Electronic coherence effects in photosynthetic light harvesting

Photosynthetic light harvesting is a paradigmatic example for quantum effects in biology. In this work, we review studies on quantum coherence effects in the LH2 antenna complex from purple bacteria to demonstrate how quantum mechanical rules play important roles in the speedup of excitation energy transfer, the stabilization of electronic excitations, and the robustness of light harvesting in photosynthesis. Subsequently, we present our recent theoretical studies on exciton dynamical localization and excitonic coherence generation in photosynthetic systems. We apply a variational-polaron approach to investigate decoherence of exciton states induced by dynamical fluctuations due to system-environment interactions. The results indicate that the dynamical localization of photoexcitations in photosynthetic complexes is significant and imperative for a complete understanding of coherence and excitation dynamics in photosynthesis. Moreover, we use a simple model to investigate quantum coherence effects in intercomplex excitation energy transfer in natural photosynthesis, with a focus on the likelihoods of generating excitonic coherences during the process. Our model simulations reveal that excitonic coherence between acceptor exciton states and transient nonlocal quantum correlation between distant pairs of chromophores can be generated through intercomplex energy transfer. Finally, we discuss the implications of these theoretical works and important open questions that remain to be answered.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Population and coherence dynamics in light harvesting complex II (LH2)

The electronic excitation population and coherence dynamics in the chromophores of the photosynthetic light harvesting complex 2 (LH2) B850 ring from purple bacteria (Rhodopseudomonas acidophila) have been studied theoretically at both physiological and cryogenic temperatures. Similar to the well-studied Fenna-Matthews-Olson (FMO) protein, oscillations of the excitation population and coherence in the site basis are observed in LH2 by using a scaled hierarchical equation of motion approach. However, this oscillation time (300 fs) is much shorter compared to the FMO protein (650 fs) at cryogenic temperature. Both environment and high temperature are found to enhance the propagation speed of the exciton wave packet yet they shorten the coherence time and suppress the oscillation amplitude of coherence and the population. Our calculations show that a long-lived coherence between chromophore electronic excited states can exist in such a noisy biological environment.     

A Complex Comprising a Cyanine Dye Rotaxane and a Porphyrin Nanoring as a Model Light‐Harvesting System

A nanoring‐rotaxane supramolecular assembly with a Cy7 cyanine dye (hexamethylindotricarbocyanine) threaded along the axis of the nanoring was synthesized as a model for the energy transfer between the light‐harvesting complex LH1 and the reaction center in purple bacteria photosynthesis. The complex displays efficient energy transfer from the central cyanine dye to the surrounding zinc porphyrin nanoring. We present a theoretical model that reproduces the absorption spectrum of the nanoring and quantifies the excitonic coupling between the nanoring and the central dye, thereby explaining the efficient energy transfer and demonstrating similarity with structurally related natural light‐harvesting systems.     

A Structural Basis of Light Energy and Electron Transfer in Biology (Nobel Lecture)

Aspects of intramolecular light energy and electron transfer are discussed for three protein cofactor complexes whose three-dimensional structures have been elucidated by X-ray crystallography: the light harvesting phycobilisomes of cyanobacteria, the reaction center of purple bacteria, and the blue multi-copper oxidases. A wealth of functional data is available for these systems which allows specific correlations to be made between structure and function and general conclusions to be drawn about light energy and electron transfer in biological materials.     

Multichromophoric Förster resonance energy transfer from b800 to b850 in the light harvesting complex 2: evidence for subtle energetic optimization by purple bacteria

This work provides a detailed account of the application of our multichromophoric F?rster resonance energy transfer (MC-FRET) theory (Phys. Rev. Lett. 2004, 92, 218301) for the calculation of the energy transfer rate from the B800 unit to the B850 unit in the light harvesting complex 2 (LH2) of purple bacteria. The model Hamiltonian consists of the B800 unit represented by a single bacteriochlorophyll (BChl), the B850 unit represented by its entire set of BChls, the electronic coupling between the two units, and the bath terms representing all environmental degrees of freedom. The model parameters are determined, independent of the rate calculation, from the literature data and by a fitting to an ensemble line shape. Comparing our theoretical rate and a low-temperature experimental rate, we estimate the magnitude of the BChl-Qy transition dipole to be in the range of 6.5-7.5 D, assuming that the optical dielectric constant of the medium is in the range of 1.5-2. We examine how the bias of the average excitation energy of the B800-BChl relative to that of the B850-BChl affects the energy transfer time by calculating the transfer rates based on both our MC-FRET theory and the original FRET theory, varying the value of the bias. Within our model, we find that the value of bias 260 cm-1, which we determine from the fitting to an ensemble line shape, is very close to the value at which the ratio between MC-FRET and FRET rates is a maximum. This provides evidence that the bacterial system utilizes the quantum mechanical coherence among the multiple chromophores within the B850 in a constructive way so as to achieve efficient energy transfer from B800 to B850.     

