1
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Novoderezhkin VI. Excitonic interactions and Stark fluorescence spectra. J Chem Phys 2023; 159:054114. [PMID: 37548302 DOI: 10.1063/5.0158393] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 07/20/2023] [Indexed: 08/08/2023] Open
Abstract
We develop the theory for the Stark fluorescence (SF) of molecular aggregates by taking into account the mixing of the excited states [including the states with charge-transfer (CT) characters]. We use the sum-over-state approach and modified rotating wave approximation to describe interactions of the static and optical fields with the permanent and transition dipoles of the excited states. The SF spectral profiles are calculated using the standard and modified Redfield theories for the emission lineshapes. The resulting expression allows an interpretation of the SF response based on the calculation of only one-exciton states (i.e., the calculation of two-exciton states is not needed). The shape and amplitude of the SF spectrum can exhibit dramatic changes in the presence of the CT states, especially when the CT state is mixed with the red-most emitting exciton levels. In this case, the SF responses are much more sensitive to the exciton-CT mixing as compared with the usual Stark absorption. The limitation of the proposed theory is related to the simplified nature of the Redfield picture, which neglects the dynamic localization within the mixed exciton-CT configuration.
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Affiliation(s)
- Vladimir I Novoderezhkin
- A. N. Belozersky Institute of Physico-Chemical Biology, Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia
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2
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Lyu N, Mulvihill E, Soley MB, Geva E, Batista VS. Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations. J Chem Theory Comput 2023; 19:1111-1129. [PMID: 36719350 DOI: 10.1021/acs.jctc.2c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion and dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations and are compared with those obtained from an approximate linearized semiclassical method, allowing for assessment of the accuracy of these approximate memory kernels and inhomogeneous terms. Moreover, we have analyzed the computational cost of the full and reduced-dimensionality GQMEs. The scaling of the computational cost is dependent on several factors, sometimes with opposite scaling trends. The TT-TFD memory kernels can provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for the development of quantum circuits that implement GQMEs on digital quantum computers.
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Affiliation(s)
- Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Ellen Mulvihill
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Micheline B Soley
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States.,Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.,Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, United States
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3
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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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4
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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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5
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Yan Y, Liu Y, Xing T, Shi Q. Theoretical study of excitation energy transfer and nonlinear spectroscopy of photosynthetic light‐harvesting complexes using the nonperturbative reduced dynamics method. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1498] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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 Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing China
| | - Yanying Liu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species Institute of Chemistry, Chinese Academy of Sciences Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing 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 Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing 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 Beijing China
- University of Chinese Academy of Sciences Beijing China
- Physical Science Laboratory Huairou National Comprehensive Science Center Beijing China
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6
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Teh HH, Jin BY, Cheng YC. Frozen-mode small polaron quantum master equation with variational bound for excitation energy transfer in molecular aggregates. J Chem Phys 2019; 150:224110. [DOI: 10.1063/1.5096287] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hung-Hsuan Teh
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Bih-Yaw Jin
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
| | - Yuan-Chung Cheng
- Department of Chemistry, National Taiwan University, Taipei City 10617, Taiwan
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7
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Gururangan K, Harel E. Coherent and dissipative quantum process tensor reconstructions in two-dimensional electronic spectroscopy. J Chem Phys 2019; 150:164127. [PMID: 31042925 DOI: 10.1063/1.5082165] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
A major goal of time-resolved spectroscopy is to resolve the dynamical processes that follow photoexcitation. This amounts to identifying all the quantum states involved and the rates of population transfer between them. Unfortunately, such quantum state and kinetic reconstructions are ambiguous using one-dimensional methods such as transient absorption even when all the states of the system are fully resolved. Higher-dimensionality methods like two-dimensional spectroscopy lift some of the ambiguity, but unless the spectral features are well-separated, current inversion methods generally fail. Here, we show that, using both coherence and population signals of the nonlinear response, it is indeed possible to accurately extract both static and dynamic information from the 2D spectrum even when features are highly congested. Coherences report on the positions of the vibronic states of the system, providing a useful constraint for extracting the full kinetic scheme. We model time-resolved 2D photon echo spectra using a sum-over-states approach and show in which regimes the Hamiltonian and kinetic schemes may be recovered. Furthermore, we discuss how such algorithms may be applied to experimental data and where some of the underlying assumptions may fail. The ability to systematically extract the maximal information content of multidimensional spectroscopic data is an important step toward utilizing the full power of these techniques and elucidating the structure and dynamics of increasingly complex molecular systems.
