1
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Dani R, Kundu S, Makri N. Coherence Maps and Flow of Excitation Energy in the Bacterial Light Harvesting Complex 2. J Phys Chem Lett 2023; 14:3835-3843. [PMID: 37067041 DOI: 10.1021/acs.jpclett.3c00670] [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: 06/19/2023]
Abstract
We present and analyze coherence maps [ J. Phys. Chem. B 2022, 126, 9361-9375] to investigate the quantum coherences that are created, sustained, and damped by vibrational modes during the transfer of excitation energy from the B800 (outer) to the B850 (inner) ring of the light harvesting complex 2 (LH2) of purple bacteria with a variety of initial conditions. The reduced density matrix of the 24-pigment complex, where the ground and excited electronic states of each bacteriochlorophyll are explicitly coupled to 50 intramolecular vibrations at room temperature, is obtained from fully quantum-mechanical small matrix path integral (SMatPI) calculations. The coherence maps show a very rapid localization within the outer ring, accompanied by the formation of inter-ring quantum superpositions that evolve to a partial quantum delocalization at equilibrium, and quantify in state-to-state detail the flow of energy within the complex.
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Affiliation(s)
- Reshmi Dani
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
| | - Sohang Kundu
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
| | - Nancy Makri
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Department of Physics, University of Illinois, Urbana, Illinois 61801, United States
- Illinois Quantum Information Science and Technology Center, University of Illinois, Urbana, Illinois 61801, United States
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2
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Cupellini L, Qian P, Nguyen-Phan TC, Gardiner AT, Cogdell RJ. Quantum chemical elucidation of a sevenfold symmetric bacterial antenna complex. PHOTOSYNTHESIS RESEARCH 2023; 156:75-87. [PMID: 35672557 PMCID: PMC10070313 DOI: 10.1007/s11120-022-00925-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/09/2022] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
The light-harvesting complex 2 (LH2) of purple bacteria is one of the most studied photosynthetic antenna complexes. Its symmetric structure and ring-like bacteriochlorophyll arrangement make it an ideal system for theoreticians and spectroscopists. LH2 complexes from most bacterial species are thought to have eightfold or ninefold symmetry, but recently a sevenfold symmetric LH2 structure from the bacterium Mch. purpuratum was solved by Cryo-Electron microscopy. This LH2 also possesses unique near-infrared absorption and circular dichroism (CD) spectral properties. Here we use an atomistic strategy to elucidate the spectral properties of Mch. purpuratum LH2 and understand the differences with the most commonly studied LH2 from Rbl. acidophilus. Our strategy exploits a combination of molecular dynamics simulations, multiscale polarizable quantum mechanics/molecular mechanics calculations, and lineshape simulations. Our calculations reveal that the spectral properties of LH2 complexes are tuned by site energies and exciton couplings, which in turn depend on the structural fluctuations of the bacteriochlorophylls. Our strategy proves effective in reproducing the absorption and CD spectra of the two LH2 complexes, and in uncovering the origin of their differences. This work proves that it is possible to obtain insight into the spectral tuning strategies of purple bacteria by quantitatively simulating the spectral properties of their antenna complexes.
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Affiliation(s)
- Lorenzo Cupellini
- Department of Chemistry and Industrial Chemistry, University of Pisa, 56124, Pisa, Italy.
