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.     

One-dimensional exciton diffusion in perylene bisimide aggregates

The dynamics and mobility of excitons in J-aggregates of perylene bisimides are investigated by transient absorption spectroscopy with a time resolution of 50 fs. The transient spectra are compatible with an exciton delocalization length of two monomers and indicate that vibrational and configurational relaxation processes are not relevant for the spectroscopic properties of the aggregates. Increasing the pump pulse energy and in that way the initial exciton density results in an accelerated signal decay and pronounced exciton-exciton annihilation dynamics. Modeling the data by assuming a diffusive exciton motion reveals that the excitons cannot migrate freely in all three directions of space but their mobility is restricted to one dimension. The observed anisotropy supports this picture and points against direct Fo?rster-transfer-mediated annihilation between the excitons. A diffusion constant of 1.29 nm(2)/ps is deduced from the fitting procedure that corresponds to a maximal exciton diffusion length of 96 nm for the measured exciton lifetime of 3.6 ns. The findings indicate that J-aggregates of perylene bisimides are promising building blocks to facilitate directed energy transport in optoelectronic organic devices or artificial light-harvesting systems.     

Wave function engineering for efficient extraction of up to nineteen electrons from one CdSe/CdS quasi-type II quantum dot

Solar-to-fuel conversion devices require not only efficient catalysts to accelerate the reactions, but also light harvesting and charge separation components to absorb multiple photons and to deliver multiple electrons/holes to the catalytic centers. In this paper, we show that the spatial distribution of electron and hole wave functions in CdSe/CdS quasi-type II quantum dots enables simultaneous ultrafast charge separation (0.18 ps to adsorbed Methylviologen), ultraslow charge recombination (0.4 μs), and slow multiple-exciton Auger annihilation (biexciton lifetime 440 ps). Up to nineteen excitons per QD can be generated by absorbing multiple 400 nm photons and all excitons can be dissociated with unity yield by electron transfer to adsorbed methylviologen molecules. Our finding demonstrates that (quasi-) type II nanoheterostructures can be engineered to efficiently dissociate multiple excitons and deliver multiple electrons to acceptors, suggesting their potential applications as light harvesting and charge separation components in artificial photosynthetic devices.     

A study on thermal oxidation mechanism of styrene-butadiene-styrene block copolymer (SBS)

The thermal oxidation process of SBS was studied by in situ FTIR and programming heating up DSC. The thermal oxidation mechanism of SBS was analyzed according to the activation energy and pre-exponential factor calculated by Friedman method. The results show that the oxidation of SBS is mainly on butadiene blocks. It is a self-catalyzed reaction containing four steps. The first step is the initiation of chain by free radical. The second is the growth and decomposition of polymer chain. The third is the formation of anhydride coming from dehydrated carbonyl. The fourth is the annihilation of active centers. Antioxidant which provides H atom easily can annihilate active free radical to protect SBS from thermal oxidation at lower temperature.     

Low-temperature dynamics of weakly localized Frenkel excitons in disordered linear chains

We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible nonequilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excitation conditions (resonant or nonresonant). A Pauli master equation, with microscopically calculated transition rates, is used to describe the redistribution of the exciton population over the manifold of localized exciton states. We find a counterintuitive nonmonotonic temperature dependence of the Stokes shift. In addition, we show that depending on experimental conditions, the observed fluorescence decay time may be determined by vibration-induced intraband relaxation, rather than radiative relaxation to the ground state. The model considered has relevance to a wide variety of materials, such as linear molecular aggregates, conjugated polymers, and polysilanes.     

Transfer of excitation energy in a three-dimensional-doped molecular crystal. V. Self-consistency of the temporal processes involved in energy transfer in photosynthetic units