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Affiliation(s)
- Karthik Gururangan
- Department of Materials Science and Engineering, Northwestern University, 2200 Campus Drive, Evanston, Illinois 60208, USA
| | - Elad Harel
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
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8
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Xu M, Yan Y, Liu Y, Shi Q. Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model. J Chem Phys 2018; 148:164101. [DOI: 10.1063/1.5022761] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Meng Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yanying Liu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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9
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Tempelaar R, Reichman DR. Generalization of fewest-switches surface hopping for coherences. J Chem Phys 2018; 148:102309. [DOI: 10.1063/1.5000843] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roel Tempelaar
- Department of Chemistry, Columbia University, 3000 Broadway,
New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway,
New York, New York 10027, USA
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10
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Han Y, Meng Q, Rasulev B, May PS, Berry MT, Kilin DS. Photoinduced Charge Transfer versus Fragmentation Pathways in Lanthanum Cyclopentadienyl Complexes. J Chem Theory Comput 2017. [DOI: 10.1021/acs.jctc.7b00050] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Yulun Han
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
- Department
of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108, United States
| | - Qingguo Meng
- Shenyang
Institute of Automation, Guangzhou, Chinese Academy of Sciences, Guangzhou 511458, China
| | - Bakhtiyor Rasulev
- Center
for Computationally Assisted Science and Technology, North Dakota State University, Fargo, North Dakota 58102, United States
- Department of Coatings and Polymeric Materials, North Dakota State University, Fargo, North Dakota 58102, United States
| | - P. Stanley May
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Mary T. Berry
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
| | - Dmitri S. Kilin
- Department
of Chemistry, University of South Dakota, Vermillion, South Dakota 57069, United States
- Department
of Chemistry and Biochemistry, North Dakota State University, Fargo, North Dakota 58108, United States
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11
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Zhang HD, Qiao Q, Xu RX, Zheng X, Yan Y. Efficient steady-state solver for hierarchical quantum master equations. J Chem Phys 2017; 147:044105. [DOI: 10.1063/1.4995424] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qin Qiao
- Discipline of Neuroscience, Department of Anatomy, Histology and Embryology, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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12
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Kumpulainen T, Lang B, Rosspeintner A, Vauthey E. Ultrafast Elementary Photochemical Processes of Organic Molecules in Liquid Solution. Chem Rev 2016; 117:10826-10939. [DOI: 10.1021/acs.chemrev.6b00491] [Citation(s) in RCA: 249] [Impact Index Per Article: 31.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Tatu Kumpulainen
- Department of Physical Chemistry,
Sciences II, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
| | - Bernhard Lang
- Department of Physical Chemistry,
Sciences II, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
| | - Arnulf Rosspeintner
- Department of Physical Chemistry,
Sciences II, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
| | - Eric Vauthey
- Department of Physical Chemistry,
Sciences II, University of Geneva, 30 Quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland
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13
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Herbert JM, Zhang X, Morrison AF, Liu J. Beyond Time-Dependent Density Functional Theory Using Only Single Excitations: Methods for Computational Studies of Excited States in Complex Systems. Acc Chem Res 2016; 49:931-41. [PMID: 27100899 DOI: 10.1021/acs.accounts.6b00047] [Citation(s) in RCA: 66] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Single-excitation methods, namely, configuration interaction singles and time-dependent density functional theory (TDDFT), along with semiempirical versions thereof, represent the most computationally affordable electronic structure methods for describing electronically excited states, scaling as [Formula: see text] absent further approximations. This relatively low cost, combined with a treatment of electron correlation, has made TDDFT the most widely used excited-state quantum chemistry method over the past 20+ years. Nevertheless, certain inherent problems (beyond just the accuracy of this or that exchange-correlation functional) limit the utility of traditional TDDFT. For one, it affords potential energy surfaces whose topology is incorrect in the vicinity of any conical intersection (CI) that involves the ground state. Since CIs are the conduits for transitions between electronic states, the TDDFT description of photochemistry (internal conversion and intersystem crossing) is therefore suspect. Second, the [Formula: see text] cost can become prohibitive in large systems, especially those that involve multiple electronically coupled chromophores, for example, the antennae structures of light-harvesting complexes or the conjugated polymers used in organic photovoltaics. In such cases, the smallest realistic mimics might already be quite large from the standpoint of ab initio quantum chemistry. This Account describes several new computational methods that address these problems. Topology around a CI can be rigorously corrected using a "spin-flip" version of TDDFT, which involves an α → β spin-flipping transition in addition to occupied → virtual excitation of one electron. Within this formalism, singlet states are generated via excitation from a high-spin triplet reference state, doublets from a quartet, etc. This provides a more balanced treatment of electron correlation between ground and excited states. Spin contamination is problematic away from the Franck-Condon region, but we describe a "spin-complete" version of the theory in which proper spin eigenstates are obtained by construction. For systems of coupled chromophores, we have developed an ab initio version of the Frenkel-Davydov exciton model in which collective excitations of the system are expanded in a basis of excited states computed for individual chromophores. The monomer calculations are trivially parallelizable, as is computation of the coupling matrix elements needed to construct the exciton Hamiltonian, and systems containing hundreds of chromophores can be tackled on commodity hardware. This enables calculations on organic semiconductors, where even small model systems exhibit a semicontinuum of excited states that renders traditional TDDFT computationally challenging. Despite including only single excitations on each monomer, the exciton model can describe entangled spins on two or more monomers, an effect that is responsible for excitation energy transfer between chromophores, for example, in singlet fission. Excitonic approximations can also be applied to the TDDFT equations themselves, and a particularly promising application is to describe the effects of environment on an excitation that is localized on a single chromophore. This "local excitation approximation" to TDDFT allows an essentially arbitrary number of solvent molecules to be included in the calculation in a highly parallelizable way such that the time-to-solution increases only very slowly as additional solvent molecules are added. It is therefore possible to converge the calculation with respect to describing an ever-larger portion of the environment at a quantum-mechanical level.
