USA
| | - David N Beratan
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Biochemistry, Duke University, Durham, NC, USA.
| | - Kenneth R Brown
- Duke Quantum Center, Duke University, Durham, NC, USA.
- Department of Physics, Duke University, Durham, NC, USA.
- Department of Chemistry, Duke University, Durham, NC, USA.
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.
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5
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Lawrence JE, Mannouch JR, Richardson JO. Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping. J Phys Chem Lett 2024; 15:707-716. [PMID: 38214476 PMCID: PMC10823533 DOI: 10.1021/acs.jpclett.3c03197] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 12/22/2023] [Accepted: 01/05/2024] [Indexed: 01/13/2024]
Abstract
It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.
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Affiliation(s)
- Joseph E. Lawrence
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
| | - Jonathan R. Mannouch
- Hamburg
Center for Ultrafast Imaging, Universität
Hamburg and Max Planck Institute for the Structure and Dynamics of
Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jeremy O. Richardson
- Department
of Chemistry and Applied Biosciences, ETH
Zurich, 8093 Zurich, Switzerland
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6
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Abstract
We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.
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7
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Montoya-Castillo A, Markland TE. A derivation of the conditions under which bosonic operators exactly capture fermionic structure and dynamics. J Chem Phys 2023; 158:094112. [PMID: 36889969 DOI: 10.1063/5.0138664] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023] Open
Abstract
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces to transport through nanojunctions and offer a prime target for quantum computing applications. Here, we derive the set of conditions under which fermionic operators can be exactly replaced by bosonic operators that render the problem amenable to a large toolbox of dynamical methods while still capturing the correct dynamics of n-body operators. Importantly, our analysis offers a simple guide on how one can exploit these simple maps to calculate nonequilibrium and equilibrium single- and multi-time correlation functions essential in describing transport and spectroscopy. We use this to rigorously analyze and delineate the applicability of simple yet effective Cartesian maps that have been shown to correctly capture the correct fermionic dynamics in select models of nanoscopic transport. We illustrate our analytical results with exact simulations of the resonant level model. Our work provides new insights as to when one can leverage the simplicity of bosonic maps to simulate the dynamics of many-electron systems, especially those where an atomistic representation of nuclear interactions becomes essential.
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Affiliation(s)
| | - Thomas E Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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8
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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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9
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Lai Y, Geva E. Electronic Absorption Spectra from Off-Diagonal Quantum Master Equations. J Chem Phys 2022; 157:104115. [DOI: 10.1063/5.0106888] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrodinger picture electronic coherences from them. A key experimental quantity that relies on the ability to obtain accurate Schrodinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrodinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained in this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion (HEOM) method.
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Affiliation(s)
- Yifan Lai
- Chemistry, University of Michigan, United States of America
| | - Eitan Geva
- Department of Chemistry, University of Michigan Department of Chemistry, United States of America
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10
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Saller MAC, Lai Y, Geva E. An Accurate Linearized Semiclassical Approach for Calculating Cavity-Modified Charge Transfer Rate Constants. J Phys Chem Lett 2022; 13:2330-2337. [PMID: 35245071 DOI: 10.1021/acs.jpclett.2c00122] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We show that combining the linearized semiclasscial approximation with Fermi's golden rule (FGR) rate theory gives rise to a general-purpose cost-effective and scalable computational framework that can accurately capture the cavity-induced rate enhancement of charge transfer reactions that occurs when the molecular system is placed inside a microcavity. Both partial linearization with respect to the nuclear and photonic degrees of freedom and full linerization with respect to nuclear, photonic, and electronic degrees of freedom (the latter within the mapping Hamiltonian approach) are shown to be highly accurate, provided that the Wigner transforms of the product (WoP) of operators at the initial time is not replaced by the product of their Wigner transforms. We also show that the partial linearization method yields the quantum-mechanically exact cavity-modified FGR rate constant for a model system in which the donor and acceptor potential energy surfaces are harmonic and identical except for a shift in the equilibrium energy and geometry, if WoP is applied.
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Affiliation(s)
- Maximilian A C Saller
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Yifan Lai
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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11
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Lai Y, Geva E. On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation. J Chem Phys 2021; 155:204101. [PMID: 34852488 DOI: 10.1063/5.0069313] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg-Onuchic-Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrödinger picture coherences can be obtained from interaction picture electronic inputs.
