Delocalized excitons in natural light-harvesting complexes

Natural organisms such as photosynthetic bacteria, algae, and plants employ complex molecular machinery to convert solar energy into biochemical fuel. An important common feature shared by most of these photosynthetic organisms is that they capture photons in the form of excitons typically delocalized over a few to tens of pigment molecules embedded in protein environments of light-harvesting complexes (LHCs). Delocalized excitons created in such LHCs remain well protected despite being swayed by environmental fluctuations and are delivered successfully to their destinations over 100 nanometer distances in about 100 ps times. Decades of experimental and theoretical investigation have produced a large body of information offering insight into major structural, energetic, and dynamical features contributing to LHCs’ extraordinary capability to harness photons using delocalized excitons. The objective of this review is (i) to provide a comprehensive account of major theoretical, computational, and spectroscopic advances that have contributed to this body of knowledge, and (ii) to clarify the issues concerning the role of delocalized excitons in achieving efficient energy transport mechanisms. The focus of this review is on three representative systems: the Fenna-Matthews-Olson complex of green sulfur bacteria, the light-harvesting 2 complex of purple bacteria, and phycobiliproteins of cryptophyte algae. Although we offer a more in-depth and detailed description of theoretical and computational aspects, major experimental results and their implications are also assessed in the context of achieving excellent light-harvesting functionality. Future theoretical and experimental challenges to be addressed in gaining a better understanding and utilization of delocalized excitons are also discussed.

Figure 1

(a) A simple evolutionary tree of photosynthetic organisms. From Gregory D. Scholes. (b) Major light-harvesting antennas and their spectral regions. Adapted from [286].

Figure 2

A schematic of three domains constituting photosynthesis, performing light harvesting (LH), charge separation (CS), and biochemical reaction (BR). Their respective time scales are denoted as ${\tau }_{\mathrm{LH}}$, ${\tau }_{\mathrm{CS}}$, and ${\tau }_{\mathrm{BR}}$. The length scales of these domains are denoted as $l_{\mathrm{LH}}$, $l_{\mathrm{CS}}$, and $l_{\mathrm{BR}}$, respectively. The ranges of energy changes that occur in these domains are, respectively, denoted as $\mathrm{\Delta }{E}_{\mathrm{LH}}$, $\mathrm{\Delta }{E}_{\mathrm{CS}}$, and $\mathrm{\Delta }{E}_{\mathrm{BR}}$.

Figure 3

(a) The FMO trimer complex. (b) View of the eight BChls of the monomer unit A (only the heavy atoms of the BChls ring are shown). (c) Chemical structure of the BChl pigment.

Figure 4

(a) Side view of the pigment arrangement in the LH2 complex: $\alpha$ and $\beta$ BChl molecules of the B850 ring constitute the upper circular aggregate whereas $\gamma$ BChl molecules of B800 form the lower circular aggregate. The carotenoids are also reported in purple. (b) Side view of the LH2 complex within its membrane from a snapshot of an all-atomistic molecular dynamics (MD) simulation (the carotenoids are not shown). (c) Geometric representation of the arrangement of the BChl molecules in the B800 and B850 rings. Here a reflection of 180° has been used for clarity’s sake leading the B800 ring above the B850 ring. Adapted from [213].

Figure 5

(a) PBP complex. (b) View of the eight bilins (only the heavy atoms are shown) present in PE545 (black) and PC645 (orange or gray). (c) Chemical structure of the different bilins present in PE545 (PEB, DBV) and PC645 (PCB, DBV, MBV). The ellipses indicate the double bond which is used to create the second cysteine bond to the protein in PE545 (PEB) and PC645 (DBV).

Figure 6

Experimental and theoretical absorption spectra of the FMO complex at three different temperatures. The two simulation data in the middle and right panels show that improvement in the bath spectral density brings qualitative features of theoretical line shapes closer to those of experimental ones. Adapted from [265].

