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Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

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Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford, OX1 3QZ, United Kingdom
Quantum Chemistry Laboratory, Department of Chemistry, Kyoto University, 606-8502, Kyoto, Japan
School of Materials Science and Engineering, Nanyang Technological University, Block N4.1, Nanyang Avenue, Singapore 639798
*E-mail: [email protected] (D. M. Wilkins).
*E-mail: [email protected] (N. S. Dattani).
Cite this: J. Chem. Theory Comput. 2015, 11, 7, 3411–3419
Publication Date (Web):March 4, 2015
https://doi.org/10.1021/ct501066k
Copyright © 2015 American Chemical Society

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    Abstract

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    We develop and present an improvement to the conventional technique for solving the Hierarchical Equations of Motion (HEOM), which can reduce the memory cost by up to 75% while retaining the same (or even better) convergence rate and accuracy. This allows for a full calculation of the population dynamics of the 24-site FMO trimer for long time scales with very little effort, and we present the first fully converged, exact results for the 7-site subsystem of the monomer, and for the full 24-site trimer. We then show where our exact 7-site results deviate from the approximation of Ishizaki and Fleming [A. Ishizaki and G. R. Fleming, Proc. Natl. Acad. Sci. U.S.A., 2009, 106, 17255]. Our exact results are then compared to calculations using the incoherent Förster theory, and it is found that the time scale of energy transfer is roughly the same, regardless of whether or not coherence is considered. This means that coherence is not likely to improve the efficiency of the transfer. In fact, the incoherent theory often tends to overpredict the rates of energy transfer, suggesting that, in some cases, quantum coherence may actually slow the photosynthetic process.

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    Summary of run-time and memory costs for our HEOM calculations, and Padé parameters used to test convergence. This material is available free of charge via the Internet at http://pubs.acs.org.

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