1
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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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2
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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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3
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Lin K, Peng J, Xu C, Gu FL, Lan Z. Trajectory Propagation of Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian Using Machine Learning. J Phys Chem Lett 2022; 13:11678-11688. [PMID: 36511563 DOI: 10.1021/acs.jpclett.2c02159] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The long short-term memory recurrent neural network (LSTM-RNN) approach is applied to realize the trajectory-based nonadiabatic dynamics within the framework of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC). After construction, the LSTM-RNN model allows us to propagate the entire trajectory evolutions of all involved degrees of freedoms (DOFs) from initial conditions. The proposed idea is proven to be reliable and accurate in the simulations of the dynamics of several site-exciton electron-phonon coupling models and three Tully's scattering models. It indicates that the LSTM-RNN model perfectly captures the dynamical information on the trajectory evolution in the MM-SQC dynamics. Our work proposes a novel machine learning approach in the simulation of trajectory-based nonadiabatic dynamic of complex systems with a large number of DOFs.
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Affiliation(s)
- Kunni Lin
- School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Jiawei Peng
- School of Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
| | - Chao Xu
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Feng Long Gu
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
| | - Zhenggang Lan
- MOE Key Laboratory of Environmental Theoretical Chemistry, South China Normal University, Guangzhou 510006, P. R. China
- SCNU Environmental Research Institute, Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety, School of Environment, South China Normal University, Guangzhou 510006, P. R. China
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4
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Bossion DL, Ying W, Chowdhury S, Huo P. Non-adiabatic Mapping Dynamics in the Phase Space of the ${SU}(N)$ Lie Group. J Chem Phys 2022; 157:084105. [DOI: 10.1063/5.0094893] [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
We present the rigorous theoretical framework of the generalized spin mapping representation for non-adiabatic dynamics. Our work is based up a new mapping formalism recently introduced by Runeson and Richardson in [J. Chem. Phys. 152, 084110 (2020)], which uses the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space. Following this interesting idea, the Stratonovich-Weyl transform is used to map an operator in the Hilbert space to a continuous function on the SU(N) Lie group, i.e., a smooth manifold which is a phase space of continuous variables. We further use the Wigner representation to describe the nuclear degrees of freedom, and derived an exact expression of the time-correlation function as well as the exact quantum Liouvillian for the non-adiabatic system. Making the linearization approximation, this exact Liouvillian is reduced to the Liouvillian of several recently proposed methods, and the performance of this Linearized method is tested using non-adiabatic models. We envision that the theoretical work presented here provides a rigorous and unified framework to formally derive non-adiabatic quantum dynamics approaches with continuous variables and connect the previous methods in a clear and concise manner.
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Affiliation(s)
| | | | - Sutirtha Chowdhury
- Department of Chemistry, University of Rochester, United States of America
| | - Pengfei Huo
- Department of Chemsitry, University of Rochester Department of Chemistry, United States of America
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5
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Mannouch JR, Richardson JO. A partially linearized spin-mapping approach for simulating nonlinear optical spectra. J Chem Phys 2022; 156:024108. [PMID: 35032975 DOI: 10.1063/5.0077744] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.
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6
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Cho KH, Rhee YM. Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes. Phys Chem Chem Phys 2021; 23:26623-26639. [PMID: 34842245 DOI: 10.1039/d1cp04615b] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.
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Affiliation(s)
- Kwang Hyun Cho
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea.
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea.
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7
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Braver Y, Valkunas L, Gelzinis A. Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications. J Chem Theory Comput 2021; 17:7157-7168. [PMID: 34618457 PMCID: PMC8719324 DOI: 10.1021/acs.jctc.1c00777] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Indexed: 01/20/2023]
Abstract
Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum-classical theory─it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum-classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum-classical Liouville equation, namely, the forward-backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna-Matthews-Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [Gelzinis, A.; J. Chem. Phys. 2020, 152, 051103] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.
