1
|
Iles-Smith J, Diba O, Nazir A. Capturing non-Markovian polaron dressing with the master equation formalism. J Chem Phys 2024; 161:134111. [PMID: 39360686 DOI: 10.1063/5.0228779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2024] [Accepted: 09/15/2024] [Indexed: 10/04/2024] Open
Abstract
Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work, we re-evaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g., populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g., coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.
Collapse
Affiliation(s)
- Jake Iles-Smith
- Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- School of Mathematical and Physical Sciences, The University of Sheffield, Sheffield S10 2TN, United Kingdom
| | - Owen Diba
- Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Ahsan Nazir
- Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| |
Collapse
|
2
|
Grechishnikova G, Wat JH, de Cordoba N, Miyake E, Phadkule A, Srivastava A, Savikhin S, Slipchenko L, Huang L, Reppert M. Controlling Vibronic Coupling in Chlorophyll Proteins: The Effects of Excitonic Delocalization and Vibrational Localization. J Phys Chem Lett 2024; 15:9456-9465. [PMID: 39250712 DOI: 10.1021/acs.jpclett.4c01826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/11/2024]
Abstract
Vibrational-electronic (vibronic) coupling plays a critical role in excitation energy transfer in molecular aggregates and pigment-protein complexes (PPCs). But the interplay between excitonic delocalization and vibronic interactions is complex, often leaving even qualitative questions as to what conceptual framework (e.g., Redfield versus Förster theory) should be used to interpret experimental results. To shed light on this issue, we report here on the interplay between excitonic delocalization and vibronic coupling in site-directed mutants of the water-soluble chlorophyll protein (WSCP), as reflected in 77 K fluorescence spectra. Experimentally, we find that in PPCs where excitonic delocalization is disrupted (either by mutagenesis or heterodimer formation), the relative intensity of the vibrational sideband (VSB) in fluorescence spectra is suppressed by up to 37% compared to that of the native protein. Numerical simulations reveal that this effect results from the localization of high-frequency vibrations in the coupled system; while excitonic delocalization suppresses the purely electronic transition due to H-aggregate-like dipole-dipole interference, high-frequency vibrations are unaffected, leading to a relative enhancement of the VSB. By comparing VSB intensities of PPCs both in the presence and absence of excitonic delocalization, we extract a set of "local" Huang-Rhys (HR) factors for Chl a in WSCP. More generally, our results suggest a significant role for geometric effects in controlling energy-transfer rates (which depend sensitively on absorption/fluorescence line shapes) in molecular aggregates and PPCs.
Collapse
Affiliation(s)
- Galina Grechishnikova
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Jacob H Wat
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Nicolas de Cordoba
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Ethan Miyake
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Amala Phadkule
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Amit Srivastava
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Sergei Savikhin
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
| | - Lyudmila Slipchenko
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Libai Huang
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| | - Mike Reppert
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
| |
Collapse
|
3
|
Diba O, Miller HJD, Iles-Smith J, Nazir A. Quantum Work Statistics at Strong Reservoir Coupling. PHYSICAL REVIEW LETTERS 2024; 132:190401. [PMID: 38804950 DOI: 10.1103/physrevlett.132.190401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Accepted: 03/25/2024] [Indexed: 05/29/2024]
Abstract
Determining the statistics of work done on a quantum system while strongly coupled to a reservoir is a formidable task, requiring the calculation of the full eigenspectrum of the combined system and reservoir. Here, we show that this issue can be circumvented by using a polaron transformation that maps the system into a new frame where weak-coupling theory can be applied. Crucially, this polaron approach reproduces the Jarzynski fluctuation theorem, thus ensuring consistency with the laws of stochastic thermodynamics. We apply our formalism to a system driven across the Landau-Zener transition, where we identify clear signatures in the work distribution arising from a non-negligible coupling to the environment. Our results provide a new method for studying the stochastic thermodynamics of driven quantum systems beyond Markovian, weak-coupling regimes.
Collapse
Affiliation(s)
- Owen Diba
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Harry J D Miller
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Jake Iles-Smith
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Ahsan Nazir
- Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| |
Collapse
|
4
|
Upadhyay AK, Sasihithlu K. Tunability in 3-Site Electronic Excitation Transfer Dynamics: Insights into the Role of Perturbative Coupling. J Phys Chem B 2024; 128:4047-4052. [PMID: 38652834 DOI: 10.1021/acs.jpcb.3c07968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
Electronic excitation transfer dynamics in photosynthetic systems, including the Fenna-Matthews-Olson complex, are often modeled using the interaction picture of three two-level systems, also known as the 3-site system. Among the two possible configurations, uphill and downhill, a recent publication reported an intriguing correlation between population dynamics and the intersite coupling. Specifically, the uphill configuration has been shown to have a pronounced dependence on perturbations in the intersite coupling, whereas the downhill configuration displays negligible dependence. In this study, we consider a generic 3-site configuration and model site interactions through the Markovian master equation. Through this approach, we derive succinct analytical expressions for the population dynamics between the sites, shedding light on the differences in behavior between the two configurations. Using these analytical expressions, we demonstrate the range of tunability in population dynamics achievable with minimal changes in intersite coupling, and we validate these findings through simulation results. These insights into the population dynamics of a 3-site system are expected to play a crucial role in facilitating the design of efficient energy-transfer pathways in molecular systems.
