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Structure-Based Calculation of Pigment–Protein and Excitonic Pigment–Pigment Coupling in Photosynthetic Light-Harvesting Complexes

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The Biophysics of Photosynthesis

Part of the book series: Biophysics for the Life Sciences ((BIOPHYS,volume 11))

Abstract

In photosynthesis, specialized pigment–protein assemblies, termed light-harvesting complexes (LHCs) or antenna proteins, absorb solar photons and deliver the excitation energy by exciton transfer (XT) to the photochemically active centers. To understand this process, it has to be linked to molecular structures and spectroscopic properties of LHCs. In this chapter, we show how this link is provided by theoretical modeling. We first describe what excitons are and how the mechanism of XT is influenced by the coupling of excited states to molecular vibrations. This description defines key parameters that are important for a modeling of XT: (1) site energies, (2) excitonic couplings, and (3) exciton-vibrational coupling constants. Next, we discuss how these parameters can be calculated from a crystal structure of the LHC within the framework of an electrostatic model of intermolecular interactions. Finally, we show applications to the Fenna–Matthews–Olson (FMO) protein of green sulfur bacteria and the major LHC of higher plants (LHCII) to illustrate how this approach works and what has already been learned from it.

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Notes

  1. 1.

    In Eq. (1.1), spin-orbit coupling and other terms related to spin are neglected.

  2. 2.

    This coupling is characterized by the coupling constant g ξ, which is defined as half the displacement of the minima of the two PES for reasons that will become evident below. The negative sign is merely a convention that allows a positive g ξ (as, e.g., in Eqs. (1.12) and (1.13) below) to shift the excited state PES to the right with respect to the ground state PES as in Fig. 1.3a.

  3. 3.

    The Franck–Condon principle states that during the time of an electronic transition, the nuclear motion can be neglected, so that the nuclei are practically “frozen” during the process of light excitation of the molecule. In a plot of the PESs, this means that the transition occurs at constant Q (valid for all Q). Hence, it is termed a “vertical” transition.

  4. 4.

    Actually, each electron occupies one spin orbital. In the restricted closed-shell Hartree–Fock approach, two of these spin orbitals with different spin functions have the same spatial wave-function, so that two electrons occupy the same spatial orbital [19]. The energy levels depicted in usual MO schemes (as for example in Fig. 1.3b) refer to these spatial orbitals.

  5. 5.

    In fact, it is the neglect of electron exchange between the pigments that justifies the use of the term “Frenkel exciton.”

  6. 6.

    We have to be careful, however, if B is another pigment. Below, we shall focus on the S0 → S1 transitions of A (a = 0,1). Then, we have to exclude the S0 → S1 transitions of the other pigments. This is no restriction, since the couplings between these transitions are treated explicitly in the exciton formalism and do not require a perturbative approximation; see [30].

  7. 7.

    The term “van der Waals interaction” is sometimes used to subsume inductive and dispersive interactions.

  8. 8.

    Readers interested in alternative approaches that go beyond this level will find information in Renger and Müh [30] and the references therein.

  9. 9.

    We note that there are other types of light-harvesting complexes that contain more flexible pigments (e.g., bilins, see [41]). In these cases, the contribution from conformational variations may become dominant.

  10. 10.

    A systematic procedure for finding these positions is described in [50].

  11. 11.

    We define the effective dipole strength as vacuum dipole strength divided by εeff.

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Acknowledgement

Financial support by the Austrian Science Fund (FWF): P 24774-N27 is gratefully acknowledged.

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Authors and Affiliations

  1. Institute for Theoretical Physics, Johannes Kepler University Linz, Altenberger Strasse 69, 4040, Linz, Austria

    Frank Müh Ph.D. & Thomas Renger Ph.D.

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  1. Frank Müh Ph.D.
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Correspondence to Frank Müh Ph.D. .

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Editors and Affiliations

  1. Dept of Biochemistry & Molecular Biology, Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania, USA

    John Golbeck

  2. Dept of Chemistry, Brock University, St. Catharines, Ontario, Canada

    Art van der Est

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Müh, F., Renger, T. (2014). Structure-Based Calculation of Pigment–Protein and Excitonic Pigment–Pigment Coupling in Photosynthetic Light-Harvesting Complexes. In: Golbeck, J., van der Est, A. (eds) The Biophysics of Photosynthesis. Biophysics for the Life Sciences, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1148-6_1

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