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Affiliation(s)
- Yakov Braver
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| | - Andrius Gelzinis
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
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8
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Weight BM, Mandal A, Huo P. Ab initio symmetric quasi-classical approach to investigate molecular Tully models. J Chem Phys 2021; 155:084106. [PMID: 34470343 DOI: 10.1063/5.0061934] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (the so-called γ correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted γ-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.
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Affiliation(s)
- Braden M Weight
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Arkajit Mandal
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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9
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Lang H, Vendrell O, Hauke P. Generalized discrete truncated Wigner approximation for nonadiabatic quantum-classical dynamics. J Chem Phys 2021; 155:024111. [PMID: 34266254 DOI: 10.1063/5.0054696] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system's complexity increases, and it is thus desirable to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g., the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two linear vibronic coupling models and Tully's models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independent of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.
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Affiliation(s)
- Haifeng Lang
- Theoretical Chemistry, Institute of Physical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Oriol Vendrell
- Theoretical Chemistry, Institute of Physical Chemistry, Heidelberg University, Im Neuenheimer Feld 229, 69120 Heidelberg, Germany
| | - Philipp Hauke
- INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
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10
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Cho KH, Rhee YM. Cooperation between Excitation Energy Transfer and Antisynchronously Coupled Vibrations. J Phys Chem B 2021; 125:5601-5610. [PMID: 34013724 DOI: 10.1021/acs.jpcb.1c01194] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The effects of the environment in energy transfer systems have been continuously studied for decades. Here, we investigate how the energy transfer and the emergence of vibrational correlations cooperate with each other based on simulations with a few numerically approximate mixed quantum classical (MQC) methods. By adopting a two-state system with locally coupled underdamped vibrations that are resonant with the electronic energy gap, we observe prominent energy dissipations from the electronic system to the vibrations, rehighlighting the role of underdamped vibrations as a temporal electronic energy buffer. More importantly, this energy dissipation generates specific phase relations between the two vibrations. Namely, the vibrations become anticorrelated right after the initiation of the energy transfer but then synchronized as the transfer completes. These phase relations are interpreted as a selective activation of an anticorrelated motion of the vibrations and a subsequent deactivation by thermal energy redistribution. Furthermore, we show that a single vibration simultaneously coupled to the two electronic states with opposite phases induces a completely equivalent energy transfer dynamics as the two localized vibrations. Finally, we discuss how the vibrational energy dissipation dynamics is affected by the adopted MQC approaches and warn about the increased subtlety toward properly treating dissipation effects over having reliable population dynamics.
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Affiliation(s)
- Kwang Hyun Cho
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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11
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Santoro F, Green JA, Martinez-Fernandez L, Cerezo J, Improta R. Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives. Phys Chem Chem Phys 2021; 23:8181-8199. [PMID: 33875988 DOI: 10.1039/d0cp05907b] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.
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Affiliation(s)
- 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.
| | - James A Green
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), via Mezzocannone 16, I-80136 Napoli, Italy.
| | - Lara Martinez-Fernandez
- Departamento de Química, Facultad de Ciencias and Institute for Advanced Research in Chemistry (IADCHEM), Universidad Autónoma de Madrid, Campus de Excelencia UAM-CSIC, 28049 Madrid, Spain
| | - Javier Cerezo
- Departamento de Química, Facultad de Ciencias and Institute for Advanced Research in Chemistry (IADCHEM), Universidad Autónoma de Madrid, Campus de Excelencia UAM-CSIC, 28049 Madrid, Spain
| | - Roberto Improta
- CNR-Consiglio Nazionale delle Ricerche, Istituto di Biostrutture e Bioimmagini (IBB-CNR), via Mezzocannone 16, I-80136 Napoli, Italy.