Collapse
Affiliation(s)
- Amit Kumar Upadhyay
- Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Karthik Sasihithlu
- Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
| |
Collapse
|
5
|
Mattioni A, Staab JK, Blackmore WJA, Reta D, Iles-Smith J, Nazir A, Chilton NF. Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets. Nat Commun 2024; 15:485. [PMID: 38212305 PMCID: PMC10784566 DOI: 10.1038/s41467-023-44486-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 12/13/2023] [Indexed: 01/13/2024] Open
Abstract
Single-molecule magnets are among the most promising platforms for achieving molecular-scale data storage and processing. Their magnetisation dynamics are determined by the interplay between electronic and vibrational degrees of freedom, which can couple coherently, leading to complex vibronic dynamics. Building on an ab initio description of the electronic and vibrational Hamiltonians, we formulate a non-perturbative vibronic model of the low-energy magnetic degrees of freedom in monometallic single-molecule magnets. Describing their low-temperature magnetism in terms of magnetic polarons, we are able to quantify the vibronic contribution to the quantum tunnelling of the magnetisation, a process that is commonly assumed to be independent of spin-phonon coupling. We find that the formation of magnetic polarons lowers the tunnelling probability in both amorphous and crystalline systems by stabilising the low-lying spin states. This work, thus, shows that spin-phonon coupling subtly influences magnetic relaxation in single-molecule magnets even at extremely low temperatures where no vibrational excitations are present.
Collapse
Affiliation(s)
- Andrea Mattioni
- Department of Chemistry, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
| | - Jakob K Staab
- Department of Chemistry, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - William J A Blackmore
- Department of Chemistry, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Daniel Reta
- Department of Chemistry, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
- Faculty of Chemistry, The University of the Basque Country UPV/EHU, Donostia, 20018, Spain
- Donostia International Physics Center (DIPC), Donostia, 20018, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, 48013, Spain
| | - Jake Iles-Smith
- Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Ahsan Nazir
- Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
| | - Nicholas F Chilton
- Department of Chemistry, School of Natural Sciences, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK.
| |
Collapse
|
6
|
Novoderezhkin VI. Resonant vibrations produce quantum bridge over high-energy states in heterogeneous antenna. PHOTOSYNTHESIS RESEARCH 2023; 158:13-21. [PMID: 37584896 DOI: 10.1007/s11120-023-01042-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 07/29/2023] [Indexed: 08/17/2023]
Abstract
Photosynthetic light-harvesting complexes usually contain several pools of molecules with a big difference in transition energies, for example, chlorophylls a and b in plant antennas. Some pathways of the excitation energy transfer may include pigments from the low-energy pool separated by a site occupied by a high-energy molecule. We demonstrate that such pathways may be functional if high-frequency intramolecular vibrations fall in resonance with the energy gap between the neighboring molecules belonging to different pools. In this case, a vibration-assisted mixing of the excited states can produce delocalized vibronic states playing a role of 'quantum bridge' that facilitates a passage over high-energy barrier. We perform calculations of the excitation dynamics in the model three-state system with the parameters emerging from our previous studies of real antennas. Simulation of the dynamics in an explicit electron-vibrational basis demonstrates that the rate of transfer between the two chlorophylls a through the chlorophyll b intermediate is increased by a factor of 1.7-2 in the presence of resonant vibration. A possible influence of energetic disorder and other (non-resonant) vibrations on this effect is discussed.
Collapse
Affiliation(s)
- Vladimir I Novoderezhkin
- A. N. Belozersky Institute of Physico-Chemical Biology, Lomonosov Moscow State University, Leninskie Gory, 119992, Moscow, Russia.
| |
Collapse
|
7
|
Balzer D, Kassal I. Mechanism of Delocalization-Enhanced Exciton Transport in Disordered Organic Semiconductors. J Phys Chem Lett 2023; 14:2155-2162. [PMID: 36802583 DOI: 10.1021/acs.jpclett.2c03886] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Large exciton diffusion lengths generally improve the performance of organic semiconductor devices, because they enable energy to be transported farther during the exciton lifetime. However, the physics of exciton motion in disordered organic materials is not fully understood, and modeling the transport of quantum-mechanically delocalized excitons in disordered organic semiconductors is a computational challenge. Here, we describe delocalized kinetic Monte Carlo (dKMC), the first model of three-dimensional exciton transport in organic semiconductors that includes delocalization, disorder, and polaron formation. We find that delocalization can dramatically increase exciton transport; for example, delocalization across less than two molecules in each direction can increase the exciton diffusion coefficient by over an order of magnitude. The mechanism for the enhancement is 2-fold: delocalization enables excitons to hop both more frequently and further in each hop. We also quantify the effect of transient delocalization (short-lived periods where excitons become highly delocalized) and show that it depends strongly upon the disorder and transition dipole moments.
Collapse
Affiliation(s)
- Daniel Balzer
- School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
| | - Ivan Kassal
- School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
| |
Collapse
|
8
|
Sayer T, Montoya-Castillo A. Compact and complete description of non-Markovian dynamics. J Chem Phys 2023; 158:014105. [PMID: 36610963 DOI: 10.1063/5.0132614] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.