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Affiliation(s)
- John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Xing Zhang
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Adrian F. Morrison
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Jie Liu
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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14
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Song L, Shi Q. Calculation of correlated initial state in the hierarchical equations of motion method using an imaginary time path integral approach. J Chem Phys 2015; 143:194106. [DOI: 10.1063/1.4935799] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Linze Song
- 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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15
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Montoya-Castillo A, Berkelbach TC, Reichman DR. Extending the applicability of Redfield theories into highly non-Markovian regimes. J Chem Phys 2015; 143:194108. [DOI: 10.1063/1.4935443] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Timothy C. Berkelbach
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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16
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Liu H, Zhu L, Bai S, Shi Q. Reduced quantum dynamics with arbitrary bath spectral densities: hierarchical equations of motion based on several different bath decomposition schemes. J Chem Phys 2015; 140:134106. [PMID: 24712779 DOI: 10.1063/1.4870035] [Citation(s) in RCA: 87] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.
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Affiliation(s)
- Hao Liu
- 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
| | - Lili Zhu
- 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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17
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Tscherbul TV, Brumer P. Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems. J Chem Phys 2015; 142:104107. [PMID: 25770526 DOI: 10.1063/1.4908130] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
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Affiliation(s)
- Timur V Tscherbul
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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18
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Basilevsky MV, Odinokov AV, Titov SV, Mitina EA. Golden rule kinetics of transfer reactions in condensed phase: the microscopic model of electron transfer reactions in disordered solid matrices. J Chem Phys 2013; 139:234102. [PMID: 24359347 DOI: 10.1063/1.4838335] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
The algorithm for a theoretical calculation of transfer reaction rates for light quantum particles (i.e., the electron and H-atom transfers) in non-polar solid matrices is formulated and justified. The mechanism postulated involves a local mode (an either intra- or inter-molecular one) serving as a mediator which accomplishes the energy exchange between the reacting high-frequency quantum mode and the phonon modes belonging to the environment. This approach uses as a background the Fermi golden rule beyond the usually applied spin-boson approximation. The dynamical treatment rests on the one-dimensional version of the standard quantum relaxation equation for the reduced density matrix, which describes the frequency fluctuation spectrum for the local mode under consideration. The temperature dependence of a reaction rate is controlled by the dimensionless parameter ξ0 = ℏω0/k(B)T where ω0 is the frequency of the local mode and T is the temperature. The realization of the computational scheme is different for the high/intermediate (ξ0 < 1 - 3) and for low (ξ0 ≫ 1) temperature ranges. For the first (quasi-classical) kinetic regime, the Redfield approximation to the solution of the relaxation equation proved to be sufficient and efficient in practical applications. The study of the essentially quantum-mechanical low-temperature kinetic regime in its asymptotic limit requires the implementation of the exact relaxation equation. The coherent mechanism providing a non-vanishing reaction rate has been revealed when T → 0. An accurate computational methodology for the cross-over kinetic regime needs a further elaboration. The original model of the hopping mechanism for electronic conduction in photosensitive organic materials is considered, based on the above techniques. The electron transfer (ET) in active centers of such systems proceeds via local intra- and intermolecular modes. The active modes, as a rule, operate beyond the kinetic regimes, which are usually postulated in the existing theories of the ET. Our alternative dynamic ET model for local modes immersed in the continuum harmonic medium is formulated for both classical and quantum regimes, and accounts explicitly for the mode∕medium interaction. The kinetics of the energy exchange between the local ET subsystem and the surrounding environment essentially determine the total ET rate. The efficient computer code for rate computations is elaborated on. The computations are available for a wide range of system parameters, such as the temperature, external field, local mode frequency, and characteristics of mode/medium interaction. The relation of the present approach to the Marcus ET theory and to the quantum-statistical reaction rate theory [V. G. Levich and R. R. Dogonadze, Dokl. Akad. Nauk SSSR, Ser. Fiz. Khim. 124, 213 (1959); J. Ulstrup, Charge Transfer in Condensed Media (Springer, Berlin, 1979); M. Bixon and J. Jortner, Adv. Chem. Phys. 106, 35 (1999)] underlying it is discussed and illustrated by the results of computations for practically important target systems.
