Dephasing and Dissipation in a Source–Drain Model of Light‐Harvesting Systems

The energy transport process in natural‐light‐harvesting systems is investigated by solving the time‐dependent Schrödinger equation for a source–network–drain model incorporating the effects of dephasing and dissipation, owing to coupling with the environment. In this model, the network consists of electronically coupled chromophores, which can host energy excitations (excitons) and are connected to source channels, from which the excitons are generated, thereby simulating exciton creation from sunlight. After passing through the network, excitons are captured by the reaction centers and converted into chemical energy. In addition, excitons can reradiate in green plants as photoluminescent light or be destroyed by nonphotochemical quenching (NPQ). These annihilation processes are described in the model by outgoing channels, which allow the excitons to spread to infinity. Besides the photoluminescent reflection, the NPQ processes are the main outgoing channels accompanied by energy dissipation and dephasing. From the simulation of wave‐packet dynamics in a one‐dimensional chain, it is found that, without dephasing, the motion remains superdiffusive or ballistic, despite the strong energy dissipation. At an increased dephasing rate, the wave‐packet motion is found to switch from superdiffusive to diffusive in nature. When a steady energy flow is injected into a site of a linear chain, exciton dissipation along the chain, owing to photoluminescence and NPQ processes, is examined by using a model with coherent and incoherent outgoing channels. It is found that channel coherence leads to suppression of dissipation and multiexciton super‐radiance. With this method, the effects of NPQ and dephasing on energy transfer in the Fenna–Matthews–Olson complex are investigated. The NPQ process and the photochemical reflection are found to significantly reduce the energy‐transfer efficiency in the complex, whereas the dephasing process slightly enhances the efficiency. The calculated absorption spectrum reproduces the main features of the measured counterpart. As a comparison, the exciton dynamics are also studied in a linear chain of pigments and in a multiple‐ring system of light‐harvesting complexes II (LH2) from purple bacteria by using the Davydov D₁ ansatz. It is found that the exciton transport shows superdiffusion characteristics in both the chain and the LH2 rings.     

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.     

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.     

Ultrafast Exciton Self‐Trapping and Delocalization in Cycloparaphenylenes: The Role of Excited‐State Symmetry in Electron‐Vibrational Coupling

Upon photon absorption, π‐conjugated organics are apt to undergo ultrafast structural reorganization via electron‐vibrational coupling during non‐adiabatic transitions. Ultrafast nuclear motions modulate local planarity and quinoid/benzenoid characters within conjugated backbones, which control primary events in the excited states, such as localization, energy transfer, and so on. Femtosecond broadband fluorescence upconversion measurements were conducted to investigate exciton self‐trapping and delocalization in cycloparaphenylenes as ultrafast structural reorganizations are achieved via excited‐state symmetry‐dependent electron‐vibrational coupling. By accessing two high‐lying excited states, one‐photon and two‐photon allowed states, a clear discrepancy in the initial time‐resolved fluorescence spectra and the temporal dynamics/spectral evolution of fluorescence spectra were monitored. Combined with quantum chemical calculations, a novel insight into the effect of the excited‐state symmetry on ultrafast structural reorganization and exciton self‐trapping in the emerging class of π‐conjugated materials is provided.     

Excitation energy transfer in multiporphyrin arrays with cyclic architectures: towards artificial light-harvesting antenna complexes

Since highly symmetric cyclic architecture of light-harvesting antenna complex LH2 in purple bacteria was revealed in 1995, there has been a renaissance in developing cyclic porphyrin arrays to duplicate natural systems in terms of high efficiency, in particular, in transferring excitation energy. This tutorial review highlights the mechanisms and rates of excitation energy transfer (EET) in a variety of synthetic cyclic porphyrin arrays on the basis of time-resolved spectroscopic measurements performed at both ensemble and single-molecule levels. Subtle change in structural parameters such as connectivity, distance, and orientation between neighboring porphyrin moieties exquisitely modulates not only the nature of interchromophoric interactions but also the rates and efficiencies of EET. The relationship between the structure and EET dynamics described here should assist a rational design of novel cyclic porphyrin arrays, more contiguous to real applications in artificial photosynthesis.     