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12
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Chowdhury SN, Huo P. Non-adiabatic Matsubara dynamics and non-adiabatic ring-polymer molecular dynamics. J Chem Phys 2021; 154:124124. [PMID: 33810665 DOI: 10.1063/5.0042136] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
We present the non-adiabatic Matsubara dynamics, a general framework for computing the time-correlation function (TCF) of electronically non-adiabatic systems. This new formalism is derived based on the generalized Kubo-transformed TCF using the Wigner representation for both the nuclear degrees of freedom and the electronic mapping variables. By dropping the non-Matsubara nuclear normal modes in the quantum Liouvillian and explicitly integrating these modes out from the expression of the TCF, we derived the non-adiabatic Matsubara dynamics approach. Further making the approximation to drop the imaginary part of the Matsubara Liouvillian and enforce the nuclear momentum integral to be real, we arrived at the non-adiabatic ring-polymer molecular dynamics (NRPMD) approach. We have further justified the capability of NRPMD for simulating the non-equilibrium TCF. This work provides the rigorous theoretical foundation for several recently proposed state-dependent RPMD approaches and offers a general framework for developing new non-adiabatic quantum dynamics methods in the future.
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Affiliation(s)
- Sutirtha N Chowdhury
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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13
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Brown SE, Shakib FA. Recent progress in approximate quantum dynamics methods for the study of proton-coupled electron transfer reactions. Phys Chem Chem Phys 2021; 23:2535-2556. [PMID: 33367437 DOI: 10.1039/d0cp05166g] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Proton-coupled electron transfer (PCET) reactions are ubiquitous natural processes at the heart of energy conversion reactions in photosynthesis and respiration, DNA repair, and diverse enzymatic reactions. Theoretical formulation and computational method developments have eyed modeling of thermal and photoinduced PCET for the last three decades. The accumulation of these studies, collected in dozens of reviews, accounts, and perspectives, has firmly established the influence of quantum effects, including non-adiabatic electronic transitions, vibrational relaxation, zero-point energy, and proton tunneling, on the rate and mechanism of PCET reactions. Here, we focus on some recently-developed methods, spanning the last eight years, that can quantitatively capture these effects in the PCET context and provide efficient means for their qualitative description in complex systems. The theoretical background of each method and their accuracy with respect to exact results are discussed and the results of relevant PCET simulations based on each method are presented.
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Affiliation(s)
- Sandra E Brown
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA 90095, USA
| | - Farnaz A Shakib
- Department of Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, NJ 07102, USA.
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14
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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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15
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Kim HW, Rhee YM. Two-oscillator mapping modification of the Poisson bracket mapping equation formulation of the quantum-classical Liouville equation. J Chem Phys 2020; 153:214103. [PMID: 33291890 DOI: 10.1063/5.0027799] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
Mapping basis solutions provide efficient ways for simulating mixed quantum-classical (MQC) dynamics in complex systems by matching multiple quantum states of interest to some fictitious physical states. Recently, various MQC methods were devised such that two harmonic oscillators are employed to represent each electronic state, showing improvements over one-oscillator-based methods. Here, we introduce and analyze newly modified mapping approximations of the quantum-classical Liouville equation (QCLE) using two oscillators for each electronic state. We design two separate mapping relations that we can adopt toward simulating dynamics and computing expectation values. Through the process, two MQC methods can be constructed, one of which actually reproduces the population dynamics of the forward and backward trajectory solution of QCLE. By applying the methods to spin-boson systems with a range of parameters, we find out that the choice of mapping relations greatly affects the simulation results. We also show that further improvement is possible through using modified identity operator formulations. Our findings may be helpful in constructing improved MQC methods in the future.