Light Harvesting and White‐Light Generation in a Composite of Carbon Dots and Dye‐Encapsulated BSA‐Protein‐Capped Gold Nanoclusters

Several strategies have been adopted to design an artificial light‐harvesting system in which light energy is captured by peripheral chromophores and it is subsequently transferred to the core via energy transfer. A composite of carbon dots and dye‐encapsulated BSA‐protein‐capped gold nanoclusters (AuNCs) has been developed for efficient light harvesting and white light generation. Carbon dots (C‐dots) act as donor and AuNCs capped with BSA protein act as acceptor. Analysis reveals that energy transfer increases from 63 % to 83 % in presence of coumarin dye (C153), which enhances the cascade energy transfer from carbon dots to AuNCs. Bright white light emission with a quantum yield of 19 % under the 375 nm excitation wavelength is achieved by changing the ratio of components. Interesting findings reveal that the efficient energy transfer in carbon‐dot–metal‐cluster nanocomposites may open up new possibilities in designing artificial light harvesting systems for future applications.     

Modeling of photosynthetic light-harvesting: From structure to function

In order to bridge the gap between the crystal structure of photosynthetic pigment-protein complexes and the data gathered in optical experiments, two essential problems need to be solved. On one hand, theories of optical spectra and excitation energy transfer have to be developed that take into account the pigment-pigment (excitonic) and the pigment-protein (exciton-vibrational) coupling on an equal footing. On the other hand, the parameters entering these theories need to be calculated from the structural data. Good agreement between simulations and experimental data then allows to draw conclusions on structure-function relationships of these complexes and to make predictions. In the development of theory, a delicate question is how to describe the interplay between the quantum dynamics of excitons and the dephasing of coherences by the coupling of excitons to protein vibrations. Quantum mechanic coherences are utilized for efficient light harvesting. In the reaction centers of purple bacteria an energy sink is created by a coherent coupling of exciton states to intermolecular charge transfer states. The dephasing of coherences can be monitored, e.g., by the temperature dependent shift of optical lines. In the Fenna-Matthews-Olson protein, which acts as an excitation energy wire between the outer chlorosome antenna and the reaction center complex, an energy funnel for efficient light-harvesting is formed by the pigment-protein coupling. The protein shifts the local transition energies of the pigments, the so-called site energies in a specific way, such that pigments facing the reaction center are redshifted with respect to those on the chlorosome side. In the light-harvesting complex of higher plants an excitation energy funnel is created by the use of two different types of chlorophyll (Chl) pigments, Chla and Chlb and by the pigment-protein coupling that creates an energy sink at Chla 610 located in the stromal layer at the periphery of the complex. The close contact between Chla and Chlb gives rise to ultrafast subpicosecond exciton transfer, whereas dynamic localization effects are inferred to lead to long ps relaxation times between the majority of Chla pigments.     

Quantum chemical insights in energy dissipation and carotenoid radical cation formation in light harvesting complexes

Light harvesting complexes (LHCs) have been identified in all photosynthetic organisms. To understand their function in light harvesting and energy dissipation, detailed knowledge about possible excitation energy transfer (EET) and electron transfer (ET) processes in these pigment proteins is of prime importance. This again requires the study of electronically excited states of the involved pigment molecules, in LHCs of chlorophylls and carotenoids. This paper represents a critical review of recent quantum chemical calculations on EET and ET processes between pigment pairs relevant for the major LHCs of green plants (LHC-II) and of purple bacteria (LH2). The theoretical methodology for a meaningful investigation of such processes is described in detail, and benefits and limitations of standard methods are discussed. The current status of excited state calculations on chlorophylls and carotenoids is outlined. It is focused on the possibility of EET and ET in the context of chlorophyll fluorescence quenching in LHC-II and carotenoid radical cation formation in LH2. In the context of non-photochemical quenching of green plants, it is shown that replacement of the carotenoid violaxanthin by zeaxanthin in its binding pocket of LHC-II can not result in efficient quenching. In LH2, our computational results give strong evidence that the S(1) states of the carotenoids are involved in carotenoid cation formation. By comparison of theoretical findings with recent experimental data, a general mechanism for carotenoid radical cation formation is suggested.     

