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The Importance of Excitation and Trapping Conditions in Photosynthetic Environment-assisted Energy Transport Roberto de J. Leon-Montiel, Ivan Kassal, and Juan P. Torres J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp505179h • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014
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The Journal of Physical Chemistry
The Importance of Excitation and Trapping Conditions in Photosynthetic Environment-Assisted Energy Transport Roberto de J. Le´on-Montiel,∗,† Ivan Kassal,‡ and Juan P. Torres†,¶ ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain, Centre for Engineered Quantum Systems, Centre for Quantum Computation and Communication Technology, and School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia, and Department of Signal Theory and Communications, Campus Nord D3, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain E-mail:
[email protected] ∗
To whom correspondence should be addressed ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain ‡ Centre for Engineered Quantum Systems, Centre for Quantum Computation and Communication Technology, and School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072, Australia ¶ Department of Signal Theory and Communications, Campus Nord D3, Universitat Politecnica de Catalunya, 08034 Barcelona, Spain †
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Abstract It has been argued that excitonic energy transport in photosynthetic complexes is efficient because of a balance between coherent evolution and decoherence, a phenomenon called environment-assisted quantum transport (ENAQT). Studies of ENAQT have usually assumed that the excitation is initially localized on a particular chromophore, and that it is transferred to a reaction center through a similarly localized trap. However, these assumptions are not physically accurate. We show that more realistic models of excitation and trapping can lead to very different predictions about the importance of ENAQT. In particular, although ENAQT is a robust effect if one assumes a localized trap, its effect is negligible if the trapping is more accurately modeled as F¨ orster transfer to a reaction center. Our results call into question the suggested role of ENAQT in the photosynthetic process of green sulfur bacteria and highlight the subtleties associated with drawing lessons for designing biomimetic light-harvesting complexes.
Keywords: Excitonic energy transfer, environment-assisted quantum transport, incoherent photoexcitation, F¨orster resonant energy transfer
INTRODUCTION Mechanisms of energy transport in photosynthetic systems 1 have attracted renewed attention 2–4 in recent years because of the experimental observation of long-lived coherences in bacterial and algal light-harvesting complexes. 5–8 Indeed, it has been suggested that coherent quantum effects may play an important role in energy transport in photosynthetic complexes. 9–15 In particular, it has been proposed that the high efficiency of photosynthetic energy transport arises out of the interplay between coherent evolution and environmentally induced 2
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noise, an effect dubbed environment-assisted quantum transport (ENAQT) 16 or dephasingassisted energy transport. 17,18 In coherent systems, disorder can cause localization and thus inhibit transfer. In those cases, ENAQT can be understood as the suppression of coherent localization through noise, which helps the excitation move through the disordered photosynthetic complex and toward its destination, the reaction center (RC), where the energy is used to power the first chemical steps of photosynthesis. Although it has been shown that ENAQT can occur in a wide variety of quantum 16–22 and classical 23–25 transport systems, these findings are usually based on specific assumptions that have been challenged. In particular, in most models, it is assumed that the system starts out with only one pigment molecule initially excited and that only one pigment molecule (the “trap”) is responsible for the ultimate exciton transfer to the RC. These assumptions might be incorrect: unless the system is so disordered that each eigenstate is effectively localized on one site, both the initial state and the trap state will be at least partially delocalized. Here we examine ENAQT in situations where both the excitation and the trapping are treated in more physically realistic ways. Most importantly, we show that the description of the coupling to the RC significantly influences the magnitude and, consequently, the importance of the predicted ENAQT. If the trap is localized at a particular site, as it has been assumed previously, we show that ENAQT persists under almost all excitation conditions, including excitation by incoherent light (as predicted in Ref. 15 ) as well as excitation transfer from an antenna complex. However, ENAQT is either absent or negligible if the coupling to the RC is treated as F¨orster transfer (as we argue it should be), meaning that it is unlikely to be important for influencing the biological function of light-harvesting complexes.
THEORETICAL METHODS We consider the dynamics of excitons in a network of N chromophores (or sites). Under the usual weak illumination, it is rare to find more than one exciton in a single complex.
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Therefore, we restrict ourselves to the single-exciton manifold, with state |ii indicating that the exciton is on site i. The system is then described by a tight-binding Hamiltonian (see May and K¨ uhn 26 , sec. 9.2)
Hs =
N X i=1
εi |ii hi| +
N X i