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Affiliation(s)
- M V Basilevsky
- Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow, Russia
| | - A V Odinokov
- Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow, Russia
| | - S V Titov
- Karpov Institute of Physical Chemistry, 3-1∕12, Building 6, Obuha pereulok, Moscow, Russia
| | - E A Mitina
- Photochemistry Center, Russian Academy of Sciences, 7a, Novatorov ul., Moscow, Russia
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Guan C, Wu N, Zhao Y. Optimization of exciton currents in photosynthetic systems. J Chem Phys 2013; 138:115102. [PMID: 23534666 DOI: 10.1063/1.4795204] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
In an approach analogous to that used to treat electronic currents in semiconductor quantum dots, we investigate the exciton current in a pigment network that is sandwiched between two exciton reservoirs, also known as the emitter and the acceptor. Employing the master equation for the reduced density matrix, the exciton current is obtained analytically for a two-site model, and numerically for an eight-site Fenna-Matthews-Olson (FMO) subunit model. It is found that, to maximize the exciton current with a specific network configuration, there exist optimal emitter temperatures and exciton transfer rates between the network and the reservoirs. The steady state current in the FMO model is consistent with the trapping time calculated by network optimization in the one-exciton picture. The current optimization with respect to various control parameters is discussed for the FMO model. At and below the biologically relevant transfer rate 1 ps(-1), the FMO network is more efficient for excitation energy transfer than the two-site model. Beyond this scale, the FMO network shows robustness with respect to the interplay with the reservoirs.
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Affiliation(s)
- Chengbo Guan
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
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21
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Berkelbach TC, Hybertsen MS, Reichman DR. Microscopic theory of singlet exciton fission. II. Application to pentacene dimers and the role of superexchange. J Chem Phys 2013; 138:114103. [PMID: 23534623 DOI: 10.1063/1.4794427] [Citation(s) in RCA: 227] [Impact Index Per Article: 20.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
We apply our theoretical formalism for singlet exciton fission, introduced in the previous paper [T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, J. Chem. Phys. 138, 114102 (2013)] to molecular dimers of pentacene, a widely studied material that exhibits singlet fission in the crystal phase. We address a longstanding theoretical issue, namely whether singlet fission proceeds via two sequential electron transfer steps mediated by charge-transfer states or via a direct two-electron transfer process. We find evidence for a superexchange mediated mechanism, whereby the fission process proceeds through virtual charge-transfer states which may be very high in energy. In particular, this mechanism predicts efficient singlet fission on the sub-picosecond timescale, in reasonable agreement with experiment. We investigate the role played by molecular vibrations in mediating relaxation and decoherence, finding that different physically reasonable forms for the bath relaxation function give similar results. We also examine the competing direct coupling mechanism and find it to yield fission rates slower in comparison with the superexchange mechanism for the dimer. We discuss implications for crystalline pentacene, including the limitations of the dimer model.
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Affiliation(s)
- Timothy C Berkelbach
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA.
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Palii A, Bosch-Serrano C, Clemente-Juan JM, Coronado E, Tsukerblat B. Dissipative electron transfer dynamics in mixed valence dimers: Microscopic approach to the solid state problem. J Chem Phys 2013; 139:044304. [DOI: 10.1063/1.4813855] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Affiliation(s)
- Andrew Palii
- Institute of Applied Physics, Academy of Sciences of Moldova, Kishinev, Moldova.
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23
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Berkelbach TC, Hybertsen MS, Reichman DR. Microscopic theory of singlet exciton fission. I. General formulation. J Chem Phys 2013; 138:114102. [DOI: 10.1063/1.4794425] [Citation(s) in RCA: 184] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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24
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Jing Y, Chen L, Bai S, Shi Q. Equilibrium excited state and emission spectra of molecular aggregates from the hierarchical equations of motion approach. J Chem Phys 2013; 138:045101. [DOI: 10.1063/1.4775843] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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YAN YIJING, ZHANG HOUYU. TOWARD THE MECHANISM OF LONG-RANGE CHARGE TRANSFER IN DNA: THEORIES AND MODELS. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2012. [DOI: 10.1142/s0219633602000154] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This article reviews our recent theoretical development toward understanding the interplay of electronic structure and dephasing effects on charge transfer/transport through molecular donor-bridge-acceptor systems. Both the generalized scattering matrix and Green's function formalisms for partially incoherent tunneling processes are summarized. Presented is also an exact mapping between the kinetic rate constants and the electric conductances in evaluation of chemical yields of sequential charge transfer in the presence of competing branching reactions. As an important example, the mechanism of long-range charge transfer in DNA in aqueous solution is investigated with a quantum chemistry implementation of the generalized Green's function formalism. A time scale of about 5 ps is found for the partially incoherent tunneling through a thymine/adenine π-stack in DNA. Numerical results further show that while the carrier oxidative charge does hop sequentially over all guanine sites in a DNA duplex, its tunneling over thymine/adenine bridge base pairs deviates substantially from the superexchange regime. Presented are also evidences for the involvement of both intrastrand and interstrand pathways in the ground state hole charge transfer in DNA.