Numerical experiments were carried out to determine the timewise self-consistency of different physical processes involved in the energy transfer in green plant photosynthetic units. A 6 × 6 × 6 array of chlorophyll-a with cubic lattice constants a = b = c = 20 Å was chosen as a model of the thylakoid disc. Another model aggregate was obtained by substituting chlorophyll-b molecules for some of the chlorophyll-a molecules. In both models, a reaction center occupied a central site in the last xy plane. Two extreme arrangements were considered for the orientation of molecules. In one, the transition moments of all molecules were directed along the y-axis. The other had chlorophyll molecules randomly oriented. The four resulting model systems were used in our investigation on exciton generation, transport, decay by fluorescence, and trapping. All excitons were assumed to be generated by a 20 ms exposure to sunlight at high altitudes. The general trends noticed from these computations are as follows: The number of excitons generated is influenced by lattice disorders. Disorders also increase the time for the establishment of an equilibrium distribution. The decay of excitons by fluorescence is always a monotonic function of time. The energy transfer is adversely affected by a lower degree of orientation in the crystal: The trapping time increases with disorder. The number of trappings decreases with the onset of fluorescence of the host molecules and the trap. From these investigations, we also made three specific observations: (1) The efficiency of exciton utilization varies from 12% for a completely random arrangement of transition dipoles to 46% for a perfectly ordered arrangement. This agrees with the experimental efficiency, about 20%. (2) The number of excitons trapped varies from one to six. This tallies with the time scale of electron transfer along the Z-scheme that requires at least two excitons trapped in about 20 ms. Thus, the photon density and the exciton transfer rate are consistent with the rates of electron transfers. (3) The trapping rate also indicates that the thylakoid disc must resemble a considerably ordered system. © 1996 John Wiley & Sons, Inc.     

Exciton dynamics in molecular crystals from line shape analysis. Time response function of singlet excitons in crystal anthracene

From an accurate measure of the temperature dependence of the line shape function ω ?₂ (ω) information is obtained about the time behaviour of the response function of singlet excitons of small wavevector encompassed by the (0-0) band of the 4000 A Å transition in crystal anthracene. An apparatus to determine the reflection band profile with high accuracy needed to give correct ω ?₂ (ω) data is described. Although the data analysis is not without problems, there is strong evidence that the time behaviour of excitons in this transition is characterized by a stochastic collision time τ_c. The temperature dependence of τ_c is consistent with a model in which the intermolecular phonons are weakly coupled with the exciton created by either b or a polarized light. Phonon annihilation is predominant for the b-polarized transition but both phonon creation and annihilation are active for these polarized transition. The similar values of the exciton—phonon coupling function for both polarizations may indicate either the importance of higher multipole terms for that function or strong interband scattering. The relationships between τ_c and parameters from other experimental results on singlet excitons in crystal anthracene are considered. The results may allow for a better understanding of the mechanism of exciton—phonon coupling in crystals.     

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.     

A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.     

Nonlinear Exciton Annihilation and Local Heating Effects in Photosynthetic Antenna Systems

Abstract— Generation of the nonequilibrium distribution of excited vibrational modes stimulated by electronic energy relaxation in pigment-protein complexes of the light-harvesting antenna of some photosynthetic systems is discussed in this paper. It is shown that the simplest approach to this problem can be achieved by introducing a local temperature, which is a good parameter for describing the nonequilibrium distribution of the local vibrational modes of the pigment molecules and its nearest protein surroundings. Then the transient absorption kinetics is determined by the kinetics of the excitation relaxation as I well as the heating/cooling of the local vibrational modes. Experimentally, this process can be investigated in the i singlet-singlet annihilation conditions that create the i greatest amount of local heating. The systems under in-: vestigation are trimers of bacteriochlorophyll a contain- i ing pigment-protein complexes from the green sulfur i bacterium Chlorobium tepid urn (so-called FMO complexes) and aggregates of the light-harvesting complexes of photosystem II (LHC2) from higher plants containing chlorophyll alb. It was shown that at 77 K the heat redistribution kinetics in LHC2 is on the order of 3040 ps and in FMO it is approximately equal to 26 ps. The local heating effect at room temperature is less pronounced; however, by using longer pulses and at higher excitation energies (on the order of a magnitude higher), an additional kinetics of hundreds of ps, also related to the heating/cooling process, was observed.     

Heat flow in proteins: computation of thermal transport coefficients

The rate of vibrational energy transfer and thermal transport coefficients are computed for two structurally distinct proteins, green fluorescent protein (GFP) and myoglobin. The computation of thermal transport coefficients exploits the scaling of the energy diffusion coefficient with the vibrational mode frequency of a protein. Near 300 K we find that vibrational energy transfer due to anharmonicity contributes substantially to thermal transport because of the localization of many thermally accessible normal modes. The thermal diffusivity for the beta-barrel GFP is larger than that for myoglobin, particularly at low temperature due to a mean free path for vibrational energy propagation that is twice as large at low frequency. Vibrational energy transfer is also faster in GFP than in myoglobin for most vibrational modes.     