| | - Pu Qian
- Materials and Structure Analysis, Thermofisher Scientific, Achtseweg Nordic 5, 5651 GTC, Eindhoven, The Netherlands
| | - Tu C Nguyen-Phan
- Institute of Molecular, Cell and Systems Biology, University of Glasgow, Glasgow, G12 8QQ, UK
| | - Alastair T Gardiner
- Laboratory of Anoxygenic Phototrophs, Centre Algatech, Novohradská 237 - Opatovický mlýn, 379 01, Třeboň, Czech Republic
| | - Richard J Cogdell
- Institute of Molecular, Cell and Systems Biology, University of Glasgow, Glasgow, G12 8QQ, UK
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3
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Novoderezhkin VI, Croce R. The location of the low-energy states in Lhca1 favors excitation energy transfer to the core in the plant PSI-LHCI supercomplex. PHOTOSYNTHESIS RESEARCH 2023; 156:59-74. [PMID: 36374368 DOI: 10.1007/s11120-022-00979-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 10/19/2022] [Indexed: 06/16/2023]
Abstract
Lhca1 is one of the four pigment-protein complexes composing the outer antenna of plant Photosystem I-light-havesting I supercomplex (PSI-LHCI). It forms a functional dimer with Lhca4 but, differently from this complex, it does not contain 'red-forms,' i.e., pigments absorbing above 700 nm. Interestingly, the recent PSI-LHCI structures suggest that Lhca1 is the main point of delivering the energy harvested by the antenna to the core. To identify the excitation energy pathways in Lhca1, we developed a structure-based exciton model based on the simultaneous fit of the low-temperature absorption, linear dichroism, and fluorescence spectra of wild-type Lhca1 and two mutants, lacking chlorophylls contributing to the long-wavelength region of the absorption. The model enables us to define the locations of the lowest energy pigments in Lhca1 and estimate pathways and timescales of energy transfer within the complex and to the PSI core. We found that Lhca1 has a particular energy landscape with an unusual (compared to Lhca4, LHCII, and CP29) configuration of the low-energy states. Remarkably, these states are located near the core, facilitating direct energy transfer to it. Moreover, the low-energy states of Lhca1 are also coupled to the red-most state (red forms) of the neighboring Lhca4 antenna, providing a pathway for effective excitation energy transfer from Lhca4 to the core.
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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.
| | - Roberta Croce
- Department of Physics and Astronomy, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands
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4
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Braver Y, Valkunas L, Gelzinis A. Stark absorption and Stark fluorescence spectroscopies: Theory and simulations. J Chem Phys 2021; 155:244101. [PMID: 34972359 DOI: 10.1063/5.0073962] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Stark spectroscopy experiments are widely used to study the properties of molecular systems, particularly those containing charge-transfer (CT) states. However, due to the small transition dipole moments and large static dipole moments of the CT states, the standard interpretation of the Stark absorption and Stark fluorescence spectra in terms of the Liptay model may be inadequate. In this work, we provide a theoretical framework for calculations of Stark absorption and Stark fluorescence spectra and propose new methods of simulations that are based on the quantum-classical theory. In particular, we use the forward-backward trajectory solution and a variant of the Poisson bracket mapping equation, which have been recently adapted for the calculation of conventional (field-free) absorption and fluorescence spectra. For comparison, we also apply the recently proposed complex time-dependent Redfield theory, while exact results are obtained using the hierarchical equations of motion approach. We show that the quantum-classical methods produce accurate results for a wide range of systems, including those containing CT states. The CT states contribute significantly to the Stark spectra, and the standard Liptay formalism is shown to be inapplicable for the analysis of spectroscopic data in those cases. We demonstrate that states with large static dipole moments may cause a pronounced change in the total fluorescence yield of the system in the presence of an external electric field. This effect is correctly captured by the quantum-classical methods, which should therefore prove useful for further studies of Stark spectra of real molecular systems. As an example, we calculate the Stark spectra for the Fenna-Matthews-Olson complex of green sulfur bacteria.
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Affiliation(s)
- Yakov Braver
- Faculty of Physics, Institute of Chemical Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania and Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| | - Leonas Valkunas
- Faculty of Physics, Institute of Chemical Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania and Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
| | - Andrius Gelzinis
- Faculty of Physics, Institute of Chemical Physics, Vilnius University, Saulėtekio Ave. 9-III, LT-10222 Vilnius, Lithuania and Department of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio Ave. 3, LT-10257 Vilnius, Lithuania
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5
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Cho KH, Rhee YM. Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes. Phys Chem Chem Phys 2021; 23:26623-26639. [PMID: 34842245 DOI: 10.1039/d1cp04615b] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.
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Affiliation(s)
- Kwang Hyun Cho
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea.
| | - Young Min Rhee
- Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea.
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Braver Y, Valkunas L, Gelzinis A. Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications. J Chem Theory Comput 2021; 17:7157-7168. [PMID: 34618457 PMCID: PMC8719324 DOI: 10.1021/acs.jctc.1c00777] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Indexed: 01/20/2023]
Abstract
Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum-classical theory─it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum-classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum-classical Liouville equation, namely, the forward-backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna-Matthews-Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [Gelzinis, A.; J. Chem. Phys. 2020, 152, 051103] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.