Efficient Light‐Harvesting Systems with Tunable Emission through Controlled Precipitation in Confined Nanospace

Light harvesting is a key step in photosynthesis but creation of synthetic light‐harvesting systems (LHSs) with high efficiencies has been challenging. When donor and acceptor dyes with aggregation‐induced emission were trapped within the interior of cross‐linked reverse vesicles, LHSs were obtained readily through spontaneous hydrophobically driven aggregation of the dyes in water. Aggregation in the confined nanospace was critical to the energy transfer and the light‐harvesting efficiency. The efficiency of the excitation energy transfer (EET) reached 95 % at a donor/acceptor ratio of 100:1 and the energy transfer was clearly visible even at a donor/acceptor ratio of 10 000:1. Multicolor emission was achieved simply by tuning the donor/acceptor feed ratio in the preparation and the quantum yield of white light emission from the system was 0.38, the highest reported for organic materials in water to date.     

Quantum nonlocality in the excitation energy transfer in the Fenna–Matthews–Olson complex

The Fenna–Matthews–Olson (FMO) complex—a pigment protein complex involved in photosynthesis in green sulfur bacteria—is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger‐than‐entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs, on the other hand, is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.     

Excitonic Coupling Strength and Coherence Length in the Singlet and Triplet Excited States of meso–meso Directly Linked Zn(II)porphyrin Arrays

Excitation‐energy transport (EET) phenomena in meso–meso directly linked Zn(II )porphyrin arrays in the singlet and triplet excited states were investigated with a view to electronic coupling strength and coherence length by steady‐state and time‐resolved spectroscopic measurements. To investigate energy transfer in the triplet states, we modified the Zn(II )porphyrin arrays with bromo substituents at both ends. The coupling strength of the Soret bands of the arrays was estimated to be about 2200 cm^?1, and that of the Q bands is about 570 cm^?1. The coherence length in the S₁ state of the Zn(II )porphyrin arrays was determined to be 4–5 porphyrin units, which is comparable to that of the well‐ordered two‐dimensional circular structure B850 in the peripheral light‐harvesting antenna (LH2) in photosynthetic purple bacteria. This indicates that the Zn(II )porphyrin arrays are well suited for mimicking natural light‐harvesting antenna complexes. On the other hand, the rate of energy transfer in the triplet state is estimated to be on the order of 100 μs^?1, and the very weak coupling between the triplet states (ca. 0.003 cm^?1), indicates that the triplet excitation energy is essentially localized on a single porphyrin moiety.     

Excited state dynamics in photosynthetic reaction center and light harvesting complex 1

Key to efficient harvesting of sunlight in photosynthesis is the first energy conversion process in which electronic excitation establishes a trans-membrane charge gradient. This conversion is accomplished by the photosynthetic reaction center (RC) that is, in case of the purple photosynthetic bacterium Rhodobacter sphaeroides studied here, surrounded by light harvesting complex 1 (LH1). The RC employs six pigment molecules to initiate the conversion: four bacteriochlorophylls and two bacteriopheophytins. The excited states of these pigments interact very strongly and are simultaneously influenced by the surrounding thermal protein environment. Likewise, LH1 employs 32 bacteriochlorophylls influenced in their excited state dynamics by strong interaction between the pigments and by interaction with the protein environment. Modeling the excited state dynamics in the RC as well as in LH1 requires theoretical methods, which account for both pigment-pigment interaction and pigment-environment interaction. In the present study we describe the excitation dynamics within a RC and excitation transfer between light harvesting complex 1 (LH1) and RC, employing the hierarchical equation of motion method. For this purpose a set of model parameters that reproduce RC as well as LH1 spectra and observed oscillatory excitation dynamics in the RC is suggested. We find that the environment has a significant effect on LH1-RC excitation transfer and that excitation transfers incoherently between LH1 and RC.     

Light‐Harvesting Systems Based on Organic Nanocrystals To Mimic Chlorosomes

We report the first highly efficient artificial light‐harvesting systems based on nanocrystals of difluoroboron chromophores to mimic the chlorosomes, one of the most efficient light‐harvesting systems found in green photosynthetic bacteria. Uniform nanocrystals with controlled donor/acceptor ratios were prepared by simple coassembly of the donors and acceptors in water. The light‐harvesting system funneled the excitation energy collected by a thousand donor chromophores to a single acceptor. The well‐defined spatial organization of individual chromophores in the nanocrystals enabled an energy transfer efficiency of 95 %, even at a donor/acceptor ratio as high as 1000:1, and a significant fluorescence of the acceptor was observed up to donor/acceptor ratios of 200 000:1.     