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Affiliation(s)
- Hyun Woo Kim
- Center for Molecular Modeling and Simulation, Korea Research Institute of Chemical Technology (KRICT), Daejeon 34114, South Korea
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, South Korea
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16
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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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17
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Mannouch JR, Richardson JO. A partially linearized spin-mapping approach for nonadiabatic dynamics. II. Analysis and comparison with related approaches. J Chem Phys 2020; 153:194110. [DOI: 10.1063/5.0031173] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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18
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Braver Y, Valkunas L, Gelzinis A. Benchmarking the forward–backward trajectory solution of the quantum-classical Liouville equation. J Chem Phys 2020; 152:214116. [DOI: 10.1063/5.0006538] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yakov Braver
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania
- Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania
- Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| | - Andrius Gelzinis
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania
- Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
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19
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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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20
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Runeson JE, Richardson JO. Generalized spin mapping for quantum-classical dynamics. J Chem Phys 2020; 152:084110. [DOI: 10.1063/1.5143412] [Citation(s) in RCA: 27] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Affiliation(s)
- Johan E. Runeson
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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21
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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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22
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Kelly A. Exciton dissociation and charge separation at donor–acceptor interfaces from quantum-classical dynamics simulations. Faraday Discuss 2020; 221:547-563. [DOI: 10.1039/c9fd00069k] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Nonadiabatic dynamics simulations based on the quantum-classical Liouville equation are employed to study the real-time dynamics of exciton dissociation and charge separation at a model donor–acceptor interface.
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Affiliation(s)
- Aaron Kelly
- Department of Chemistry
- Dalhousie University
- Halifax
- Canada
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23
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Hoffmann NM, Schäfer C, Säkkinen N, Rubio A, Appel H, Kelly A. Benchmarking semiclassical and perturbative methods for real-time simulations of cavity-bound emission and interference. J Chem Phys 2019; 151:244113. [PMID: 31893926 DOI: 10.1063/1.5128076] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We benchmark a selection of semiclassical and perturbative dynamics techniques by investigating the correlated evolution of a cavity-bound atomic system to assess their applicability to study problems involving strong light-matter interactions in quantum cavities. The model system of interest features spontaneous emission, interference, and strong coupling behavior and necessitates the consideration of vacuum fluctuations and correlated light-matter dynamics. We compare a selection of approximate dynamics approaches including fewest switches surface hopping (FSSH), multitrajectory Ehrenfest dynamics, linearized semiclassical dynamics, and partially linearized semiclassical dynamics. Furthermore, investigating self-consistent perturbative methods, we apply the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy in the second Born approximation. With the exception of fewest switches surface hopping, all methods provide a reasonable level of accuracy for the correlated light-matter dynamics, with most methods lacking the capacity to fully capture interference effects.
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Affiliation(s)
- Norah M Hoffmann
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
| | - Christian Schäfer
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
| | - Niko Säkkinen
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
| | - Angel Rubio
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
| | - Heiko Appel
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
| | - Aaron Kelly
- Department of Physics, Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, 22761 Hamburg, Germany
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24
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Zheng J, Xie Y, Jiang S, Long Y, Ning X, Lan Z. Initial sampling in symmetrical quasiclassical dynamics based on Li-Miller mapping Hamiltonian. Phys Chem Chem Phys 2019; 21:26502-26514. [PMID: 31777888 DOI: 10.1039/c9cp03975a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
A symmetrical quasiclassical (SQC) dynamics approach based on the Li-Miller (LM) mapping Hamiltonian (SQC-LM) was employed to describe nonadiabatic dynamics. In principle, the different initial sampling procedures may be applied in the SQC-LM dynamics, and the results may be dependent on different initial sampling. We provided various initial sampling approaches and checked their influence. We selected two groups of models including site-exciton models for exciton dynamics and linear vibronic coupling models for conical intersections to test the performance of SQC-LM dynamics with the different initial sampling methods. The results were examined with respect to those of the accurate multiconfigurational time-dependent Hartree (MCTDH) quantum dynamics. For both the models, the SQC-LM method more-or-less gives a reasonable description of the population dynamics, while the influence of the initial sampling approaches on the final results is noticeable. It seems that the suitable initial sampling methods should be determined by the system under study. This indicates that the combination of the SQC-LM method with a suitable sampling approach may be a potential method in the description of nonadiabatic dynamics.
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Affiliation(s)
- Jie Zheng
- Industrial Research Institute of Nonwovens & Technical Textiles, College of Textiles Clothing, Qingdao University, Qingdao 266071, China.