Collapse
Affiliation(s)
- Thomas Sayer
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | | |
Collapse
|
9
|
Balzer D, Kassal I. Even a little delocalization produces large kinetic enhancements of charge-separation efficiency in organic photovoltaics. SCIENCE ADVANCES 2022; 8:eabl9692. [PMID: 35960797 PMCID: PMC9374333 DOI: 10.1126/sciadv.abl9692] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Accepted: 06/28/2022] [Indexed: 05/25/2023]
Abstract
In organic photovoltaics, charges can separate efficiently even if their Coulomb attraction is an order of magnitude greater than the available thermal energy. Delocalization has been suggested to explain this fact, because it could increase the initial separation of charges in the charge-transfer (CT) state, reducing their attraction. However, understanding the mechanism requires a kinetic model of delocalized charge separation, which has proven difficult because it involves tracking the correlated quantum-mechanical motion of the electron and the hole in large simulation boxes required for disordered materials. Here, we report the first three-dimensional simulations of charge-separation dynamics in the presence of disorder, delocalization, and polaron formation, finding that even slight delocalization, across less than two molecules, can substantially enhance the charge-separation efficiency, even starting with thermalized CT states. Delocalization does not enhance efficiency by reducing the Coulomb attraction; instead, the enhancement is a kinetic effect produced by the increased overlap of electronic states.
Collapse
|
10
|
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.
Collapse
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
| |
Collapse
|
11
|
Seibt J, Kühn O. Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics Using the Polaron Transformation in HEOM Space. J Phys Chem A 2021; 125:7052-7065. [PMID: 34353023 DOI: 10.1021/acs.jpca.1c02684] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In Frenkel exciton dynamics of aggregated molecules, the polaron transformation (PT) technique leads to decoupling of diagonal elements in the subspace of excited electronic states from vibrations. In this article we describe for the first time how PT becomes applicable in the framework of the "Hierarchical Equations of Motion" (HEOM) approach for treatment of open quantum systems. We extend the concept of formulating operators in HEOM space by deriving hierarchical equations of PT which lead to a shift in the excited state potential energy surface to compensate its displacement. While the assumption of thermal equilibration of the vibrational oscillators, introduced by PT, results in a stationary state in a monomer, in a dimer under the same assumption nonequilibrium dynamics appears because of the interplay of the transfer process and vibrational equilibration. Both vertical transitions generating a vibrationally hot state and initially equilibrated vibrational oscillators evolve toward the same stationary asymptotic state associated with polaron formation. The effect of PT on the dynamics of this process depends on initial excitation and basis representation of the electronic system. The developed approach facilitates a generic formulation of quantum master equations involving perturbative treatment of polaron dynamics.
Collapse
Affiliation(s)
- Joachim Seibt
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany.,Institute for Theoretical Physics, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| |
Collapse
|
12
|
Du M, Qin M, Cui H, Wang C, Xu Y, Ma X, Yi X. Role of Spatially Correlated Fluctuations in Photosynthetic Excitation Energy Transfer with an Equilibrium and a Nonequilibrium Initial Bath. J Phys Chem B 2021; 125:6417-6430. [PMID: 34105973 DOI: 10.1021/acs.jpcb.1c02041] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The transfer of excitation energy in photosynthetic light-harvesting complexes has inspired growing interest for its scientific and engineering significance. Recent experimental findings have suggested that spatially correlated environmental fluctuations may account for the existence of long-lived quantum coherent energy transfer observed even at physiological temperature. In this paper, we investigate the effects of spatial correlations on the excitation energy transfer dynamics by including a nonequilibrium initial bath in a simulated donor-acceptor model. The initial bath state, which is assumed to be either equilibrium or nonequilibrium, is expanded in powers of coupling strength within the polaron formalism of a quantum master equation. The spatial correlations of bath fluctuations strongly influence the decay of coherence in the dynamics. The role of a nonequilibrium initial bath is also influenced by spatial correlations and becomes the most conspicuous for certain degrees of spatial correlations from which we propose a picture that the spatial correlations of bath fluctuations open up new energy transfer pathways, playing a role of protecting coherence. Besides, we apply the polaron master equation approach to study the dynamics in a two-site subsystem of the FMO complex and provide a practical example that shows the versatility of this approach.
Collapse
Affiliation(s)
- Min Du
- College of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Ming Qin
- College of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China.,Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
| | - Haitao Cui
- College of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China.,Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
| | - Chunyang Wang
- College of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Yuqing Xu
- College of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Xiaoguang Ma
- College of Physics and Optoelectronic Engineering, Ludong University, Yantai 264025, China
| | - Xuexi Yi
- Center for Quantum Sciences and School of Physics, Northeast Normal University, Changchun 130024, China
| |
Collapse
|
13
|
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
| |
Collapse
|
14
|
Gelzinis A, Valkunas L. Analytical derivation of equilibrium state for open quantum system. J Chem Phys 2020; 152:051103. [PMID: 32035455 DOI: 10.1063/1.5141519] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
Calculation of the equilibrium state of an open quantum system interacting with a bath remains a challenge to this day, mostly due to a huge number of bath degrees of freedom. Here, we present an analytical expression for the reduced density operator in terms of an effective Hamiltonian for a high temperature case. Comparing with numerically exact results, we show that our theory is accurate for slow baths and up to intermediate system-bath coupling strengths. Our results demonstrate that the equilibrium state does not depend on the shape of spectral density in the slow bath regime. The key quantity in our theory is the effective coupling between the states, which depends exponentially on the ratio of the reorganization energy to temperature and, thus, has opposite temperature dependence than could be expected from the small polaron transformation.