Measurement of 13C-1H dipolar couplings in solids by using ultra-fast magic-angle spinning NMR spectroscopy with symmetry-based sequences

We show that (13)C-(1)H dipolar couplings in fully protonated organic solids can be measured by applying a Symmetry-based Resonance-Echo DOuble-Resonance (S-REDOR) experiment at ultra-fast Magic-Angle Spinning (MAS). The (13)C-(1)H dipolar couplings are recovered by using the R12 recoupling scheme, while the interference of (1)H-(1)H dipolar couplings are suppressed by the symmetry properties of this sequence and the use of high MAS frequency (65 kHz). The R12 method is especially advantageous for large (13)C-(1)H dipolar interactions, since the dipolar recoupling time can be incremented by steps as short as one rotor period. This allows a fine sampling for the rising part of the dipolar dephasing curve. We demonstrate experimentally that one-bond (13)C-(1)H dipolar coupling in the order of 22 kHz can be accurately determined. Furthermore, the proposed method allows a rapid evaluation of the dipolar coupling by fitting the S-REDOR dipolar dephasing curve with an analytical expression.     

Efficient light harvesting in dye-endcapped conjugated polymers probed by single molecule spectroscopy

The development of sophisticated microscopic models of energy transfer in linear multichromophoric systems such as conjugated polymers is rarely matched by suitable experimental studies on the microscopic level. To assess the roles of structural, temporal, and energetic disorder in energy transfer, single molecule spectroscopic investigations of the elementary processes leading to energetic relaxation in conjugated polymers are desirable. We present a detailed study of energy transfer processes occurring in dye-endcapped conjugated polymer molecules on the single molecule level. These processes are mostly masked in ensemble investigations. Highly efficient intramolecular energy transfer along a single polyindenofluorene chain to a perylene endcap occurs in many instances and is resolved in real time. We further consider the spectral emission characteristics of the single molecule, the polarization anisotropy which reveals the chain conformation, the fluorescence intermittency, and the temperature dependence and conclude that the efficiency of energy transfer in the ensemble is controlled by the statistics of the individual molecules. The weak thermal activation of energy transfer indicates the involvement of vibrational modes in interchromophoric coupling. Whereas backbone-endcap coupling is strong, the rate-limiting step for intramolecular energy transfer is the migration along the backbone. The results are particularly relevant to understanding undesired exciton trapping on fluorenone defects in polyfluorenes.     

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 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.     

Exciton Derealization in the Light-Harvesting LH2 Complex of Photosynthetic Purple Bacteria

Abstract— Absorption and circular dichroism spectra for both long-wavelength bands of the antenna LH2 complex from photosynthetic purple bacteria have been calculated. Calculations were performed taking into account resonant interactions between all 27 bacteriochlorophyll (BChl) molecules for different values of site inhomogeneity. The exciton derealization length within BChl800 and BChl850 rings was estimated on the basis of calculated exciton wavefunctions for different temperatures and site inhomogeneity values. The relationship between anomalously high bleaching values in pump-probe spectra and the exciton derealization length is discussed.     

Long range excitonic transport in a biomimetic system inspired by the bacterial light-harvesting apparatus