Energy and hole transfer between dyes attached to titania in cosensitized dye-sensitized solar cells

Cosensitization of broadly absorbing ruthenium metal complex dyes with highly absorptive near-infrared (NIR) organic dyes is a clear pathway to increase near-infrared light harvesting in liquid-based dye-sensitized solar cells (DSCs). In cosensitized DSCs, dyes are intimately mixed, and intermolecular charge and energy transfer processes play an important role in device performance. Here, we demonstrate that an organic NIR dye incapable of hole regeneration is able to produce photocurrent via intermolecular energy transfer with an average excitation transfer efficiency of over 25% when cosensitized with a metal complex sensitizing dye (SD). We also show that intermolecular hole transfer from the SD to NIR dye is a competitive process with dye regeneration, reducing the internal quantum efficiency and the electron lifetime of the DSC. This work demonstrates the general feasibility of using energy transfer to boost light harvesting from 700 to 800 nm and also highlights a key challenge for developing highly efficient cosensitized dye-sensitized solar cells.     

Enhanced Light‐Harvesting Capacity by Micellar Assembly of Free Accessory Chromophores and LH1‐like Antennas

Biohybrid light‐harvesting antennas are an emerging platform technology with versatile tailorability for solar‐energy conversion. These systems combine the proven peptide scaffold unit utilized for light harvesting by purple photosynthetic bacteria with attached synthetic chromophores to extend solar coverage beyond that of the natural systems. Herein, synthetic unattached chromophores are employed that partition into the organized milieu (e.g. detergent micelles) that house the LH1‐like biohybrid architectures. The synthetic chromophores include a hydrophobic boron‐dipyrrin dye (A1) and an amphiphilic bacteriochlorin (A2), which transfer energy with reasonable efficiency to the bacteriochlorophyll acceptor array (B875) of the LH1‐like cyclic oligomers. The energy‐transfer efficiencies are markedly increased upon covalent attachment of a bacteriochlorin (B1 or B2) to the peptide scaffold, where the latter likely acts as an energy‐transfer relay site for the (potentially diffusing) free chromophores. The efficiencies are consistent with a Förster (through‐space) mechanism for energy transfer. The overall energy‐transfer efficiency from the free chromophores via the relay to the target site can approach those obtained previously by relay‐assisted energy transfer from chromophores attached at distant sites on the peptides. Thus, the use of free accessory chromophores affords a simple design to enhance the overall light‐harvesting capacity of biohybrid LH1‐like architectures.     

Integrating DNA Photonic Wires into Light‐Harvesting Supramolecular Polymers

An approach combining DNA nanoscaffolds with supramolecular polymers for the efficient and directional propagation of light‐harvesting cascades has been developed. A series of photonic wires with different arrangements of fluorophores in DNA‐organized nanostructures were linked to light‐harvesting supramolecular phenanthrene polymers (SPs) in a self‐assembled fashion. Among them, a light‐harvesting complex (LHC) composed of SPs and a photonic wire of phenanthrene, Cy3, Cy5, and Cy5.5 chromophores reveals a remarkable energy transfer efficiency of 59 %. Stepwise transfer of the excitation energy collected by the light‐harvesting SPs via the intermediate Cy3 and Cy5 chromophores to the final Cy5.5 acceptor proceeds through a Förster resonance energy transfer mechanism. In addition, the light‐harvesting properties are documented by antenna effects ranging from 1.4 up to 23 for different LHCs.     

Optically nonlinear energy transfer in light-harvesting dendrimers

Dendrimeric polymers are the subject of intense research activity geared towards their implementation in nanodevice applications such as energy harvesting systems, organic light-emitting diodes, photosensitizers, low-threshold lasers, and quantum logic elements, etc. A recent development in this area has been the construction of dendrimers specifically designed to exhibit novel forms of optical nonlinearity, exploiting the unique properties of these materials at high levels of photon flux. Starting from a thorough treatment of the underlying theory based on the principles of molecular quantum electrodynamics, it is possible to identify and characterize several optically nonlinear mechanisms for directed energy transfer and energy pooling in multichromophore dendrimers. Such mechanisms fall into two classes: first, those where two-photon absorption by individual donors is followed by transfer of the net energy to an acceptor; second, those where the excitation of two electronically distinct but neighboring donor groups is followed by a collective migration of their energy to a suitable acceptor. Each transfer process is subject to minor dissipative losses. In this paper we describe in detail the balance of factors and the constraints that determines the favored mechanism, which include the excitation statistics, structure of the energy levels, laser coherence factors, chromophore selection rules and architecture, possibilities for the formation of delocalized excitons, spectral overlap, and the overall distribution of donors and acceptors. Furthermore, it transpires that quantum interference between different mechanisms can play an important role. Thus, as the relative importance of each mechanism determines the relevant nanophotonic characteristics, the results reported here afford the means for optimizing highly efficient light-harvesting dendrimer devices.