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25
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Zhou W, Mandal A, Huo P. Quasi-Diabatic Scheme for Nonadiabatic On-the-Fly Simulations. J Phys Chem Lett 2019; 10:7062-7070. [PMID: 31665889 DOI: 10.1021/acs.jpclett.9b02747] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We use the quasi-diabatic (QD) propagation scheme to perform on-the-fly nonadiabatic simulations of the photodynamics of ethylene. The QD scheme enables a seamless interface between accurate diabatic-based quantum dynamics approaches and adiabatic electronic structure calculations, explicitly avoiding any efforts to construct global diabatic states or reformulate the diabatic dynamics approach to the adiabatic representation. Using the partial linearized path-integral approach and the symmetrical quasi-classical approach as the diabatic dynamics methods, the QD propagation scheme enables direct nonadiabatic simulation with complete active space self-consistent field on-the-fly electronic structure calculations. The population dynamics obtained from both approaches are in a close agreement with the quantum wavepacket-based method and outperform the widely used trajectory surface-hopping approach. Further analysis of the ethylene photodeactivation pathways demonstrates the correct predictions of competing processes of nonradiative relaxation mechanism through various conical intersections. This work provides the foundation of using accurate diabatic dynamics approaches and on-the-fly adiabatic electronic structure information to perform ab initio nonadiabatic simulation.
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Affiliation(s)
- Wanghuai Zhou
- Advanced Functional Material and Photoelectric Technology Research Institution, School of Science , Hubei University of Automotive Technology , Shiyan , Hubei 442002 , People's Republic of China
- Department of Chemistry , University of Rochester , 120 Trustee Road , Rochester , New York 14627 , United States
| | - Arkajit Mandal
- Department of Chemistry , University of Rochester , 120 Trustee Road , Rochester , New York 14627 , United States
| | - Pengfei Huo
- Department of Chemistry , University of Rochester , 120 Trustee Road , Rochester , New York 14627 , United States
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26
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Provazza J, Coker DF. Multi-level description of the vibronic dynamics of open quantum systems. J Chem Phys 2019; 151:154114. [DOI: 10.1063/1.5120253] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Justin Provazza
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - David F. Coker
- Department of Chemistry, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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27
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Runeson JE, Richardson JO. Spin-mapping approach for nonadiabatic molecular dynamics. J Chem Phys 2019; 151:044119. [DOI: 10.1063/1.5100506] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Johan E. Runeson
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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28
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Chowdhury SN, Huo P. State dependent ring polymer molecular dynamics for investigating excited nonadiabatic dynamics. J Chem Phys 2019; 150:244102. [DOI: 10.1063/1.5096276] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sutirtha N. Chowdhury
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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29
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Carli M, Turelli M, Faccioli P. Microscopic calculation of absorption spectra of macromolecules: An analytic approach. J Chem Phys 2019; 150:144103. [PMID: 30981270 DOI: 10.1063/1.5084120] [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
We develop a cross-disciplinary approach to analytically compute optical response functions of open macromolecular systems by exploiting the mathematical formalism of quantum field theory (QFT). Indeed, the entries of the density matrix for the electronic excitations interacting with their open dissipative environment are mapped into vacuum-to-vacuum Green's functions in a fictitious relativistic closed quantum system. We show that by re-summing appropriate self-energy diagrams in this dual QFT, it is possible to obtain analytic expressions for the response functions in Mukamel's theory. This yields physical insight into the structure and dynamics of vibronic resonances, since their frequency and width is related to fundamental physical constants and microscopic model parameters. For illustration, we apply this scheme to compute the linear absorption spectrum of the Fenna-Matthews-Olson light harvesting complex, comparing analytic calculations, numerical Monte Carlo simulations, and experimental data.