Photochemistry of supramolecular systems containing C60

Fullerenes have been used successfully in the covalent assembly of supramolecular systems that mimic some of the electron transfer steps of photosynthetic reaction centers. In these constructs C60 is most often used as the primary electron acceptor; it is linked to cyclic tetrapyrroles or other chromophores which act as primary electron donors in photoinduced electron transfer processes. In artificial photosynthetic systems, fullerenes exhibit several differences from the superficially more biomimetic quinone electron acceptors. The lifetime of the initial charge-separated state in fullerene-based molecules is, in general, considerably longer than in comparable systems containing quinones. Moreover, photoinduced electron transfer processes take place in non-polar solvents and at low temperature in frozen glasses in a number of fullerene-based dyads and triads. These features are unusual in photosynthetic model systems that employ electron acceptors such as quinones, and are more reminiscent of electron transfer in natural reaction centers. This behavior can be attributed to a reduced sensitivity of the fullerene radical anion to solvent charge stabilization effects and small internal and solvent reorganization energies for electron transfer in the fullerene systems, relative to quinone-based systems.     

Coarse-graining kinetic networks in photosynthetic energy transport

Photosynthetic systems utilize hundreds of chlorophylls to collect sunlight and transport the energy to the reaction center with remarkably high quantum efficiency, however, the large size of the system together with the complex interactions among the components make it extremely challenging to understand the dynamics of light harvesting in large photosynthetic systems. To shed light on this problem, we present a structure-based theoretical framework that can be used to calculate transition rate matrix describing energy transport in photosynthetic systems and network clustering methods that provide simplified coarse-grained model revealing key structures guiding the light harvesting process. We constructed an effective model for energy transport in a Photosystem II supercomplex and applied several network clustering methods to generate coarse-grained kinetic cluster models for the system. Furthermore, we evaluated the performances of the network clustering methods, and show that a spectral clustering method and a minimum cut approach produce accurate coarse-grained models for the PSII-sc system. The results indicate that finding bottlenecks of energy transport is a crucial factor for reduced representations of photosynthetic light harvesting, and the overall work presented in this paper should provide a comprehensive theoretical framework to elucidate the dynamics of light harvesting in photosynthetic systems.     

Efficient exciton transport in layers of self-assembled porphyrin derivatives

The photosynthetic apparatus of green sulfur bacteria, the chlorosome, is generally considered as a highly efficient natural light-harvesting system. The efficient exciton transport through chlorosomes toward the reaction centers originates from self-assembly of the bacteriochlorophyll molecules. The aim of the present work is to realize a long exciton diffusion length in an artificial light-harvesting system using the concept of self-assembled natural chlorosomal chromophores. The ability to transport excitons is studied for porphyrin derivatives with different tendencies to form molecular stacks by self-assembly. A porphyrin derivative denoted as ZnOP, containing methoxymethyl substituents ({meso-tetrakis[3,5-bis(methoxymethyl)phenyl]porphyrinato}zinc(II)) is found to form self-assembled stacks, in contrast to a derivative with tert-butyl substituents, ZnBuP ({meso-tetrakis[3,5-bis(tert-butyl)phenyl]porphyrinato}zinc(II)). Exciton transport and dissociation in a bilayer of these porphyrin derivatives and TiO2 are studied using the time-resolved microwave conductivity (TRMC) method. For ZnOP layers it is found that excitons undergo diffusive motion between the self-assembled stacks, with the exciton diffusion length being as long as 15 +/- 1 nm, which is comparable to that in natural chlorosomes. For ZnBuP a considerably shorter exciton diffusion length of 3 +/- 1 nm is found. Combining these exciton diffusion lengths with exciton lifetimes of 160 ps for ZnOP and 74 ps for ZnBuP yields exciton diffusion coefficients equal to 1.4 x 10(-6) m2/s and 1 x 10(-7) m2/s, respectively. The larger exciton diffusion coefficient for ZnOP originates from a strong excitonic coupling for interstack energy transfer. The findings show that energy transfer is strongly affected by the molecular organization. The efficient interstack energy transfer shows promising prospects for application of such self-assembled porphyrins in optoelectronics.     