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Affiliation(s)
- YI JING YAN
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR, China
| | - HOUYU ZHANG
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR, China
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27
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Fleming CH, Roura A, Hu BL. Initial-state preparation with dynamically generated system-environment correlations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:021106. [PMID: 21928948 DOI: 10.1103/physreve.84.021106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2011] [Indexed: 05/31/2023]
Abstract
The dependence of the dynamics of open quantum systems upon initial correlations between the system and environment is an utterly important yet poorly understood subject. For technical convenience most prior studies assume factorizable initial states where the system and its environments are uncorrelated, but these conditions are not very realistic and give rise to peculiar behaviors. One distinct feature is the rapid buildup or a sudden jolt of physical quantities immediately after the system is brought in contact with its environments. The ultimate cause of this is an initial imbalance between system-environment correlations and coupling. In this paper we demonstrate explicitly how to avoid these unphysical behaviors by proper adjustments of correlations and/or the coupling, for setups of both theoretical and experimental interest. We provide simple analytical results in terms of quantities that appear in linear (as opposed to affine) master equations derived for factorized initial states.
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Affiliation(s)
- C H Fleming
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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28
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Lloveras V, Vidal-Gancedo J, Figueira-Duarte TM, Nierengarten JF, Novoa JJ, Mota F, Ventosa N, Rovira C, Veciana J. Tunneling versus Hopping in Mixed-Valence Oligo-p-phenylenevinylene Polychlorinated Bis(triphenylmethyl) Radical Anions. J Am Chem Soc 2011; 133:5818-33. [DOI: 10.1021/ja1083859] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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29
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Fleming CH, Cummings NI. Accuracy of perturbative master equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031117. [PMID: 21517464 DOI: 10.1103/physreve.83.031117] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2010] [Revised: 01/12/2011] [Indexed: 05/30/2023]
Abstract
We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
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Affiliation(s)
- C H Fleming
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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30
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Liang XT. Excitation energy transfer: study with non-Markovian dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051918. [PMID: 21230511 DOI: 10.1103/physreve.82.051918] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2010] [Revised: 08/25/2010] [Indexed: 05/30/2023]
Abstract
In this paper, we investigate the non-markovian dynamics of a model to mimic the excitation energy transfer (EET) between chromophores in photosynthesis systems. The numerical path integral method is used. This method includes the non-Markovian effects of the environmental affects, and it does not need the perturbation approximation in solving the dynamics of systems of interest. It implies that the coherence helps the EET between chromophores through lasting the transfer time rather than enhancing the transfer rate of the EET. In particular, the non-markovian environment greatly increases the efficiency of the EET in the photosynthesis systems.
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Affiliation(s)
- Xian-Ting Liang
- Department of Physics and Institute of Modern Physics, Ningbo University, Ningbo 315211, China.
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Chen X, Silbey RJ. Effect of correlation of local fluctuations on exciton coherence. J Chem Phys 2010; 132:204503. [PMID: 20515096 DOI: 10.1063/1.3435211] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recent experimental studies have shown both oscillations of exciton populations and long lasting coherence in multichromophoric systems such as photosynthetic light harvesting systems and conjugated polymers. It has been suggested that this quantum effect is due to correlations of the fluctuations of site energies among the closely packed chromophores in the protein environment. In addition to these, there is the strong possibility of correlations between site energies and transfer matrix elements. In order to understand the role of such correlations we generalize the Haken-Strobl-Reineker (HSR) model to include the energetic correlations and the site diagonal-off-diagonal correlations in a systematic way. The extended HSR model in the exciton basis is also constructed and allows us to study the dynamics of the exciton populations and coherences. With the extended model, we can provide insight into how these correlations affect the evolution of the populations and coherences of excitons by comparing to the original HSR model with uncorrelated fluctuating environments.