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Affiliation(s)
- Matteo Carli
- Physics Department of Trento University, Via Sommarive 14, Povo, Trento 38123, Italy
| | - Michele Turelli
- Physics Department of Trento University, Via Sommarive 14, Povo, Trento 38123, Italy
| | - Pietro Faccioli
- Physics Department of Trento University, Via Sommarive 14, Povo, Trento 38123, Italy
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30
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Mandal A, Sandoval C. JS, Shakib FA, Huo P. Quasi-Diabatic Propagation Scheme for Direct Simulation of Proton-Coupled Electron Transfer Reaction. J Phys Chem A 2019; 123:2470-2482. [DOI: 10.1021/acs.jpca.9b00077] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Juan S. Sandoval C.
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Farnaz A. Shakib
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
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31
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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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32
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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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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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Mandal A, Shakib FA, Huo P. Investigating photoinduced proton coupled electron transfer reaction using quasi diabatic dynamics propagation. J Chem Phys 2018; 148:244102. [DOI: 10.1063/1.5030634] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Farnaz A. Shakib
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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35
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Zauleck JPP, Peschel MT, Rott F, Thallmair S, de Vivie-Riedle R. Ultrafast Reactive Quantum Dynamics Coupled to Classical Solvent Dynamics Using an Ehrenfest Approach. J Phys Chem A 2018; 122:2849-2857. [PMID: 29498853 DOI: 10.1021/acs.jpca.7b10372] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The inclusion of solvent effects in the theoretical analysis of molecular processes becomes increasingly important. Currently, it is not feasible to directly include the solvent on the quantum level. We use an Ehrenfest approach to study the coupled time evolution of quantum dynamically treated solutes and classical solvents system. The classical dynamics of the solvent is coupled to the wavepacket dynamics of the solute and rotational and translational degrees of freedom of the solute are included classically. This allows quantum dynamics simulations for ultrafast processes that are decided by environment interactions without explicit separation of time scales. We show the application to the dissociation of ICN in liquid Ar as a proof of principal system and to the more applied example of uracil in water.
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Affiliation(s)
- Julius P P Zauleck
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Martin T Peschel
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Florian Rott
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Sebastian Thallmair
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
| | - Regina de Vivie-Riedle
- Department of Chemistry , Ludwig-Maximilians-Universität München , D-81377 München , Germany
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36
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Ha JK, Lee IS, Min SK. Surface Hopping Dynamics beyond Nonadiabatic Couplings for Quantum Coherence. J Phys Chem Lett 2018; 9:1097-1104. [PMID: 29439572 DOI: 10.1021/acs.jpclett.8b00060] [Citation(s) in RCA: 64] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Description of correct electron-nuclear couplings is crucial in modeling of nonadiabatic dynamics. Within traditional semiclassical or mixed quantum-classical dynamics, the coupling between quantum electronic states and classical nuclear trajectories is governed by nonadiabatic coupling vectors coupled to classical nuclear momenta. This enables us to develop a very powerful nonadiabatic dynamics algorithm, namely, surface hopping dynamics, which can describe the splitting of nuclear wave packets and detailed balance. Despite its efficiency and practicality, it suffers from the lack of quantum decoherence due to incorrect accounts for the electron-nuclear coupling. Here we present a new surface hopping algorithm based on the exact electron-nuclear correlation from the exact factorization of molecular wave functions. This algorithm demands comparable computational costs to existing surface hopping methods. Numerical simulations with two-state models and a multidimensional multistate realistic molecule show that the electron-nuclear coupling beyond the nonadiabatic coupling terms can describe the quantum coherence properly.
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Affiliation(s)
- Jong-Kwon Ha
- Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST) , 50 UNIST-gil, Ulsan 44919, Republic of Korea
| | - In Seong Lee
- Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST) , 50 UNIST-gil, Ulsan 44919, Republic of Korea
| | - 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
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37
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Mandal A, Yamijala SSRKC, Huo P. Quasi-Diabatic Representation for Nonadiabatic Dynamics Propagation. J Chem Theory Comput 2018; 14:1828-1840. [DOI: 10.1021/acs.jctc.7b01178] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Sharma SRKC Yamijala
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
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38
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Kananenka AA, Hsieh CY, Cao J, Geva E. Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity. J Phys Chem Lett 2018; 9:319-326. [PMID: 29239614 DOI: 10.1021/acs.jpclett.7b03002] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.