DELAYED FLUORESCENCE AND THE REVERSAL OF PRIMARY PHOTOCHEMISTRY IN RHODOPSEUDOMONAS VIRIDIS

Abstract— Delayed fluorescence from chromatophores of the photosynthetic bacterium Rhodopseudomonas viridis was measured at temperatures below 0°C. A component with a decay half-time of about 7 ms was found. Its intensity was directly proportional to the number of reaction centers in the P985⁺·A^- state. During prolonged illumination it faded as electrons moved forward along the electron transport chain from the primary acceptor, A, (P985⁺·A^-→P985⁺·A), and its decay in the dark paralleled the disappearence of the P985⁺ electron paramagnetic resonance absorption. The data suggest that this component of delayed fluorescence results from a direct reversal of the primary light reaction. While the rate of the P985⁺middot;A^-→P985·A reaction was almost independent of temperature, delayed fluorescence intensity displayed an apparent activation energy of 0°2 eV. It is concluded that the P985⁺·A^-→P985·A reaction proceeds by parallel radiative and nonradiative routes. The direct proportionality between delayed fluorescence and the concentration of P985⁺·A^- pairs seems to preclude an involvement of triplet-triplet annihilation or dependence of delayed fluorescence upon the variable prompt fluorescence yield.     

The temperature dependence of radiationless transition rates from ab initio computations

The calculation of radiationless transition rates and of their temperature dependence from first principles is addressed by combining reliable electronic computations of the normal modes of the two electronic states with Kubo's generating function approach for the evaluation of the Franck-Condon weighted density of states. The whole sets of normal modes of the involved cofactors have been employed, taking into account the effects of nuclear equilibrium position displacements, of vibrational frequency changes, and of mixing of the normal modes. Application to the case of the elementary electron transfer step between bacteriopheophytin and ubiquinone cofactors of bacterial photosynthetic reaction centers yields a temperature dependence of the electron transfer rates in very good agreement with the experimental data.     

Electron transfer rates and Franck–Condon factors: an application to the early electron transfer steps in photosynthetic reaction centers

Mechanistic aspects of some of the early electron transfer steps occurring in photosynthetic reaction centers are discussed. Starting from the normal modes of the redox cofactors involved in the electron transfer processes, we show how a series of quantities which regulate electron transfer rates, such as (i) the electron transfer active modes, (ii) the intramolecular reorganization energy, and (iii) the mutual couplings between the vibronic states of the donor and the acceptor, can be obtained and used to draw qualitative conclusions on ET rates.     

The revision of the model of primary energy conversion in purple bacteria

A simulation method is suggested which enables one to check whether a model for excitation energy exchange in an ensemble of dye molecules fits available experimental data. In particular, this method may deal with photosynthetic units (PSUs) in which excitation migration in antenna chlorophylls and their substantial trapping in reaction centers (RCs) take place. Its application to the purple bacteria has proved that the model, which was generally accepted during the last 20-30 years, is in contradiction with recent experimental facts and thus requires modernization. Two physical mechanisms are discussed: femtosecond polarization of mobile hydrogen atoms near the reaction center special pair ("water latch"), and the presence of excitons delocalized over several core-bacteriochlorophylls (BChls). Our considerations give evidence that neither of these mechanisms alone can resolve the conflict, but their cumulative action appears to be sufficient. Unfortunately, these mechanisms were as yet only partially addressed experimentally.     

Triplet exciton lifetime in crystalline pyrene

The triplet exciton lifetime in crystalline pyrene is found to be 140 ± 10 msec at room temperature, over 500 times longer than previously reported values. The temperature dependence of the triplet lifetime has been measured over the range 80–300°K. The rate of bimolecular annihilation of triplet excitons in pyrene is found to be independent of temperature over the range 150–300°K. It is concluded that the transfer of triplet energy within the crystal may be described using the monomer exciton model.     

Time-resolved photoelectron spectroscopy of low-energy excitations of 4×4 C60/Cu(111)

Time-resolved two-photon photoemission is applied to investigate electron dynamics in multiple monolayers (MLs) of ordered fullerite on a copper substrate. The experimental data are analyzed assuming coupled excited state dynamics. Rate equations fitted to these dynamics yield lifetimes of about 80 ps for the lowest unoccupied molecular orbital (LUMO), about 1.2 ns for the singlet exciton and 22 μs for the triplet exciton at a surface temperature of 140 K. For trapped triplet excitons lifetimes up to 200 μs are observed. An increased excitation fluence reduces the lifetime of the excitons due to annihilation. An increased sample temperature slightly reduces the lifetime of the triplet exciton. There is no evident dependence of the exciton lifetimes on the pump photon energy in the range of hν = 2.9 to 3.3 eV. A dependence on the layer thickness (10-20 ML) is not observed as long as more than 9 ML are prepared.