Collapse
Affiliation(s)
- Andrius Gelzinis
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius, Lithuania
| |
Collapse
|
15
|
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.
Collapse
Affiliation(s)
| | - Aaron Kelly
- Department of Chemistry
- Dalhousie University
- Halifax
- Canada
| | | |
Collapse
|
16
|
Trushechkin A. Calculation of coherences in Förster and modified Redfield theories of excitation energy transfer. J Chem Phys 2019; 151:074101. [DOI: 10.1063/1.5100967] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Anton Trushechkin
- Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia and National University of Science and Technology MISIS, Leninsky Avenue 2, 119049 Moscow, Russia
| |
Collapse
|
17
|
Toa ZSD, deGolian MH, Jumper CC, Hiller RG, Scholes GD. Consistent Model of Ultrafast Energy Transfer in Peridinin Chlorophyll-a Protein Using Two-Dimensional Electronic Spectroscopy and Förster Theory. J Phys Chem B 2019; 123:6410-6420. [DOI: 10.1021/acs.jpcb.9b04324] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Zi S. D. Toa
- Department of Chemistry, Princeton University, Washington Road, Princeton, New Jersey 08540, United States
| | - Mary H. deGolian
- Department of Chemistry, Princeton University, Washington Road, Princeton, New Jersey 08540, United States
| | - Chanelle C. Jumper
- Department of Chemistry, Princeton University, Washington Road, Princeton, New Jersey 08540, United States
| | - Roger G. Hiller
- Department of Biology, Faculty of Science and Engineering, Macquarie University, Sydney NSW 2109, Australia
| | - Gregory D. Scholes
- Department of Chemistry, Princeton University, Washington Road, Princeton, New Jersey 08540, United States
| |
Collapse
|
18
|
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
| |
Collapse
|
19
|
Jumper CC, Rafiq S, Wang S, Scholes GD. From coherent to vibronic light harvesting in photosynthesis. Curr Opin Chem Biol 2018; 47:39-46. [DOI: 10.1016/j.cbpa.2018.07.023] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Accepted: 07/18/2018] [Indexed: 11/27/2022]
|
20
|
|
21
|
Wang Y, Ke Y, Zhao Y. The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1375] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Yu‐Chen Wang
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Yaling Ke
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Lab of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University Xiamen China
| |
Collapse
|
22
|
Fetherolf JH, Berkelbach TC. Linear and nonlinear spectroscopy from quantum master equations. J Chem Phys 2018; 147:244109. [PMID: 29289132 DOI: 10.1063/1.5006824] [Citation(s) in RCA: 37] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.
Collapse
Affiliation(s)
- Jonathan H Fetherolf
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| | - Timothy C Berkelbach
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
23
|
Gelzinis A, Rybakovas E, Valkunas L. Applicability of transfer tensor method for open quantum system dynamics. J Chem Phys 2018; 147:234108. [PMID: 29272940 DOI: 10.1063/1.5009086] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.
Collapse
Affiliation(s)
- Andrius Gelzinis
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius, Lithuania
| | - Edvardas Rybakovas
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute of Chemical Physics, Faculty of Physics, Vilnius University, Sauletekio 9-III, 10222 Vilnius, Lithuania
| |
Collapse
|
24
|
Kananenka AA, Sun X, Schubert A, Dunietz BD, Geva E. A comparative study of different methods for calculating electronic transition rates. J Chem Phys 2018; 148:102304. [DOI: 10.1063/1.4989509] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexei A. Kananenka
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexander Schubert
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Barry D. Dunietz
- Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio 44242, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| |
Collapse
|
25
|
Ke Y, Zhao Y. Perturbation expansions of stochastic wavefunctions for open quantum systems. J Chem Phys 2017; 147:184103. [DOI: 10.1063/1.4996737] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yaling Ke
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| | - Yi Zhao
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China
| |
Collapse
|
26
|
Quantum design of photosynthesis for bio-inspired solar-energy conversion. Nature 2017; 543:355-365. [PMID: 28300093 DOI: 10.1038/nature22012] [Citation(s) in RCA: 205] [Impact Index Per Article: 29.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Accepted: 02/01/2017] [Indexed: 12/15/2022]
Abstract
Photosynthesis is the natural process that converts solar photons into energy-rich products that are needed to drive the biochemistry of life. Two ultrafast processes form the basis of photosynthesis: excitation energy transfer and charge separation. Under optimal conditions, every photon that is absorbed is used by the photosynthetic organism. Fundamental quantum mechanics phenomena, including delocalization, underlie the speed, efficiency and directionality of the charge-separation process. At least four design principles are active in natural photosynthesis, and these can be applied practically to stimulate the development of bio-inspired, human-made energy conversion systems.
Collapse
|
27
|
Abstract
We introduce the concept of spatio-temporal steering (STS), which reduces, in special cases, to Einstein-Podolsky-Rosen steering and the recently-introduced temporal steering. We describe two measures of this effect referred to as the STS weight and robustness. We suggest that these STS measures enable a new way to assess nonclassical correlations in an open quantum network, such as quantum transport through nano-structures or excitation transfer in a complex biological system. As one of our examples, we apply STS to check nonclassical correlations among sites in a photosynthetic pigment-protein complex in the Fenna-Matthews-Olson model.