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Affiliation(s)
- Yakov Braver
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| | - Leonas Valkunas
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
| | - Andrius Gelzinis
- Institute
of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio Avenue 9-III, LT-10222 Vilnius, Lithuania
- Department
of Molecular Compound Physics, Center for
Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10257 Vilnius, Lithuania
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7
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Osella S. Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead? NANOMATERIALS 2021; 11:nano11020299. [PMID: 33498961 PMCID: PMC7911014 DOI: 10.3390/nano11020299] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Revised: 01/19/2021] [Accepted: 01/20/2021] [Indexed: 12/13/2022]
Abstract
A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.
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Affiliation(s)
- Silvio Osella
- Chemical and Biological Systems Simulation Lab, Center of New Technologies, University of Warsaw, Banacha 2C, 02-097 Warsaw, Poland
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8
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Cupellini L, Lipparini F, Cao J. Absorption and Circular Dichroism Spectra of Molecular Aggregates With the Full Cumulant Expansion. J Phys Chem B 2020; 124:8610-8617. [PMID: 32901476 PMCID: PMC7901647 DOI: 10.1021/acs.jpcb.0c05180] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
The exciton Hamiltonian of multichromophoric aggregates can be probed by spectroscopic
techniques such as linear absorption and circular dichroism. To compare calculated
Hamiltonians to experiments, a lineshape theory is needed, which takes into account the
coupling of the excitons with inter- and intramolecular vibrations. This coupling is
normally introduced in a perturbative way through the cumulant expansion formalism and
further approximated by assuming a Markovian exciton dynamics, for example with the
modified Redfield theory. Here, we present the implementation of the full cumulant
expansion (FCE) formalism (142, 2015, 09410625747060) to
efficiently compute absorption and circular dichroism spectra of molecular aggregates
beyond the Markov approximation, without restrictions on the form of
exciton–phonon coupling. By employing the LH2 system of purple bacteria as a
challenging test case, we compare the FCE lineshapes with the Markovian lineshapes
obtained with the modified Redfield theory, showing that the latter presents a less
satisfying agreement with experiments. The FCE approach instead accurately describes the
lineshapes, especially in the vibronic sideband of the B800 peak. We envision that the
FCE approach will become a valuable tool for accurately comparing model exciton
Hamiltonians with optical spectroscopy experiments.
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Affiliation(s)
- Lorenzo Cupellini
- Dipartimento di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Filippo Lipparini
- Dipartimento di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Jianshu Cao
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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9
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10
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Tao MJ, Zhang NN, Wen PY, Deng FG, Ai Q, Long GL. Coherent and incoherent theories for photosynthetic energy transfer. Sci Bull (Beijing) 2020; 65:318-328. [PMID: 36659097 DOI: 10.1016/j.scib.2019.12.009] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2019] [Revised: 10/28/2019] [Accepted: 11/21/2019] [Indexed: 01/21/2023]
Abstract
There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Förster theory and modified Redfield theory (MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion (HEOM), quantum path integral, coherent modified Redfield theory (CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer (EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.
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Affiliation(s)
- Ming-Jie Tao
- Department of Physics, Tsinghua University, Beijing 100084, China; Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Na-Na Zhang
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Peng-Yu Wen
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
| | - Fu-Guo Deng
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China; NAAM-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
| | - Qing Ai
- Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China.
| | - Gui-Lu Long
- Department of Physics, Tsinghua University, Beijing 100084, China.
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11
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Segatta F, Cupellini L, Garavelli M, Mennucci B. Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems. Chem Rev 2019; 119:9361-9380. [PMID: 31276384 PMCID: PMC6716121 DOI: 10.1021/acs.chemrev.9b00135] [Citation(s) in RCA: 64] [Impact Index Per Article: 12.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2019] [Indexed: 01/21/2023]
Abstract
Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.