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Affiliation(s)
- Xin Chen
- Department of Chemistry and Center for Excitonics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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32
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Biggs JD, Cina JA. Calculations of nonlinear wave-packet interferometry signals in the pump-probe limit as tests for vibrational control over electronic excitation transfer. J Chem Phys 2010; 131:224302. [PMID: 20001031 DOI: 10.1063/1.3257597] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The preceding paper [J. D. Biggs and J. A. Cina, J. Chem. Phys. 131, 224101 (2009)] (referred to here as Paper 1), describes a strategy for externally influencing the course of short-time electronic excitation transfer (EET) in molecular dimers and observing the process by nonlinear wave-packet interferometry (nl-WPI). External influence can, for example, be exerted by inducing coherent intramolecular vibration in one of the chromophores prior to short-pulse electronic excitation of the other. Within a sample of isotropically oriented dimers having a specified internal geometry, a vibrational mode internal to the acceptor chromophore can be preferentially driven by electronically nonresonant impulsive stimulated Raman (or resonant infrared) excitation with a short polarized "control" pulse. A subsequent electronically resonant polarized pump then preferentially excites the donor, and EET ensues. Paper 1 investigates control-pulse-influenced nl-WPI as a tool for the spectroscopic evaluation of the effect of coherent molecular vibration on excitation transfer, presenting general expressions for the nl-WPI difference signal from a dimer following the action of a control pulse of arbitrary polarization and shape. Electronic excitation is to be effected and its interchromophore transfer monitored by resonant pump and probe "pulses," respectively, each consisting of an optical-phase-controlled ultrashort pulse-pair having arbitrary polarization, duration, center frequency, and other characteristics. Here we test both the control strategy and its spectroscopic investigation-with some sacrifice of amplitude-level detail-by calculating the pump-probe difference signal. That signal is the limiting case of the control-influenced nl-WPI signal in which the two pulses in the pump pulse-pair coincide, as do the two pulses in the probe pulse-pair. We present calculated pump-probe difference signals for (1) a model excitation-transfer complex in which two equal-energy monomers each support one moderately Franck-Condon active intramolecular vibration; (2) a simplified model of the covalent dimer dithia-anthracenophane, representing its EET dynamics following selective impulsive excitation of the weakly Franck-Condon active nu(12) anthracene vibration at 385 cm(-1); and (3) a model complex featuring moderate electronic-vibrational coupling in which the site energy of the acceptor chromophore is lower than that of the donor.
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Affiliation(s)
- Jason D Biggs
- Department of Chemistry and Oregon Center for Optics, University of Oregon, Eugene, Oregon 97403, USA
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Venkataraman C, Soudackov AV, Hammes-Schiffer S. Photoinduced homogeneous proton-coupled electron transfer: Model study of isotope effects on reaction dynamics. J Chem Phys 2009; 131:154502. [DOI: 10.1063/1.3249964] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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Shi Q, Geva E. A self-consistent treatment of electron transfer in the limit of strong friction via the mixed quantum classical Liouville method. J Chem Phys 2009; 131:034511. [DOI: 10.1063/1.3176509] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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Ishizaki A, Fleming GR. Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach. J Chem Phys 2009; 130:234111. [DOI: 10.1063/1.3155372] [Citation(s) in RCA: 530] [Impact Index Per Article: 35.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
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36
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Nan G, Shi Q, Shuai Z. Nonperturbative time-convolutionless quantum master equation from the path integral approach. J Chem Phys 2009; 130:134106. [DOI: 10.1063/1.3108521] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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37
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Chen L, Zheng R, Shi Q, Yan Y. Optical line shapes of molecular aggregates: Hierarchical equations of motion method. J Chem Phys 2009; 131:094502. [DOI: 10.1063/1.3213013] [Citation(s) in RCA: 111] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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38
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Navrotskaya I, Soudackov AV, Hammes-Schiffer S. Model system-bath Hamiltonian and nonadiabatic rate constants for proton-coupled electron transfer at electrode-solution interfaces. J Chem Phys 2008; 128:244712. [DOI: 10.1063/1.2940203] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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Role of vibrational energy relaxation in the photoinduced nonadiabatic dynamics of pyrrole at the conical intersection. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2008.01.049] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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40
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Dobryakov A, Pérez Lustres J, Kovalenko S, Ernsting N. Femtosecond transient absorption with chirped pump and supercontinuum probe: Perturbative calculation of transient spectra with general lineshape functions, and simplifications. Chem Phys 2008. [DOI: 10.1016/j.chemphys.2007.11.003] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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41
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Chapman CT, Cina JA. Semiclassical treatments for small-molecule dynamics in low-temperature crystals using fixed and adiabatic vibrational bases. J Chem Phys 2007; 127:114502. [PMID: 17887852 DOI: 10.1063/1.2754270] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Time-resolved coherent nonlinear optical experiments on small molecules in low-temperature host crystals are exposing valuable information on quantum mechanical dynamics in condensed media. We make use of generic features of these systems to frame two simple, comprehensive theories that will enable the efficient calculations of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Without resorting to a simple harmonic analysis, both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath. Both approaches expand the overall wave function as a sum of product states between fully anharmonic vibrational basis states for the system and approximate Gaussian wave packets for the bath degrees of freedom. The theories exploit the fact that ultrafast experiments typically drive large-amplitude motion in a few intermolecular degrees of freedom of higher frequency than the crystal phonons, while these intramolecular vibrations indirectly induce smaller-amplitude--but still perhaps coherent--motion among the lattice modes. The equations of motion for the time-dependent parameters of the bath wave packets are fairly compact in a fixed vibrational basis/Gaussian bath (FVB/GB) approach. An alternative adiabatic vibrational basis/Gaussian bath (AVB/GB) treatment leads to more complicated equations of motion involving adiabatic and nonadiabatic vector potentials. Computational demands for propagation of the parameter equations of motion appear quite manageable for tens or hundreds of atoms and scale similarly with system size in the two cases. Because of the time-scale separation between intermolecular and lattice vibrations, the AVB/GB theory may in some instances require fewer vibrational basis states than the FVB/GB approach. Either framework should enable practical first-principles calculations of nonlinear optical signals from molecules in cryogenic matrices and their semiclassical interpretation in terms of electronic and vibrational decoherence and vibrational population relaxation, all within a pure-state description of the macroscopic many-body complex.