Collapse
|
28
|
Quantum - coherent dynamics in photosynthetic charge separation revealed by wavelet analysis. Sci Rep 2017; 7:2890. [PMID: 28588203 PMCID: PMC5460264 DOI: 10.1038/s41598-017-02906-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2016] [Accepted: 04/20/2017] [Indexed: 11/22/2022] Open
Abstract
Experimental/theoretical evidence for sustained vibration-assisted electronic (vibronic) coherence in the Photosystem II Reaction Center (PSII RC) indicates that photosynthetic solar-energy conversion might be optimized through the interplay of electronic and vibrational quantum dynamics. This evidence has been obtained by investigating the primary charge separation process in the PSII RC by two-dimensional electronic spectroscopy (2DES) and Redfield modeling of the experimental data. However, while conventional Fourier transform analysis of the 2DES data allows oscillatory signatures of vibronic coherence to be identified in the frequency domain in the form of static 2D frequency maps, the real-time evolution of the coherences is lost. Here we apply for the first time wavelet analysis to the PSII RC 2DES data to obtain time-resolved 2D frequency maps. These maps allow us to demonstrate that (i) coherence between the excitons initiating the two different charge separation pathways is active for more than 500 fs, and (ii) coherence between exciton and charge-transfer states, the reactant and product of the charge separation reaction, respectively; is active for at least 1 ps. These findings imply that the PSII RC employs coherence (i) to sample competing electron transfer pathways, and ii) to perform directed, ultrafast and efficient electron transfer.
Collapse
|
29
|
Zhang Z, Wang J. Origin of long-lived quantum coherence and excitation dynamics in pigment-protein complexes. Sci Rep 2016; 6:37629. [PMID: 27876861 PMCID: PMC5120302 DOI: 10.1038/srep37629] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2016] [Accepted: 10/28/2016] [Indexed: 12/25/2022] Open
Abstract
We explore the mechanism for the long-lived quantum coherence by considering the discrete phonon modes: these vibrational modes effectively weaken the exciton-environment interaction, due to the new composite (polaron) formed by excitons and vibrons. This subsequently demonstrates the role of vibrational coherence which greatly contributes to long-lived feature of the excitonic coherence that has been observed in femtosecond experiments. The estimation of the timescale of coherence elongated by vibrational modes is given in an analytical manner. To test the validity of our theory, we study the pigment-protein complex in detail by exploring the energy transfer and coherence dynamics. The ground-state vibrational coherence generated by incoherent radiations is shown to be long-survived and is demonstrated to be significant in promoting the excitation energy transfer. This is attributed to the nonequilibriumness of the system caused by the detailed-balance-breaking, which funnels the downhill migration of excitons.
Collapse
Affiliation(s)
- Zhedong Zhang
- Department of Physics and Astronomy, SUNY Stony Brook, Stony Brook, NY 11794, USA
- Department of Chemistry, University of California Irvine, Irvine, CA 92697, USA
| | - Jin Wang
- Department of Physics and Astronomy, SUNY Stony Brook, Stony Brook, NY 11794, USA
- Department of Chemistry, SUNY Stony Brook, Stony Brook, NY 11794, USA
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute for Applied Chemistry, Chinese, Academy of Sciences, Changchun, Jilin 130022, P. R. China
| |
Collapse
|
30
|
Novoderezhkin VI, Romero E, van Grondelle R. How exciton-vibrational coherences control charge separation in the photosystem II reaction center. Phys Chem Chem Phys 2016; 17:30828-41. [PMID: 25854607 DOI: 10.1039/c5cp00582e] [Citation(s) in RCA: 53] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
In photosynthesis absorbed sun light produces collective excitations (excitons) that form a coherent superposition of electronic and vibrational states of the individual pigments. Two-dimensional (2D) electronic spectroscopy allows a visualization of how these coherences are involved in the primary processes of energy and charge transfer. Based on quantitative modeling we identify the exciton-vibrational coherences observed in 2D photon echo of the photosystem II reaction center (PSII-RC). We find that the vibrations resonant with the exciton splittings can modify the delocalization of the exciton states and produce additional states, thus promoting directed energy transfer and allowing a switch between the two charge separation pathways. We conclude that the coincidence of the frequencies of the most intense vibrations with the splittings within the manifold of exciton and charge-transfer states in the PSII-RC is not occurring by chance, but reflects a fundamental principle of how energy conversion in photosynthesis was optimized.