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Affiliation(s)
- Francesco Segatta
- Dipartimento
di Chimica Industriale “Toso Montanari” University of Bologna, Viale del Risorgimento 4, 40136 Bologna, Italy
| | - Lorenzo Cupellini
- Dipartimento
di Chimica e Chimica Industriale, University
of Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Marco Garavelli
- Dipartimento
di Chimica Industriale “Toso Montanari” University of Bologna, Viale del Risorgimento 4, 40136 Bologna, Italy
| | - Benedetta Mennucci
- Dipartimento
di Chimica e Chimica Industriale, University
of Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
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12
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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
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13
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Cupellini L, Bondanza M, Nottoli M, Mennucci B. Successes & challenges in the atomistic modeling of light-harvesting and its photoregulation. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2019; 1861:148049. [PMID: 31386831 DOI: 10.1016/j.bbabio.2019.07.004] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2019] [Revised: 07/10/2019] [Accepted: 07/15/2019] [Indexed: 12/21/2022]
Abstract
Light-harvesting is a crucial step of photosynthesis. Its mechanisms and related energetics have been revealed by a combination of experimental investigations and theoretical modeling. The success of theoretical modeling is largely due to the application of atomistic descriptions combining quantum chemistry, classical models and molecular dynamics techniques. Besides the important achievements obtained so far, a complete and quantitative understanding of how the many different light-harvesting complexes exploit their structural specificity is still missing. Moreover, many questions remain unanswered regarding the mechanisms through which light-harvesting is regulated in response to variable light conditions. Here we show that, in both fields, a major role will be played once more by atomistic descriptions, possibly generalized to tackle the numerous time and space scales on which the regulation takes place: going from the ultrafast electronic excitation of the multichromophoric aggregate, through the subsequent conformational changes in the embedding protein, up to the interaction between proteins.
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Affiliation(s)
- Lorenzo Cupellini
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Mattia Bondanza
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Michele Nottoli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy
| | - Benedetta Mennucci
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via G. Moruzzi 13, Pisa 56124, Italy.
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14
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Zazubovich V, Jankowiak R. How Well Does the Hole-Burning Action Spectrum Represent the Site-Distribution Function of the Lowest-Energy State in Photosynthetic Pigment-Protein Complexes? J Phys Chem B 2019; 123:6007-6013. [PMID: 31265294 DOI: 10.1021/acs.jpcb.9b03806] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
For the first time, we combined Monte Carlo and nonphotochemical hole burning (NPHB) master equation approaches to allow for ultrahigh-resolution (<0.005 cm-1, smaller than the typical homogeneous line widths at 5 K) simulations of the NPHB spectra of dimers and trimers of interacting pigments. These simulations reveal significant differences between the zero-phonon hole (ZPH) action spectrum and the site-distribution function (SDF) of the lowest-energy state. The NPHB of the lowest-energy pigment, following the excitation energy transfer (EET) from the higher-energy pigments which are excited directly, results in the shifts of all excited states. These shifts affect the ZPH action spectra and EET times derived from the widths of the spectral holes burned in the donor-dominated regions. The effect is present for a broad variety of realistic antihole functions, and it is maximal at relatively low values of interpigment coupling (V ≤ 5 cm-1) where the use of the Förster approximation is justified. These findings need to be considered in interpreting various optical spectra of photosynthetic pigment-protein complexes for which SDFs (describing the inhomogeneous broadening) are often obtained directly from the ZPH action spectra. Water-soluble chlorophyll-binding protein (WSCP) was considered as an example.