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Affiliation(s)
- Yifan Lai
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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12
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Brian D, Sun X. Generalized quantum master equation: A tutorial review and recent advances. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2109157] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, Shanghai 200122, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
- Department of Chemistry, New York University, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, China
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13
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Hu Z, Brian D, Sun X. Multi-state harmonic models with globally shared bath for nonadiabatic dynamics in the condensed phase. J Chem Phys 2021; 155:124105. [PMID: 34598571 DOI: 10.1063/5.0064763] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Model Hamiltonians constructed from quantum chemistry calculations and molecular dynamics simulations are widely used for simulating nonadiabatic dynamics in the condensed phase. The most popular two-state spin-boson model could be built by mapping the all-atom anharmonic Hamiltonian onto a two-level system bilinearly coupled to a harmonic bath using the energy gap time correlation function. However, for more than two states, there lacks a general strategy to construct multi-state harmonic (MSH) models since the energy gaps between different pairs of electronic states are not entirely independent and need to be considered consistently. In this paper, we extend the previously proposed approach for building three-state harmonic models for photoinduced charge transfer to the arbitrary number of electronic states with a globally shared bath and the system-bath couplings are scaled differently according to the reorganization energies between each pair of states. We demonstrate the MSH model construction for an organic photovoltaic carotenoid-porphyrin-C60 molecular triad dissolved in explicit tetrahydrofuran solvent. Nonadiabatic dynamics was simulated using mixed quantum-classical techniques, including the linearized semiclassical and symmetrical quasiclassical dynamics with the mapping Hamiltonians, mean-field Ehrenfest, and mixed quantum-classical Liouville dynamics in two-state, three-state, and four-state harmonic models of the triad system. The MSH models are shown to provide a general and flexible framework for simulating nonadiabatic dynamics in complex systems.
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Affiliation(s)
- Zhubin Hu
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Dominikus Brian
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
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14
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Choi S, Vaníček J. High-order geometric integrators for representation-free Ehrenfest dynamics. J Chem Phys 2021; 155:124104. [PMID: 34598577 DOI: 10.1063/5.0061878] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equation, Ehrenfest dynamics is symplectic, is time-reversible, and conserves exactly the total molecular energy as well as the norm of the electronic wavefunction. Here, we surpass apparent complications due to the coupling of classical nuclear and quantum electronic motions and present efficient geometric integrators for "representation-free" Ehrenfest dynamics, which do not rely on a diabatic or adiabatic representation of electronic states and are of arbitrary even orders of accuracy in the time step. These numerical integrators, obtained by symmetrically composing the second-order splitting method and exactly solving the kinetic and potential propagation steps, are norm-conserving, symplectic, and time-reversible regardless of the time step used. Using a nonadiabatic simulation in the region of a conical intersection as an example, we demonstrate that these integrators preserve the geometric properties exactly and, if highly accurate solutions are desired, can be even more efficient than the most popular non-geometric integrators.
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Affiliation(s)
- Seonghoon Choi
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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15
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Mulvihill E, Lenn KM, Gao X, Schubert A, Dunietz BD, Geva E. Simulating energy transfer dynamics in the Fenna-Matthews-Olson complex via the modified generalized quantum master equation. J Chem Phys 2021; 154:204109. [PMID: 34241158 DOI: 10.1063/5.0051101] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna-Matthews-Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model.
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Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Kristina M Lenn
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Barry D Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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16
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Begušić T, Vaníček J. Finite-Temperature, Anharmonicity, and Duschinsky Effects on the Two-Dimensional Electronic Spectra from Ab Initio Thermo-Field Gaussian Wavepacket Dynamics. J Phys Chem Lett 2021; 12:2997-3005. [PMID: 33733773 PMCID: PMC8006135 DOI: 10.1021/acs.jpclett.1c00123] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 03/08/2021] [Indexed: 05/28/2023]
Abstract
Accurate description of finite-temperature vibrational dynamics is indispensable in the computation of two-dimensional electronic spectra. Such simulations are often based on the density matrix evolution, statistical averaging of initial vibrational states, or approximate classical or semiclassical limits. While many practical approaches exist, they are often of limited accuracy and difficult to interpret. Here, we use the concept of thermo-field dynamics to derive an exact finite-temperature expression that lends itself to an intuitive wavepacket-based interpretation. Furthermore, an efficient method for computing finite-temperature two-dimensional spectra is obtained by combining the exact thermo-field dynamics approach with the thawed Gaussian approximation for the wavepacket dynamics, which is exact for any displaced, distorted, and Duschinsky-rotated harmonic potential but also accounts partially for anharmonicity effects in general potentials. Using this new method, we directly relate a symmetry breaking of the two-dimensional signal to the deviation from the conventional Brownian oscillator picture.