Figure 7

Single LH2 complex fluorescence-excitation spectra (solid black lines) and emission spectra [dashed blue and red lines (dashed gray)]). The corresponding ensemble line shapes are shown at the top. The left panel is for LH2 complexes with sharp emission line shapes, and the right panel is for LH2 complexes with broad emission line shapes. A detailed experimental method and a more comprehensive set of data are available by [176]. From Jürgen Köhler.

Figure 8

Spectroscopic data for PC645. (a) Absorption line shapes at 77 K (dashed black line) and ambient temperature (solid black line), and fluorescence line shape [solid red line (gray)] at ambient temperature. (b) Vibrational frequencies extracted from transient absorption by Fourier transform at three different emission frequencies. (c) 2DES taken at 295 K. $t_2$ refers to population time. (d) 2DES taken at 77 K. Adapted from [71].

Figure 9

Site energies (eV) of the eight BChls computed on the crystal structure with three different models: the full model (full line and circles) includes all BChl atoms, the truncated model (dotted line and triangles) does not include the atoms of the phythyl chain, and the tail@MMPol model (diamonds) describes the atoms of the phythyl chain as MMPol sites. Inset: Structure of BChl 1 for which the chain is folded in a conformation capable of interacting with the porphyrin ring.

Figure 10

Site energies (eV) for the 1–7 BChls computed on the crystal structure including the environment effects at the PCM (dotted line) and MMPol (full line) levels. A third (me)QM/PCM model combining PCM with a QM description of the interacting residues is also shown (dashed line).

Figure 11

Upper panel: The crystal structure used in the static model (left) and examples of configurations extracted from MD used in the dynamic model (right) of the LH2 complex. Lower panel: (left) measured CD spectra at 77 K (dotted line) and room-temperature (full line) and (right) calculated TD-DFT/MMPol spectra using the static model (dotted line) and the dynamic model (full line).

Figure 12

Effective dielectric constant corresponding to each pair (${\epsilon }_{ik}$) reported as a function of the interchromophore distance: circles refer to the average QM/MMPol@MD data and squares to the QM/PCM calculations on the crystal structure. The dotted line indicates the average value obtained on all MMPol@MD values. The two insets indicate the two pairs showing the smallest (${\mathrm{DBV}}_{19\mathrm{A}}-{\mathrm{DBV}}_{19\mathrm{B}}$) and largest (${\mathrm{PEB}}_{50/61\mathrm{C}}-{\mathrm{PEB}}_{50/61\mathrm{D}}$) ${\epsilon }_{ik}$ values.

Figure 13

Bath spectral densities for BChl-3 of the FMO complex. “Exp.” represents the experimental $\mathrm{\Delta }$-FNL data of [257], “Simulation (LC)” the theoretical spectral density of [181], and “Simulation (KWC)” the theoretical spectral density of [160]. The inset shows a close-up of the lower frequency region. All the data have been provided by Young Min Rhee.

Figure 14

Diagrams representing four terms contributing to the third-order polarization. The first two terms (a) and (b) correspond to echo signals satisfying the phase-matching condition of ${\mathbf{k}}_m={\mathbf{k}}_3+{\mathbf{k}}_2-{\mathbf{k}}_1$ and are in general called rephasing terms. The last two terms (c) and (d) satisfy a different phase-matching condition of ${\mathbf{k}}_m={\mathbf{k}}_3-{\mathbf{k}}_2-{\mathbf{k}}_1$ and are in general called nonrephasing terms. Blue dashed curves represent relaxation and decoherence caused by the bath that continue propagating across interaction with a radiation pulse, and $R_k$ with different $k$ represents a different bath relaxation operator. $B_g$ represents the bath of the ground electronic state and $B_e$ the bath of the manifold of the single-exciton states. Different bath states created following interaction with the radiation are expressed as different numbers of primes in the superscripts.

Figure 15

Distribution of LH2-complex–LH2-complex rates (left panel) and average population decay (right panel) of excitons on the initial LH2 complex. More details can be found in [137].