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Affiliation(s)
- Valter Zazubovich
- Department of Physics , Concordia University , 7141 Sherbrooke Street West , Montreal H4B 1R6 , Quebec , Canada
| | - Ryszard Jankowiak
- Department of Chemistry , Kansas State University , Manhattan , Kansas 66506 , United States
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15
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Cupellini L, Corbella M, Mennucci B, Curutchet C. Electronic energy transfer in biomacromolecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2018. [DOI: 10.1002/wcms.1392] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Lorenzo Cupellini
- Dipartimento di Chimica e Chimica Industriale University of Pisa Pisa Italy
| | - Marina Corbella
- Departament de Farmàcia i Tecnologia Farmacèutica i Fisicoquímica and Institut de Química Teòrica i Computacional (IQTC‐UB), Facultat de Farmàcia i Ciències de l'Alimentació Universitat de Barcelona Barcelona Spain
| | - Benedetta Mennucci
- Dipartimento di Chimica e Chimica Industriale University of Pisa Pisa Italy
| | - Carles Curutchet
- Departament de Farmàcia i Tecnologia Farmacèutica i Fisicoquímica and Institut de Química Teòrica i Computacional (IQTC‐UB), Facultat de Farmàcia i Ciències de l'Alimentació Universitat de Barcelona Barcelona Spain
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16
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Novoderezhkin VI, Croce R, van Grondelle R. Dynamics of the mixed exciton and charge-transfer states in light-harvesting complex Lhca4: Hierarchical equation approach. BIOCHIMICA ET BIOPHYSICA ACTA-BIOENERGETICS 2018; 1859:655-665. [PMID: 29981722 DOI: 10.1016/j.bbabio.2018.06.016] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Revised: 06/05/2018] [Accepted: 06/29/2018] [Indexed: 11/19/2022]
Abstract
We model the energy transfer dynamics in the Lhca4 peripheral antenna of photosystem I from higher plants. Equilibration between the bulk exciton levels of the antenna and the red-shifted charge-transfer (CT) states is described using the numerically inexpensive Redfield-Förster approach and exact hierarchical equation (HEOM) method. We propose a compartmentalization scheme allowing a quantitatively correct description of the dynamics with the Redfield-Förster theory, including the exciton-type relaxation within strongly coupled compartments and hopping-type migration between them. The Redfield-Förster method gives the kinetics close to the HEOM solution when treating the CT state as dynamically localized. We also demonstrate that the excited states strongly coupled with the CT should be considered as localized as well.
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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
| | - Roberta Croce
- 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.
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17
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Novoderezhkin VI, Romero E, Prior J, van Grondelle R. Exciton-vibrational resonance and dynamics of charge separation in the photosystem II reaction center. Phys Chem Chem Phys 2018; 19:5195-5208. [PMID: 28149991 DOI: 10.1039/c6cp07308e] [Citation(s) in RCA: 47] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
The dynamics of charge separation in the photosystem II reaction center (PSII-RC) in the presence of intramolecular vibrations with their frequency matching the energy gap between the exciton state acting as the primary electron donor and the first charge-transfer (CT) state are investigated. A reduced PSII-RC 4-state model explicitly including a CT state is analyzed within Redfield relaxation theory in the multidimensional exciton-vibrational (vibronic) basis. This model is used to study coherent energy/electron transfers and their spectral signatures obtained by two-dimensional electronic spectroscopy (2DES). Modeling of the time-resolved 2D frequency maps obtained by wavelet analysis reveals the origins of the coherences which produce the observed oscillating features in 2DES and allows comparing the lifetimes of the coherences. The results suggest faster excitonic decoherence as compared with longer-lived vibronic oscillations. The emerging picture of the dynamics unravels the role of resonant vibrations in sustaining the effective energy conversion in the PSII-RC. We demonstrate that the mixing of the exciton and CT states promoted by a resonant vibrational quantum allows faster penetration of excitation energy into the CT with subsequent dynamic localization at the bottom of the CT potential induced by the remaining non-resonant nuclear modes. The degree of vibration-assisted mixing and, correspondingly, the rate of primary charge separation, increases significantly in the case of electron-vibrational resonance. The observed features illustrate the principles of quantum design of the photosynthetic unit. These principles are connected with the phenomenon of coherent mixing within vibronic eigenstates, increasing the effectiveness of charge separation not only upon coherent and impulsive laser excitation utilized in the 2DES experiment, but also under natural conditions under non-coherent non-impulsive solar light illumination.
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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.