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17
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Gao X, Geva E. Improving the Accuracy of Quasiclassical Mapping Hamiltonian Methods by Treating the Window Function Width as an Adjustable Parameter. J Phys Chem A 2020; 124:11006-11016. [DOI: 10.1021/acs.jpca.0c09750] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xing Gao
- School of Materials, Sun Yat-sen University, Shenzhen, Guangdong 518100, China
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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18
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Yan Y, Xing T, Shi Q. A new method to improve the numerical stability of the hierarchical equations of motion for discrete harmonic oscillator modes. J Chem Phys 2020; 153:204109. [DOI: 10.1063/5.0027962] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Tao Xing
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
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19
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Mannouch JR, Richardson JO. A partially linearized spin-mapping approach for nonadiabatic dynamics. I. Derivation of the theory. J Chem Phys 2020; 153:194109. [DOI: 10.1063/5.0031168] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Begušić T, Vaníček J. On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy. J Chem Phys 2020; 153:184110. [DOI: 10.1063/5.0031216] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Tomislav Begušić
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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21
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Liu Y, Gao X, Lai Y, Mulvihill E, Geva E. Electronic Dynamics through Conical Intersections via Quasiclassical Mapping Hamiltonian Methods. J Chem Theory Comput 2020; 16:4479-4488. [DOI: 10.1021/acs.jctc.0c00177] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Yudan Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Yifan Lai
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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22
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Gao X, Saller MAC, Liu Y, Kelly A, Richardson JO, Geva E. Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics. J Chem Theory Comput 2020; 16:2883-2895. [DOI: 10.1021/acs.jctc.9b01267] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | | | - Yudan Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Aaron Kelly
- Department of Chemistry, Dalhousie University, 15000 Halifax, Nova Scotia, Canada
| | | | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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23
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R S L, Kurup GB, Vennapusa SR. Identification of a receiver triplet state in the ultrafast intersystem crossing of carbonylpyrenes. Phys Chem Chem Phys 2020; 22:6145-6153. [PMID: 32124884 DOI: 10.1039/c9cp06857k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
The near-unity triplet quantum yield of photoexcited carbonyl functionalized pyrenes is theoretically investigated. The estimated energetics of singlet-triplet manifolds and relevant spin-orbit coupling parameters strongly suggest triplet state formation via the S1→ T4/T5 pathway. Quantum wavepacket dynamics of triplet manifolds within the linear vibronic coupling approach reveal that the receiver triplet state would undergo rapid internal conversion decay to the lower triplet state(s), facilitating efficient triplet generation by minimizing the reverse intersystem crossing possibilities. On the basis of these results, a unified mechanism is proposed to describe the ultrafast intersystem crossing process in these molecules.
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Affiliation(s)
- Lekshmi R S
- School of Chemistry, Indian Institute of Science Education and Research Thiruvananthapuram (IISER TVM), Maruthamala P.O., Vithura, Thiruvananthapuram 695551, Kerala, India.