Collapse
Affiliation(s)
- Vladimir I Novoderezhkin
- A. N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Leninskie Gory, 119992, Moscow, Russia.
| | - Elisabet Romero
- Department of Biophysics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Rienk van Grondelle
- Department of Biophysics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| |
Collapse
|
31
|
Markovich T, Blau SM, Parkhill J, Kreisbeck C, Sanders JN, Andrade X, Aspuru-Guzik A. Accelerating the computation of bath spectral densities with super-resolution. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1954-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
|
32
|
Sun KW, Fujihashi Y, Ishizaki A, Zhao Y. A variational master equation approach to quantum dynamics with off-diagonal coupling in a sub-Ohmic environment. J Chem Phys 2016; 144:204106. [DOI: 10.1063/1.4950888] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ke-Wei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
| | - Yuta Fujihashi
- Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan
| | - Akihito Ishizaki
- Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585, Japan
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
| |
Collapse
|
33
|
Sun X, Geva E. Nonequilibrium Fermi’s Golden Rule Charge Transfer Rates via the Linearized Semiclassical Method. J Chem Theory Comput 2016; 12:2926-41. [DOI: 10.1021/acs.jctc.6b00236] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiang Sun
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| | - Eitan Geva
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, United States
| |
Collapse
|
34
|
Malý P, Somsen OJG, Novoderezhkin VI, Mančal T, van Grondelle R. The Role of Resonant Vibrations in Electronic Energy Transfer. Chemphyschem 2016; 17:1356-68. [PMID: 26910485 PMCID: PMC5021137 DOI: 10.1002/cphc.201500965] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2015] [Revised: 12/23/2015] [Indexed: 12/02/2022]
Abstract
Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.
Collapse
Affiliation(s)
- Pavel Malý
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands
- Institute of Physics, Charles University in Prague, Ke Karlovu 5, 12116, Prague, Czech Republic
| | - Oscar J G Somsen
- Netherlands Defence Academy, P.O. Box 10000, 1780 CA, Den Helder, The Netherlands
| | - Vladimir I Novoderezhkin
- A. N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Leninskie Gory, 119992, Moscow, Russia
| | - Tomáš Mančal
- Institute of Physics, Charles University in Prague, Ke Karlovu 5, 12116, Prague, Czech Republic
| | - Rienk van Grondelle
- Department of Physics and Astronomy, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands
| |
Collapse
|
35
|
Nazir A, McCutcheon DPS. Modelling exciton-phonon interactions in optically driven quantum dots. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:103002. [PMID: 26882465 DOI: 10.1088/0953-8984/28/10/103002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We provide a self-contained review of master equation approaches to modelling phonon effects in optically driven self-assembled quantum dots. Coupling of the (quasi) two-level excitonic system to phonons leads to dissipation and dephasing, the rates of which depend on the excitation conditions, intrinsic properties of the QD sample, and its temperature. We describe several techniques, which include weak-coupling master equations that are perturbative in the exciton-phonon coupling, as well as those based on the polaron transformation that can remain valid for strong phonon interactions. We additionally consider the role of phonons in altering the optical emission characteristics of quantum dot devices, outlining how we must modify standard quantum optics treatments to account for the presence of the solid-state environment.
Collapse
Affiliation(s)
- Ahsan Nazir
- Photon Science Institute & School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
| | | |
Collapse
|
36
|
Abstract
The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.
Collapse
Affiliation(s)
- Carles Curutchet
- Departament de Fisicoquímica, Facultat de Farmàcia, Universitat de Barcelona , Av. Joan XXIII s/n, 08028 Barcelona, Spain
| | - Benedetta Mennucci
- Dipartimento di Chimica e Chimica Industriale, University of Pisa , via G. Moruzzi 13, 56124 Pisa, Italy
| |
Collapse
|
37
|
Iles-Smith J, Dijkstra AG, Lambert N, Nazir A. Energy transfer in structured and unstructured environments: Master equations beyond the Born-Markov approximations. J Chem Phys 2016; 144:044110. [DOI: 10.1063/1.4940218] [Citation(s) in RCA: 82] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Jake Iles-Smith
- Controlled Quantum Dynamics Theory, Imperial College London, London SW7 2PG, United Kingdom
- Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- Department of Photonics Engineering, DTU Fotonik, Ørsteds Plads, 2800 Kongens Lyngby, Denmark
| | - Arend G. Dijkstra
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
| | | | - Ahsan Nazir
- Photon Science Institute and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| |
Collapse
|
38
|
Sun X, Geva E. Exact vs. asymptotic spectral densities in the Garg-Onuchic-Ambegaokar charge transfer model and its effect on Fermi's golden rule rate constants. J Chem Phys 2016; 144:044106. [PMID: 26827201 DOI: 10.1063/1.4940308] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Garg-Onuchic-Ambegaokar model [J. Chem. Phys. 83, 4491 (1985)] has been used extensively for benchmarking methods aimed at calculating charge transfer rates. Within this model, the donor and acceptor diabats are described as shifted parabolas along a single primary mode, which is bilinearly coupled to a harmonic bath consisting of secondary modes, characterized by an Ohmic spectral density with exponential cutoff. Rate calculations for this model are often performed in the normal mode representation, with the corresponding effective spectral density given by an asymptotic expression derived at the limit where the Ohmic bath cutoff frequency is much larger than the primary mode frequency. We compare Fermi's golden rule rate constants obtained with the asymptotic and exact effective spectral densities. We find significant deviations between rate constants obtained from the asymptotic spectral density and those obtained from the exact one in the deep inverted region. Within the range of primary mode frequencies commonly employed, we find that the discrepancies increase with decreasing temperature and with decreasing primary mode frequency.