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Affiliation(s)
- Craig T Chapman
- Department of Chemistry, Oregon Center for Optics, University of Oregon, Eugene, Oregon 97403, USA
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Wichterich H, Henrich MJ, Breuer HP, Gemmer J, Michel M. Modeling heat transport through completely positive maps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031115. [PMID: 17930207 DOI: 10.1103/physreve.76.031115] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2007] [Indexed: 05/25/2023]
Abstract
We investigate heat transport in a spin-1/2 Heisenberg chain, coupled locally to independent thermal baths of different temperature. The analysis is carried out within the framework of the theory of open systems by means of appropriate quantum master equations. The standard microscopic derivation of the weak-coupling Lindblad equation in the secular approximation is considered, and shown to be inadequate for the description of stationary nonequilibrium properties like a nonvanishing energy current. Furthermore, we derive an alternative master equation that is capable of describing a stationary energy current and, at the same time, leads to a completely positive dynamical map. This paves the way for efficient numerical investigations of heat transport in larger systems based on Monte Carlo wave function techniques.
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Affiliation(s)
- Hannu Wichterich
- Fachbereich Physik, Universität Osnabrück, Barbarastrasse 7, D-49069 Osnabrück, Germany.
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Novoderezhkin VI, Palacios MA, van Amerongen H, van Grondelle R. Excitation dynamics in the LHCII complex of higher plants: modeling based on the 2.72 Angstrom crystal structure. J Phys Chem B 2007; 109:10493-504. [PMID: 16852271 DOI: 10.1021/jp044082f] [Citation(s) in RCA: 210] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have modeled steady-state spectra and energy-transfer dynamics in the peripheral plant light-harvesting complex LHCII using new structural data. The dynamics of the chlorophyll (Chl) b-->Chl a transfer and decay of selectively excited "bottleneck" Chl a and b states have been studied by femtosecond pump-probe spectroscopy. We propose an exciton model of the LHCII trimer (with specific site energies) which allows a simultaneous quantitative fit of the absorption, linear-dichroism, steady-state fluorescence spectra, and transient absorption kinetics upon excitation at different wavelengths. In the modeling we use the experimental exciton-phonon spectral density and modified Redfield theory. We have found that fast b-->a transfer is determined by a good connection of the Chls b to strongly coupled Chl a clusters, i.e., a610-a611-a612 trimer and a602-a603 and a613-a614 dimers. Long-lived components of the energy-transfer kinetics are determined by a quick population of red-shifted Chl b605 and blue-shifted Chl a604 followed by a very slow (3 ps for b605 and 12 ps for a604) flow of energy from these monomeric bottleneck sites to the Chl a clusters. The dynamics within the Chl a region is determined by fast (with time constants down to sub-100 fs) exciton relaxation within the a610-a611-a612 trimer, slower 200-300 fs relaxation within the a602-a603 and a613-a614 dimers, even slower 300-800 fs migration between these clusters, and very slow transfer from a604 to the quasi-equilibrated a sites. The final equilibrium is characterized by predominant population of the a610-a611-a612 cluster (mostly the a610 site). The location of this cluster on the outer side of the LHCII trimer probably provides a good connection with the other subunits of PSII.
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Affiliation(s)
- Vladimir I Novoderezhkin
- A. N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Leninskie Gory, 119992 Moscow, Russia
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Jin J, Welack S, Luo J, Li XQ, Cui P, Xu RX, Yan Y. Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach. J Chem Phys 2007; 126:134113. [PMID: 17430022 DOI: 10.1063/1.2713104] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed.
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Affiliation(s)
- Jinshuang Jin
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong.