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24
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Abstract
Dynamics at molecule-metal interfaces are a subject of intense current interest and come in many different flavors of experiments: gas-phase scattering, chemisorption, electrochemistry, nanojunction transport, and heterogeneous catalysis, to name a few. These dynamics involve nuclear degrees of freedom entangled with many electronic degrees of freedom (in the metal), and as such there is always the possibility for nonadiabatic phenomena to appear: the nuclei do not necessarily need to move slower than the electrons to break the Born-Oppenheimer (BO) approximation. In this Feature Article, we review a set of dynamical methods developed recently to deal with such nonadiabatic phenomena at a metal surface, methods that serve as alternatives to Tully's independent electron surface hopping (IESH) model. In the weak molecule-metal coupling regime, a classical master equation (CME) can be derived and a simple surface hopping approach is proposed to propagate nuclear and electronic dynamics stochastically. In the strong molecule-metal interaction regime, a Fokker-Planck equation can be derived for the nuclear dynamics, with electronic DoFs incorporated into the overall friction and random force. Lastly, a broadened classical master equation (BCME) can interpolate between the weak and strong molecule-metal interactions. Here, we briefly review these methods and the relevant benchmarking data, showing in particular how the methods can be used to calculate nonequilibrium transport properties. We highlight several open questions and pose several avenues for future study.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry , University of California, Berkeley , Berkeley , California 94720 , United States
| | - Joseph E Subotnik
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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25
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Gong Z, Wu J. Absorption matrix of multi-site systems calculated by a hybrid quantum-classical Liouville equation. J Chem Phys 2019; 151:224109. [DOI: 10.1063/1.5138217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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26
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Chatterjee S, Makri N. Real-Time Path Integral Methods, Quantum Master Equations, and Classical vs Quantum Memory. J Phys Chem B 2019; 123:10470-10482. [DOI: 10.1021/acs.jpcb.9b08429] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sambarta Chatterjee
- Department of Chemistry, University of Illinois, 505 South Mathews Avenue, Urbana, Illinois 61801, United States
| | - Nancy Makri
- Department of Chemistry, University of Illinois, 505 South Mathews Avenue, Urbana, Illinois 61801, United States
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27
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Mulvihill E, Gao X, Liu Y, Schubert A, Dunietz BD, Geva E. Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics. J Chem Phys 2019; 151:074103. [DOI: 10.1063/1.5110891] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Yudan Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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28
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Mulvihill E, Schubert A, Sun X, Dunietz BD, Geva E. A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation. J Chem Phys 2019; 150:034101. [DOI: 10.1063/1.5055756] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ellen Mulvihill
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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29
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Li X, Hu D, Xie Y, Lan Z. Analysis of trajectory similarity and configuration similarity in on-the-fly surface-hopping simulation on multi-channel nonadiabatic photoisomerization dynamics. J Chem Phys 2018; 149:244104. [DOI: 10.1063/1.5048049] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Xusong Li
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
- Sino-Danish Center for Education and Research/Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Deping Hu
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yu Xie
- The Environmental Research Institute, MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
| | - Zhenggang Lan
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
- Sino-Danish Center for Education and Research/Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, China
- The Environmental Research Institute, MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
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30
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Xie Y, Zheng J, Lan Z. Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models. J Chem Phys 2018; 149:174105. [DOI: 10.1063/1.5047002] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yu Xie
- Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, Shandong, China
- The Environmental Research Institute; MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
| | - Jie Zheng
- Industrial Research Institute of Nonwovens and Technical Textiles, College of Textiles and Clothing, Qingdao University, Qingdao 266071, China
| | - Zhenggang Lan
- Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, Shandong, China
- The Environmental Research Institute; MOE Key Laboratory of Theoretical Chemistry of Environment, South China Normal University, Guangzhou 510006, China
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31
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32
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Abstract
Electronic friction is a correction to the Born-Oppenheimer approximation, whereby nuclei in motion experience a drag in the presence of a manifold of electronic states. The notion of electronic friction has a long history and has been (re-)discovered in the context of a wide variety of different chemical and physical systems including, but not limited to, surface scattering events, surface reactions or chemisorption, electrochemistry, and conduction through molecular-(or nano-) junctions. Over the years, quite a few different forms of electronic friction have been offered in the literature. In this perspective, we briefly review these developments of electronic friction, highlighting the fact that we can now isolate a single, unifying form for (Markovian) electronic friction. We also focus on the role of electron-electron interactions for understanding frictional effects and offer our thoughts on the strengths and weaknesses of using electronic friction to model dynamics in general.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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33
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Gong Z, Wu J. Quantum kinetic expansion in the spin-boson model: Implemented by the quantum-classical Liouville equation in an anharmonic bath. J Chem Phys 2018; 148:234107. [DOI: 10.1063/1.5028306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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34
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Kananenka AA, Sun X, Schubert A, Dunietz BD, Geva E. A comparative study of different methods for calculating electronic transition rates. J Chem Phys 2018; 148:102304. [DOI: 10.1063/1.4989509] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexei A. Kananenka
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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35
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Li X, Xie Y, Hu D, Lan Z. Analysis of the Geometrical Evolution in On-the-Fly Surface-Hopping Nonadiabatic Dynamics with Machine Learning Dimensionality Reduction Approaches: Classical Multidimensional Scaling and Isometric Feature Mapping. J Chem Theory Comput 2017; 13:4611-4623. [DOI: 10.1021/acs.jctc.7b00394] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Xusong Li