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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
- Singapore-MIT Alliance for Research and Technology (SMART) Center , Singapore 487373
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02319, United States
- Singapore-MIT Alliance for Research and Technology (SMART) Center , Singapore 487373
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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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Chowdhury SN, Huo P. Coherent state mapping ring polymer molecular dynamics for non-adiabatic quantum propagations. J Chem Phys 2017; 147:214109. [DOI: 10.1063/1.4995616] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sutirtha N. Chowdhury
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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41
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Affiliation(s)
- Timothy J. H. Hele
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
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42
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43
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Freedman H, Hanna G. Mixed quantum–classical Liouville simulation of vibrational energy transfer in a model α-helix at 300 K. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.08.015] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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44
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Lee MK, Huo P, Coker DF. Semiclassical Path Integral Dynamics: Photosynthetic Energy Transfer with Realistic Environment Interactions. Annu Rev Phys Chem 2016; 67:639-68. [DOI: 10.1146/annurev-physchem-040215-112252] [Citation(s) in RCA: 96] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Mi Kyung Lee
- Department of Chemistry, Boston University, Boston, Massachusetts 02215;
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627;
| | - David F. Coker
- Department of Chemistry, Boston University, Boston, Massachusetts 02215;
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45
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Martinez F, Hanna G. Mixed Quantum-Classical Simulations of Transient Absorption Pump–Probe Signals for a Photo-Induced Electron Transfer Reaction Coupled to an Inner-Sphere Vibrational Mode. J Phys Chem A 2016; 120:3196-205. [DOI: 10.1021/acs.jpca.5b11727] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Franz Martinez
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
| | - Gabriel Hanna
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
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46
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Hele TJH, Ananth N. Deriving the exact nonadiabatic quantum propagator in the mapping variable representation. Faraday Discuss 2016; 195:269-289. [DOI: 10.1039/c6fd00106h] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting Liouvillian is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact Liouvillian lead to existing approximate semiclassical and mixed quantum–classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact Liouvillian, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction rates in complex quantized systems.
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Affiliation(s)
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology
- Cornell University
- Ithaca
- USA
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47
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Kondorskiy AD, Nanbu S. Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering. J Chem Phys 2015; 143:114103. [DOI: 10.1063/1.4930923] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexey D. Kondorskiy
- P. N. Lebedev Physical Institute of the Russian Academy of Sciences, 53, Leninsky Prospekt, Moscow 119991, Russia
| | - Shinkoh Nanbu
- Department of Materials and Life Sciences, Faculty of Science and Technology, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
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Min SK, Agostini F, Gross EKU. Coupled-Trajectory Quantum-Classical Approach to Electronic Decoherence in Nonadiabatic Processes. PHYSICAL REVIEW LETTERS 2015; 115:073001. [PMID: 26317716 DOI: 10.1103/physrevlett.115.073001] [Citation(s) in RCA: 92] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Indexed: 06/04/2023]
Abstract
We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasiclassical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the nuclear wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.
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Affiliation(s)
- Seung Kyu Min
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
- Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Korea
| | - Federica Agostini
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - E K U Gross
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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Kelly A, Brackbill N, Markland TE. Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations. J Chem Phys 2015; 142:094110. [DOI: 10.1063/1.4913686] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Affiliation(s)
- Aaron Kelly
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Nora Brackbill
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Thomas E. Markland
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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50
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Kapral R. Quantum dynamics in open quantum-classical systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:073201. [PMID: 25634784 DOI: 10.1088/0953-8984/27/7/073201] [Citation(s) in RCA: 49] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.
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Affiliation(s)
- Raymond Kapral
- Department of Chemistry, Chemical Physics Theory Group, University of Toronto, Toronto, ON, M5S 3H6 Canada
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