Collapse
Affiliation(s)
- Xiang Sun
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
| |
Collapse
|
39
|
Mourokh LG, Nori F. Energy transfer efficiency in the chromophore network strongly coupled to a vibrational mode. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052720. [PMID: 26651736 DOI: 10.1103/physreve.92.052720] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2014] [Indexed: 06/05/2023]
Abstract
Using methods from condensed matter and statistical physics, we examine the transport of excitons through the photosynthetic complex from a receiving antenna to a reaction center. Writing the equations of motion for the exciton creation-annihilation operators, we are able to describe the exciton dynamics, even in the regime when the reorganization energy is of the order of the intrasystem couplings. We determine the exciton transfer efficiency in the presence of a quenching field and protein environment. While the majority of the protein vibrational modes are treated as a heat bath, we address the situation when specific modes are strongly coupled to excitons and examine the effects of these modes on the energy transfer efficiency in the steady-state regime. Using the structural parameters of the Fenna-Matthews-Olson complex, we find that, for vibrational frequencies below 16 meV, the exciton transfer is drastically suppressed. We attribute this effect to the formation of a "mixed exciton-vibrational mode" where the exciton is transferred back and forth between the two pigments with the absorption or emission of vibrational quanta, instead of proceeding to the reaction center. The same effect suppresses the quantum beating at the vibrational frequency of 25 meV. We also show that the efficiency of the energy transfer can be enhanced when the vibrational mode strongly couples to the third pigment only, instead of coupling to the entire system.
Collapse
Affiliation(s)
- Lev G Mourokh
- Department of Physics, Queens College, City University of New York, Flushing, New York 11367, USA
- Graduate Center of CUNY, New York, New York 10016, USA
| | - Franco Nori
- CEMS, RIKEN, Saitama, 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| |
Collapse
|
40
|
Chang Y, Cheng YC. On the accuracy of coherent modified Redfield theory in simulating excitation energy transfer dynamics. J Chem Phys 2015; 142:034109. [PMID: 25612691 DOI: 10.1063/1.4905721] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
In this study, we investigate the accuracy of a recently developed coherent modified Redfield theory (CMRT) in simulating excitation energy transfer (EET) dynamics. The CMRT is a secular non-Markovian quantum master equation that is derived by extending the modified Redfield theory to treat coherence dynamics in molecular excitonic systems. Herein, we systematically survey the applicability of the CMRT in a large EET parameter space through the comparisons of the CMRT EET dynamics in a dimer system with the numerically exact results. The results confirm that the CMRT exhibits a broad applicable range and allow us to locate the specific parameter regimes where CMRT fails to provide adequate results. Moreover, we propose an accuracy criterion based on the magnitude of second-order perturbation to characterize the applicability of CMRT and show that the criterion summarizes all the benchmark results and the physics described by CMRT. Finally, we employ the accuracy criterion to quantitatively compare the performance of CMRT to that of a small polaron quantum master equation approach. The comparison demonstrates the complementary nature of these two methods, and as a result, the combination of the two methods provides accurate simulations of EET dynamics for the full parameter space investigated in this study. Our results not only delicately evaluate the applicability of the CMRT but also reveal new physical insights for factors controlling the dynamics of EET that should be useful for developing more accurate and efficient methods for simulations of EET dynamics in molecular aggregate systems.
Collapse
Affiliation(s)
- Yu Chang
- Department of Chemistry and Center for Quantum Science and Engineering, National Taiwan University, Taipei City 106, Taiwan
| | - Yuan-Chung Cheng
- Department of Chemistry and Center for Quantum Science and Engineering, National Taiwan University, Taipei City 106, Taiwan
| |
Collapse
|
41
|
Chęcińska A, Pollock FA, Heaney L, Nazir A. Dissipation enhanced vibrational sensing in an olfactory molecular switch. J Chem Phys 2015; 142:025102. [PMID: 25591386 DOI: 10.1063/1.4905377] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Motivated by a proposed olfactory mechanism based on a vibrationally activated molecular switch, we study electron transport within a donor-acceptor pair that is coupled to a vibrational mode and embedded in a surrounding environment. We derive a polaron master equation with which we study the dynamics of both the electronic and vibrational degrees of freedom beyond previously employed semiclassical (Marcus-Jortner) rate analyses. We show (i) that in the absence of explicit dissipation of the vibrational mode, the semiclassical approach is generally unable to capture the dynamics predicted by our master equation due to both its assumption of one-way (exponential) electron transfer from donor to acceptor and its neglect of the spectral details of the environment; (ii) that by additionally allowing strong dissipation to act on the odorant vibrational mode, we can recover exponential electron transfer, though typically at a rate that differs from that given by the Marcus-Jortner expression; (iii) that the ability of the molecular switch to discriminate between the presence and absence of the odorant, and its sensitivity to the odorant vibrational frequency, is enhanced significantly in this strong dissipation regime, when compared to the case without mode dissipation; and (iv) that details of the environment absent from previous Marcus-Jortner analyses can also dramatically alter the sensitivity of the molecular switch, in particular, allowing its frequency resolution to be improved. Our results thus demonstrate the constructive role dissipation can play in facilitating sensitive and selective operation in molecular switch devices, as well as the inadequacy of semiclassical rate equations in analysing such behaviour over a wide range of parameters.