- CAS
Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy
and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
- Sino-Danish
Center for Education and Research/Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, China
- University of Chinese Academy of Sciences, Beijing 100049, China
- Department
of Chemistry, Technical University of Denmark, Kemitorvet 207, 2800, Kgs. Lyngby, Denmark
| | - Yu Xie
- CAS
Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy
and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
| | - Deping Hu
- CAS
Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy
and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Zhenggang Lan
- CAS
Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy
and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101, China
- Sino-Danish
Center for Education and Research/Sino-Danish College, University of Chinese Academy of Sciences, Beijing 100049, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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36
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Gu B, Franco I. Partial hydrodynamic representation of quantum molecular dynamics. J Chem Phys 2017; 146:194104. [PMID: 28527433 PMCID: PMC5648576 DOI: 10.1063/1.4983495] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Accepted: 05/03/2017] [Indexed: 11/14/2022] Open
Abstract
A hybrid method is proposed to propagate system-bath quantum dynamics that use both basis functions and coupled quantum trajectories. In it, the bath is represented with an ensemble of Bohmian trajectories while the system degrees of freedom are accounted through reduced density matrices. By retaining the Hilbert space structure for the system, the method is able to capture interference processes that are challenging to describe in Bohmian dynamics due to singularities that these processes introduce in the quantum potential. By adopting quantum trajectories to represent the bath, the method beats the exponential scaling of the computational cost with the bath size. This combination makes the method suitable for large-scale ground and excited state fully quantum molecular dynamics simulations. Equations of motion for the quantum trajectories and reduced density matrices are derived from the Schrödinger equation and a computational algorithm to solve these equations is proposed. Through computations in two-dimensional model systems, the method is shown to offer an accurate description of subsystem observables and of quantum decoherence, which is difficult to obtain when the quantum nature of the bath is ignored. The scaling of the method is demonstrated using a model with 21 degrees of freedom. The limit of independent trajectories is recovered when the mass of bath degrees of freedom is much larger than the one of the system, in agreement with mixed quantum-classical descriptions.
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Affiliation(s)
- Bing Gu
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Ignacio Franco
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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37
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Kananenka AA, Hsieh CY, Cao J, Geva E. Accurate Long-Time Mixed Quantum-Classical Liouville Dynamics via the Transfer Tensor Method. J Phys Chem Lett 2016; 7:4809-4814. [PMID: 27934045 DOI: 10.1021/acs.jpclett.6b02389] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.
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Affiliation(s)
- Alexei A Kananenka
- Department of Chemistry, University of Michigan , Ann Arbor, Michigan 48109, United States
| | - Chang-Yu Hsieh
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02319, United States
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02319, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan , Ann Arbor, Michigan 48109, United States
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38
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Sun X, Geva E. Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method. J Chem Phys 2016. [DOI: 10.1063/1.4960337] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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39
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Dou W, Subotnik JE. A many-body states picture of electronic friction: The case of multiple orbitals and multiple electronic states. J Chem Phys 2016; 145:054102. [DOI: 10.1063/1.4959604] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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40
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Sun X, Geva E. Non-Condon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method. J Chem Phys 2016; 144:244105. [DOI: 10.1063/1.4954509] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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41
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Subotnik JE, Jain A, Landry B, Petit A, Ouyang W, Bellonzi N. Understanding the Surface Hopping View of Electronic Transitions and Decoherence. Annu Rev Phys Chem 2016; 67:387-417. [DOI: 10.1146/annurev-physchem-040215-112245] [Citation(s) in RCA: 234] [Impact Index Per Article: 29.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Amber Jain
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Brian Landry
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Andrew Petit
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104;
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42
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Sun X, Geva E. Nonequilibrium Fermi’s Golden Rule Charge Transfer Rates via the Linearized Semiclassical Method. J Chem Theory Comput 2016; 12:2926-41. [DOI: 10.1021/acs.jctc.6b00236] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiang Sun
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Eitan Geva
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
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43
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Montoya-Castillo A, Reichman DR. Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics. J Chem Phys 2016; 144:184104. [DOI: 10.1063/1.4948408] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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44
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Kelly A, Montoya-Castillo A, Wang L, Markland TE. Generalized quantum master equations in and out of equilibrium: When can one win? J Chem Phys 2016; 144:184105. [DOI: 10.1063/1.4948612] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Aaron Kelly
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | | | - Lu Wang
- Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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45
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Bellonzi N, Jain A, Subotnik JE. An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability. J Chem Phys 2016; 144:154110. [DOI: 10.1063/1.4946810] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Amber Jain
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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46
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Agostini F, Min SK, Abedi A, Gross EKU. Quantum-Classical Nonadiabatic Dynamics: Coupled- vs Independent-Trajectory Methods. J Chem Theory Comput 2016; 12:2127-43. [PMID: 27030209 DOI: 10.1021/acs.jctc.5b01180] [Citation(s) in RCA: 84] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic nonadiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper, we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.