| | - Elisabet Romero
- Department of Biophysics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Javier Prior
- Departamento de Física Aplicada, Universidad Politécnica de Cartagena, Cartagena 30202, Spain
| | - Rienk van Grondelle
- Department of Biophysics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
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18
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Malý P, Gardiner AT, Cogdell RJ, van Grondelle R, Mančal T. Robust light harvesting by a noisy antenna. Phys Chem Chem Phys 2018; 20:4360-4372. [PMID: 29368769 PMCID: PMC5901068 DOI: 10.1039/c7cp06139k] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Accepted: 12/13/2017] [Indexed: 01/26/2023]
Abstract
Photosynthetic light harvesting can be very efficient in solar energy conversion while taking place in a highly disordered and noisy physiological environment. This efficiency is achieved by the ultrafast speed of the primary photosynthetic processes, which is enabled by a delicate interplay of quantum effects, thermodynamics and environmental noise. The primary processes take place in light-harvesting antennas built from pigments bound to a fluctuating protein scaffold. Here, we employ ultrafast single-molecule spectroscopy to follow fluctuations of the femtosecond energy transfer times in individual LH2 antenna complexes of purple bacteria. By combining single molecule results with ensemble spectroscopy through a unified theoretical description of both, we show how the protein fluctuations alter the excitation energy transfer dynamics. We find that from the thirteen orders of magnitude of possible timescales from picoseconds to minutes, the relevant fluctuations occur predominantly on a biological timescale of seconds, i.e. in the domain of slow protein motion. The measured spectra and dynamics can be explained by the protein modulating pigment excitation energies only. Moreover, we find that the small spread of pigment mean energies allows for excitation delocalization between the coupled pigments to survive. These unique features provide fast energy transport even in the presence of disorder. We conclude that this is the mechanism that enables LH2 to operate as a robust light-harvester, in spite of its intrinsically noisy biological environment.
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Affiliation(s)
- Pavel Malý
- Department of Biophysics , Faculty of Sciences , Vrije Universiteit Amsterdam , De Boeleaan 1081 , 1081HV Amsterdam , The Netherlands .
- Faculty of Mathematics and Physics , Charles University , Ke Karlovu 3 , 121 16 Prague , Czech Republic
| | - Alastair T. Gardiner
- Institute of Molecular , Cellular and Systems Biology , College of Medical , Veterinary and Life Sciences , University of Glasgow , Glasgow G128QQ , UK
| | - Richard J. Cogdell
- Institute of Molecular , Cellular and Systems Biology , College of Medical , Veterinary and Life Sciences , University of Glasgow , Glasgow G128QQ , UK
| | - Rienk van Grondelle
- Department of Biophysics , Faculty of Sciences , Vrije Universiteit Amsterdam , De Boeleaan 1081 , 1081HV Amsterdam , The Netherlands .
| | - Tomáš Mančal
- Faculty of Mathematics and Physics , Charles University , Ke Karlovu 3 , 121 16 Prague , Czech Republic
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19
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Segatta F, Cupellini L, Jurinovich S, Mukamel S, Dapor M, Taioli S, Garavelli M, Mennucci B. A Quantum Chemical Interpretation of Two-Dimensional Electronic Spectroscopy of Light-Harvesting Complexes. J Am Chem Soc 2017; 139:7558-7567. [DOI: 10.1021/jacs.7b02130] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Francesco Segatta
- European Center for Theoretical Studies in Nuclear Physics and Related Areas (ECT*-FBK) and Trento Institute for Fundamental Physics and Applications (TIFPA-INFN), 38123 Trento, Italy
- Dipartimento
di Chimica Industriale “Toso Montanari”, University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Lorenzo Cupellini
- Dipartimento
di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi
13, 56124 Pisa, Italy
| | - Sandro Jurinovich
- Dipartimento
di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi
13, 56124 Pisa, Italy
| | - Shaul Mukamel
- Department
of Chemistry, University of California, Irvine, California 92697-2025, United States
| | - Maurizio Dapor
- European Center for Theoretical Studies in Nuclear Physics and Related Areas (ECT*-FBK) and Trento Institute for Fundamental Physics and Applications (TIFPA-INFN), 38123 Trento, Italy
| | - Simone Taioli
- European Center for Theoretical Studies in Nuclear Physics and Related Areas (ECT*-FBK) and Trento Institute for Fundamental Physics and Applications (TIFPA-INFN), 38123 Trento, Italy
- Faculty
of Mathematics and Physics, Charles University, Prague 116 36, Czech Republic
| | - Marco Garavelli
- Dipartimento
di Chimica Industriale “Toso Montanari”, University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Benedetta Mennucci
- Dipartimento
di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi
13, 56124 Pisa, Italy
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20
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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.
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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
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21
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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.
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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
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22
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23
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Novoderezhkin VI, Croce R, Wahadoszamen M, Polukhina I, Romero E, van Grondelle R. Mixing of exciton and charge-transfer states in light-harvesting complex Lhca4. Phys Chem Chem Phys 2016; 18:19368-77. [DOI: 10.1039/c6cp02225a] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Structure-based modeling of spectra of the wild-type Lhca4 and NH mutant enables us to build the exciton model of the complex that includes a charge-transfer state mixed with the excited-state manifold.