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45
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Basilevsky MV, Davidovich GV, Voronin AI. The model of level broadening in condensed phase. J Chem Phys 2006; 125:194514. [PMID: 17129130 DOI: 10.1063/1.2386160] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
We study a model of non-Markovian kinetics for a harmonic oscillator embedded in a harmonic heat bath. We present a new scheme for approximately solving the quantum relaxation equation for the density matrix to find a distribution of level populations. It is found to be an extended Lorentzian with the width depending on the energy. A more convenient non-Markovian distribution called square root Fourier distribution that was implemented in the preceding paper [M. V. Basilevsky et al., J. Chem. Phys. 125, 194513 (2006)] is closely related to this extended Lorentzian model. Both distributions decay exponentially far away from their centers and reproduce well standard Lorentzian widths in the vicinity of the central region. A conventional Lorentzian model with such widths results when the Redfield approximation is applied in the frame of the present procedure.
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Affiliation(s)
- M V Basilevsky
- Photochemistry Center, Russian Academy of Science, ul. Novatorov 7a, Moscow 117421, Russia.
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Basilevsky MV, Davidovich GV, Titov SV, Voronin AI. Non-Markovian modification of the golden rule rate expression. J Chem Phys 2006; 125:194513. [PMID: 17129129 DOI: 10.1063/1.2364498] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The reformulation of the standard golden rule approach considered in this paper for treating reactive tunneling reduces the computation of the reaction rate to a derivation of band shapes for energy levels of reactant and product states. This treatment is based on the assumption that the medium environment is actively involved as a partner in the energy exchange with the reactive subsystem but its reorganization effect is negligible. Starting from the quantum relaxation equation for the density matrix, the required band shapes are represented in terms of the spectral density function, exhibiting the continuum spectrum inherent to the interaction between the reactants and the medium in the total reactive system. The simplest Lorentzian spectral bands, obtained under Redfield approximation, proved to be unsatisfactory because they produced a divergent rate expression at low temperature. The problem is resolved by invoking a refined spectral band shape, which behaves as Lorentzian one at the band center but decays exponentially at its tails. The corresponding closed non-Markovian rate expression is derived and investigated taking as an example the photochemical H-transfer reaction between fluorene and acridine proceeding in the fluorene molecular crystal. The kinetics in this reactive system was thoroughly studied experimentally in a wide temperature range [B. Prass et al., Ber. Bunsenges. Phys. Chem. 102, 498 (1998)].
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Affiliation(s)
- M V Basilevsky
- Photochemistry Center, Russian Academy of Sciences, ul. Novatorov 7a, Moscow 119421, Russia.
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Zhang ML, Ka BJ, Geva E. Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation. J Chem Phys 2006; 125:44106. [PMID: 16942133 DOI: 10.1063/1.2218342] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system's dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.
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Affiliation(s)
- Ming-Liang Zhang
- Department of Chemistry and FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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Welack S, Schreiber M, Kleinekathöfer U. The influence of ultrafast laser pulses on electron transfer in molecular wires studied by a non-Markovian density-matrix approach. J Chem Phys 2006; 124:044712. [PMID: 16460205 DOI: 10.1063/1.2162537] [Citation(s) in RCA: 120] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density-matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields nonperturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.
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Affiliation(s)
- Sven Welack
- Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.
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Pomyalov A, Tannor DJ. The non-Markovian quantum master equation in the collective-mode representation: Application to barrier crossing in the intermediate friction regime. J Chem Phys 2005; 123:204111. [PMID: 16351244 DOI: 10.1063/1.2121649] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The calculation of chemical reaction rates in the condensed phase is a central preoccupation of theoretical chemistry. At low temperatures, quantum-mechanical effects can be significant and even dominant; yet quantum calculations of rate constants are extremely challenging, requiring theories and methods capable of describing quantum evolution in the presence of dissipation. In this paper we present a new approach based on the use of a non-Markovian quantum master equation (NM-QME). As opposed to other approximate quantum methods, the quantum dynamics of the system coordinate is treated exactly; hence there is no loss of accuracy at low temperatures. However, because of the perturbative nature of the NM-QME it breaks down for dimensionless frictions larger than about 0.1. We show that by augmenting the system coordinate with a collective mode of the bath, the regime of validity of the non-Markovian master equation can be extended significantly, up to dimensionless frictions of 0.5 over the entire temperature range. In the energy representation, the scaling goes as the number of levels in the relevant energy range to the third power. This scaling is not prohibitive even for chemical systems with many levels; hence we believe that the current method will find a useful place alongside the existing techniques for calculating quantum condensed-phase rate constants.
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Affiliation(s)
- Anna Pomyalov
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, 76100 Israel
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Yang M. A reduced density-matrix theory of absorption line shape of molecular aggregate. J Chem Phys 2005; 123:124705. [PMID: 16392509 DOI: 10.1063/1.2046668] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (Förster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.
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Affiliation(s)
- Mino Yang
- Department of Chemistry and Basic Sciences Research Institute, Chungbuk National University, Cheongju, Chungbuk 361-763, South Korea.
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