Photosynthesis, the process by which energy from sunlight drives cellular metabolism, relies on a unique organization of light-harvesting and reaction center complexes. Recently, the organization of light-harvesting LH2 complexes and dimeric reaction center-light-harvesting I-PufX core complexes in membranes of purple non-sulfur bacteria was revealed by atomic force microscopy [S. Bahatyrova et al., Nature (London) 430, 1058 (2004)]. Here, we discuss optimal exciton transfer in a biomimetic system closely modeled on the structure of LH2 and its organization within the membrane using a Markovian quantum model with dissipation and trapping added phenomenologically. In a deliberate manner, we neglect the high level detail of the bacterial light-harvesting complex and its interaction with the phonon bath in order to elucidate a set of design principles that may be incorporated in artificial pigment-scaffold constructs in a supramolecular assembly. We show that our scheme reproduces many of the most salient features found in their natural counterpart and may be largely explained by simple electrostatic considerations. Most importantly, we show that quantum effects act primarily to enforce robustness with respect to spatial and spectral disorder between and within complexes. The implications of such an arrangement are discussed in the context of biomimetic photosynthetic analogs capable of transferring energy efficiently across tens to hundreds of nanometers.     

Pure optical dephasing dynamics in semiconducting single-walled carbon nanotubes

We report a detailed study of ultrafast exciton dephasing processes in semiconducting single-walled carbon nanotubes employing a sample highly enriched in a single tube species, the (6,5) tube. Systematic measurements of femtosecond pump-probe, two-pulse photon echo, and three-pulse photon echo peak shift over a broad range of excitation intensities and lattice temperature (from 4.4 to 292 K) enable us to quantify the timescales of pure optical dephasing (T(2)(*)), along with exciton-exciton and exciton-phonon scattering, environmental effects as well as spectral diffusion. While the exciton dephasing time (T(2)) increases from 205 fs at room temperature to 320 fs at 70 K, we found that further decrease of the lattice temperature leads to a shortening of the T(2) times. This complex temperature dependence was found to arise from an enhanced relaxation of exciton population at lattice temperatures below 80 K. By quantitatively accounting the contribution from the population relaxation, the corresponding pure optical dephasing times increase monotonically from 225 fs at room temperature to 508 fs at 4.4 K. We further found that below 180 K, the pure dephasing rate (1/T(2)(*)) scales linearly with temperature with a slope of 6.7 ± 0.6 μeV/K, which suggests dephasing arising from one-phonon scattering (i.e., acoustic phonons). In view of the large dynamic disorder of the surrounding environment, the origin of the long room temperature pure dephasing time is proposed to result from reduced strength of exciton-phonon coupling by motional narrowing over nuclear fluctuations. This consideration further suggests the occurrence of remarkable initial exciton delocalization and makes nanotubes ideal to study many-body effects in spatially confined systems.     

Coherent Exciton-Phonon Coupling in CdSe/ZnS Nanocrystals Studied by Two-Dimensional Electronic Spectroscopy

Coherent exciton-phonon coupling in CdSe/ZnS nanocrystals have been investigated by temperature-dependent two-dimensional electronic spectroscopy (2DES) measurements. Benefiting from the ability of 2DES to dissect assembles in nanocrystal films, we have clearly identified experimental evidences of coherent coupling between exciton and phonon in CdSe/ZnS nanocrystals. In time domain, 2DES signals of excitonic transitions beat at a frequency resonant to a longitudinal optical phonon mode; in energy domain, phonon side bands are distinct at both Stokes and anti-Stokes sides. When temperature increases, phonon-induced exciton dephasing is observed with dramatic broadening of homogeneous linewidth. The results suggest exciton-phonon coupling is essential in elucidating the quantum dynamics of excitonic transitions in semiconductor nanocrystals.     

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.     

Inter- and intraspecific variation in excited-state triplet energy transfer rates in reaction centers of photosynthetic bacteria

In protein-cofactor reaction center (RC) complexes of purple photosynthetic bacteria, the major role of the bound carotenoid (C) is to quench the triplet state formed on the primary electron donor (P) before its sensitization of the excited singlet state of molecular oxygen from its ground triplet state. This triplet energy is transferred from P to C via the bacteriochlorophyll monomer B(B). Using time-resolved electron paramagnetic resonance (TREPR), we have examined the temperature dependence of the rates of this triplet energy transfer reaction in the RC of three wild-type species of purple nonsulfur bacteria. Species-specific differences in the rate of transfer were observed. Wild-type Rhodobacter capsulatus RCs were less efficient at the triplet transfer reaction than Rhodobacter sphaeroides RCs, but were more efficient than Rhodospirillum rubrum RCs. In addition, RCs from three mutant strains of R. capsulatus carrying substitutions of amino acids near P and B(B) were examined. Two of the mutant RCs showed decreased triplet transfer rates compared with wild-type RCs, whereas one of the mutant RCs demonstrated a slight increase in triplet transfer rate at low temperatures. The results show that site-specific changes within the RC of R. capsulatus can mimic interspecies differences in the rates of triplet energy transfer. This application of TREPR was instrumental in defining critical energetic and coupling factors that dictate the efficiency of this photoprotective process.     