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Affiliation(s)
| | - Roberta Croce
- Department of Biophysics
- Faculty of Sciences
- VU University Amsterdam
- 1081 HV Amsterdam
- The Netherlands
| | - Md. Wahadoszamen
- Department of Biophysics
- Faculty of Sciences
- VU University Amsterdam
- 1081 HV Amsterdam
- The Netherlands
| | - Iryna Polukhina
- Department of Biophysics
- Faculty of Sciences
- VU University Amsterdam
- 1081 HV Amsterdam
- The Netherlands
| | - Elisabet Romero
- Department of Biophysics
- Faculty of Sciences
- VU University Amsterdam
- 1081 HV Amsterdam
- The Netherlands
| | - Rienk van Grondelle
- Department of Biophysics
- Faculty of Sciences
- VU University Amsterdam
- 1081 HV Amsterdam
- The Netherlands
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24
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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.
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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
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25
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26
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Dinh TC, Renger T. Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions. J Chem Phys 2015; 142:034104. [DOI: 10.1063/1.4904928] [Citation(s) in RCA: 48] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Thanh-Chung Dinh
- Institut für Theoretische Physik, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria
| | - Thomas Renger
- Institut für Theoretische Physik, Johannes Kepler University Linz, Altenberger Str. 69, 4040 Linz, Austria
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27
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Seibt J, Pullerits T. Combined treatment of relaxation and fluctuation dynamics in the calculation of two-dimensional electronic spectra. J Chem Phys 2014; 141:114106. [DOI: 10.1063/1.4895401] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Joachim Seibt
- Department of Chemical Physics, Lund University, Box 124, SE-2100 Lund, Sweden
| | - Tõnu Pullerits
- Department of Chemical Physics, Lund University, Box 124, SE-2100 Lund, Sweden
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28
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Kreisbeck C, Kramer T, Aspuru-Guzik A. Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes. J Chem Theory Comput 2014; 10:4045-54. [DOI: 10.1021/ct500629s] [Citation(s) in RCA: 88] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christoph Kreisbeck
- Institut
für Physik, Humboldt-Universität zu Berlin, Newtonstr.
15, 12489 Berlin, Germany
| | - Tobias Kramer
- Mads
Clausen Institute, University of Southern Denmark, Alsion 2, 6400 Sønderborg, Denmark
| | - Alán Aspuru-Guzik
- Department
of Chemistry and Chemical Biology, Harvard University, 12 Oxford
Street, Cambridge, Massachusetts 02138, United States
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29
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Rancova O, Abramavicius D. Static and Dynamic Disorder in Bacterial Light-Harvesting Complex LH2: A 2DES Simulation Study. J Phys Chem B 2014; 118:7533-7540. [DOI: 10.1021/jp5043156] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Olga Rancova
- Department of Theoretical
Physics, Faculty of Physics, Vilnius University, Sauletekio av. 9 III bld., LT-10222 Vilnius, Lithuania
| | - Darius Abramavicius
- Department of Theoretical
Physics, Faculty of Physics, Vilnius University, Sauletekio av. 9 III bld., LT-10222 Vilnius, Lithuania
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30
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List NH, Curutchet C, Knecht S, Mennucci B, Kongsted J. Toward Reliable Prediction of the Energy Ladder in Multichromophoric Systems: A Benchmark Study on the FMO Light-Harvesting Complex. J Chem Theory Comput 2013; 9:4928-38. [DOI: 10.1021/ct400560m] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Nanna Holmgaard List
- Department
of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Carles Curutchet
- Departament
de Fisicoquímica, Facultat de Farmàcia, Universitat de Barcelona, Av. Joan XXIII s/n, 08028 Barcelona, Spain
| | - Stefan Knecht
- Department
of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
- Laboratory
of Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Straße 10, 8093 Zürich, Switzerland
| | - Benedetta Mennucci
- Dipartimento
di Chimica e Chimica Industriale, University of Pisa, Via Risorgimento
35, 56126 Pisa, Italy
| | - Jacob Kongsted
- Department
of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
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