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Affiliation(s)
- Federica Agostini
- Max-Planck Institut für Mikrostrukturphysik , Weinberg 2, D-06120 Halle, Germany
| | - Seung Kyu Min
- Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST) , 50 UNIST-gil, Ulsan 44919, Republic of Korea
| | - Ali Abedi
- Nano-Bio Spectroscopy group and European Theoretical Spectroscopy Facility (ETSF), Dpto. Física de Materiales, Universidad del País Vasco, Centro de Física de Materiales CSIC-UPV/EHU-MPC and DIPC , Av. Tolosa 72, E-20018 San Sebastián, Spain
| | - E K U Gross
- Max-Planck Institut für Mikrostrukturphysik , Weinberg 2, D-06120 Halle, Germany
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47
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Antipov SV, Ye Z, Ananth N. Dynamically consistent method for mixed quantum-classical simulations: A semiclassical approach. J Chem Phys 2016; 142:184102. [PMID: 25978878 DOI: 10.1063/1.4919667] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a new semiclassical (SC) framework, the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), that can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Applying a modified Filinov transformation to a quantum-limit SC formulation leads to the association of a Filinov parameter with each degree of freedom in the system; varying this parameter from zero to infinity controls the extent of quantization of the corresponding mode. The resulting MQC-IVR expression provides a consistent dynamic framework for mixed quantum-classical simulations and we demonstrate its numerical accuracy in the calculation of real-time correlation functions for a model 1D system and a model 2D system over the full range of quantum- to classical-limit behaviors.
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Affiliation(s)
- Sergey V Antipov
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Ziyu Ye
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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48
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Xie W, Xu M, Bai S, Shi Q. Mixed Quantum-Classical Study of Nonadiabatic Curve Crossing in Condensed Phases. J Phys Chem A 2016; 120:3225-32. [DOI: 10.1021/acs.jpca.5b11695] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Weiwei Xie
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Meng Xu
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Shuming Bai
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Qiang Shi
- Beijing
National Laboratory
for Molecular Sciences, State Key Laboratory for Structural Chemistry
of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
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49
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Sun X, Geva E. Equilibrium Fermi’s Golden Rule Charge Transfer Rate Constants in the Condensed Phase: The Linearized Semiclassical Method vs Classical Marcus Theory. J Phys Chem A 2015; 120:2976-90. [DOI: 10.1021/acs.jpca.5b08280] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
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50
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Walters PL, Banerjee T, Makri N. On iterative path integral calculations for a system interacting with a shifted dissipative bath. J Chem Phys 2015; 143:074112. [DOI: 10.1063/1.4928197] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Peter L. Walters
- Department of Chemistry, 600 S. Goodwin Avenue, University of Illinois, Urbana, Illinois 61801, USA
| | - Tuseeta Banerjee
- Department of Chemistry, 600 S. Goodwin Avenue, University of Illinois, Urbana, Illinois 61801, USA
| | - Nancy Makri
- Department of Chemistry, 600 S. Goodwin Avenue, University of Illinois, Urbana, Illinois 61801, USA
- Department of Physics, 1110 W. Green Street, University of Illinois, Urbana, Illinois 61801, USA
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