Vibrational predissociation induced by exciton trapping in inert-gas clusters

The dynamics of exciton trapping, vibrational energy transfer and vibrational predissociation in an electronically excited state of Ar₁₃ clusters was explored by classical molecular dynamics. Two distinct time scales were established for vibrational energy flow, which result in a molecular-type, reactive dissociation process of Ar atoms for this cluster.     

Nonmonotonic energy harvesting efficiency in biased exciton chains

We theoretically study the efficiency of energy harvesting in linear exciton chains with an energy bias, where the initial excitation is taking place at the high-energy end of the chain and the energy is harvested (trapped) at the other end. The efficiency is characterized by means of the average time for the exciton to be trapped after the initial excitation. The exciton transport is treated as the intraband energy relaxation over the states obtained by numerically diagonalizing the Frenkel Hamiltonian that corresponds to the biased chain. The relevant intraband scattering rates are obtained from a linear exciton-phonon interaction. Numerical solution of the Pauli master equation that describes the relaxation and trapping processes reveals a complicated interplay of factors that determine the overall harvesting efficiency. Specifically, if the trapping step is slower than or comparable to the intraband relaxation, this efficiency shows a nonmonotonic dependence on the bias: it first increases when introducing a bias, reaches a maximum at an optimal bias value, and then decreases again because of dynamic (Bloch) localization of the exciton states. Effects of on-site (diagonal) disorder, leading to Anderson localization, are addressed as well.     

Dynamics of fluorescence depolarisation in star-shaped oligofluorene-truxene molecules

Star-shaped molecules are of growing interest as organic optoelectronic materials. Here a detailed study of their photophysics using fluorescence depolarisation is reported. Fluorescence depolarisation dynamics are studied in branched oligofluorene-truxene molecules with a truxene core and well-defined three-fold symmetry, and are compared with linear fluorene oligomers. An initial anisotropy value of 0.4 is observed which shows a two-exponential decay with time constants of 500 fs and 3-8 ps in addition to a long-lived component. The femtosecond component is attributed to exciton localisation on one branch of the molecule and its amplitude reduces when the excitation is tuned to the low energy tail of the absorption spectrum. The picosecond component shows a weak dependence on the excitation wavelength and is similar to the calculated rate of the resonant energy transfer of the localised exciton between the branches. These assignments are supported by density-functional theory calculations which show a disorder-induced splitting of the two degenerate excited states. Exciton localisation is much slower than previously reported in other branched molecules which suggests that efficient light-harvesting systems can be designed using oligofluorenes and truxenes as building blocks.     

Energy transfer in photosynthesis: experimental insights and quantitative models

We overview experimental and theoretical studies of energy transfer in the photosynthetic light-harvesting complexes LH1, LH2, and LHCII performed during the past decade since the discovery of high-resolution structure of these complexes. Experimental findings obtained with various spectroscopic techniques makes possible a modelling of the excitation dynamics at a quantitative level. The modified Redfield theory allows a precise assignment of the energy transfer pathways together with a direct visualization of the whole excitation dynamics where various regimes from a coherent motion of delocalized exciton to a hopping of localized excitations are superimposed. In a single complex it is possible to observe the switching between these regimes driven by slow conformational motion (as we demonstrate for LH2). Excitation dynamics under quenched conditions in higher-plant complexes is discussed.