Collapse
Affiliation(s)
- Agata Chęcińska
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
| | - Felix A Pollock
- Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Libby Heaney
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
| | - Ahsan Nazir
- Photon Science Institute and School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| |
Collapse
|
42
|
Chen L, Shenai P, Zheng F, Somoza A, Zhao Y. Optimal Energy Transfer in Light-Harvesting Systems. Molecules 2015; 20:15224-72. [PMID: 26307957 PMCID: PMC6332264 DOI: 10.3390/molecules200815224] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2015] [Revised: 08/03/2015] [Accepted: 08/14/2015] [Indexed: 01/25/2023] Open
Abstract
Photosynthesis is one of the most essential biological processes in which specialized pigment-protein complexes absorb solar photons, and with a remarkably high efficiency, guide the photo-induced excitation energy toward the reaction center to subsequently trigger its conversion to chemical energy. In this work, we review the principles of optimal energy transfer in various natural and artificial light harvesting systems. We begin by presenting the guiding principles for optimizing the energy transfer efficiency in systems connected to dissipative environments, with particular attention paid to the potential role of quantum coherence in light harvesting systems. We will comment briefly on photo-protective mechanisms in natural systems that ensure optimal functionality under varying ambient conditions. For completeness, we will also present an overview of the charge separation and electron transfer pathways in reaction centers. Finally, recent theoretical and experimental progress on excitation energy transfer, charge separation, and charge transport in artificial light harvesting systems is delineated, with organic solar cells taken as prime examples.
Collapse
Affiliation(s)
- Lipeng Chen
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue,Singapore 639798, Singapore.
| | - Prathamesh Shenai
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue,Singapore 639798, Singapore.
| | - Fulu Zheng
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue,Singapore 639798, Singapore.
| | - Alejandro Somoza
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue,Singapore 639798, Singapore.
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue,Singapore 639798, Singapore.
| |
Collapse
|
43
|
Lee CK, Moix J, Cao J. Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport. J Chem Phys 2015; 142:164103. [PMID: 25933748 DOI: 10.1063/1.4918736] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum transport in disordered systems is studied using a polaron-based master equation. The polaron approach is capable of bridging the results from the coherent band-like transport regime governed by the Redfield equation to incoherent hopping transport in the classical regime. A non-monotonic dependence of the diffusion coefficient is observed both as a function of temperature and system-phonon coupling strength. In the band-like transport regime, the diffusion coefficient is shown to be linearly proportional to the system-phonon coupling strength and vanishes at zero coupling due to Anderson localization. In the opposite classical hopping regime, we correctly recover the dynamics described by the Fermi's Golden Rule and establish that the scaling of the diffusion coefficient depends on the phonon bath relaxation time. In both the hopping and band-like transport regimes, it is demonstrated that at low temperature, the zero-point fluctuations of the bath lead to non-zero transport rates and hence a finite diffusion constant. Application to rubrene and other organic semiconductor materials shows a good agreement with experimental mobility data.
Collapse
Affiliation(s)
- Chee Kong Lee
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jeremy Moix
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| |
Collapse
|
44
|
Levi F, Mostarda S, Rao F, Mintert F. Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:082001. [PMID: 26194028 DOI: 10.1088/0034-4885/78/8/082001] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.
Collapse
Affiliation(s)
- Federico Levi
- FRIAS, Freiburg Institute for Advanced Studies, Albert-Ludgwigs Universität Freiburg, 79104 Freiburg im Breisgau, Germany
| | | | | | | |
Collapse
|
45
|
Fujihashi Y, Kimura A. Assignment of Exciton Domain in Light Harvesting Systems Based on the Variational Polaron Approach. J Phys Chem B 2015; 119:8349-56. [DOI: 10.1021/acs.jpcb.5b04503] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Yuta Fujihashi
- Graduate School of Science, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-8602, Japan
| | - Akihiro Kimura
- Graduate School of Science, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-8602, Japan
| |
Collapse
|
46
|
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.
Collapse
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
| |
Collapse
|
47
|
Affiliation(s)
- Aurélia Chenu
- Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Gregory D. Scholes
- Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544;
| |
Collapse
|
48
|
Liu J, Sun K, Wang X, Zhao Y. Quantifying non-Markovianity for a chromophore-qubit pair in a super-Ohmic bath. Phys Chem Chem Phys 2015; 17:8087-96. [PMID: 25729785 DOI: 10.1039/c4cp04922e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
An approach based on a non-Markovian time-convolutionless polaron master equation is used to probe the quantum dynamics of a chromophore-qubit in a super-Ohmic bath. Utilizing a measure of non-Markovianity based on dynamical fixed points, we study the effects of the environmental temperature and the coupling strength on the non-Markovian behavior of the chromophore in a super-Ohmic bath. It is found that an increase in the temperature results in a reduction in the backflow information from the environment to the chromophore, and therefore, a suppression of non-Markovianity. In the weak coupling regime, increasing the coupling strength will enhance the non-Markovianity, while the effect is reversed in the strong coupling regime.
Collapse
Affiliation(s)
- Jing Liu
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore.
| | | | | | | |
Collapse
|
49
|
Jeske J, Ing DJ, Plenio MB, Huelga SF, Cole JH. Bloch-Redfield equations for modeling light-harvesting complexes. J Chem Phys 2015; 142:064104. [DOI: 10.1063/1.4907370] [Citation(s) in RCA: 56] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Affiliation(s)
- Jan Jeske
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
| | - David J. Ing
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
| | - Martin B. Plenio
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - Susana F. Huelga
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - Jared H. Cole
- Chemical and Quantum Physics, School of Applied Sciences, RMIT University, Melbourne 3001, Australia
| |
Collapse
|
50
|
|