Excitation energy transfer pathways in light‐harvesting proteins: Modeling with PyFREC

Excitation energy transfer (EET) determines the fate of sunlight energy absorbed by light‐harvesting proteins in natural photosynthetic systems and photovoltaic cells. As previously reported (D. Kosenkov, J. Comput. Chem. 2016, 37(19), 1847), PyFREC software enables computation of electronic couplings between organic molecules with a molecular fragmentation approach. The present work reports implementation of direct fragmentation‐based computation of the electronic couplings and EET rates in pigment–protein complexes within the Förster theory in PyFREC. The new feature enables assessment of EET pathways in a wide range of photosynthetic complexes, as well as artificial molecular architectures that include light‐harvesting proteins or tagged fluorescent biomolecules. The developed methodology has been tested analyzing EET in the Fenna–Matthews–Olson (FMO) pigment–protein complex. The pathways of excitation energy transfer in FMO have been identified based on the kinetics studies. © 2017 Wiley Periodicals, Inc.     

A simplified approach for the coupling of excitation energy transfer

A simplified approach for computing the electronic coupling of nonradiative excitation-energy transfer is proposed by following Scholes et al.’s construction on the initial and final states [G.D. Scholes, R.D. Harcourt, K.P. Ghiggino, J. Chem. Phys. 102 (1995) 9574]. The simplification is realized through defining a set of orthogonalized localized MOs, which include the polarization effect of the charge densities. The method allows calculating the coupling of both the singlet-to-singlet and triplet-to-triplet energy transfer. Numerical tests are performed for a few of dimers with different intermolecular orientations, and the results demonstrate that Coulomb term are the major contribution to the coupling of singlet-to-singlet energy transfer whereas in the case of triplet-to-triplet energy transfer, the dominant effect is arisen from the intermolecular charge-transfer states. The present application is on the Hartree-Fock level. However, the correlated wavefunctions which are normally expanded in terms of the determinant wavefunctions can be employed in the similar way.     

Azobenzene‐Bridged Porphyrin Nanorings: Syntheses,Structures, and Photophysical Properties

Azobenzene‐bridged β‐to‐β and meso‐to‐meso porphyrin nanorings were successfully synthesized by a palladium‐catalyzed Suzuki–Miyaura coupling reaction in a logical synthesis. The dimeric structure was confirmed by XRD analysis. The azo linkages in di‐ and tetramers are in the all‐trans conformation, whereas in the trimers one azo linkage can be interconverted between cis and trans under external stimulation. When trimeric isomers are heated to 333 K or higher, the azo linkages will be in the all‐trans configurations: the pure all‐trans trimer can be kept in the dark for several months. Fluorescence anisotropy and pump‐power‐dependent decay results revealed excitation energy transfer for azobenzene‐bridged zinc–porphyrin nanorings. The distances between porphyrin units of these azobenzene‐bridged porphyrin arrays are almost the same, but the exciton energy hopping (EEH) times for each wheel are markedly different. The dimer and meso‐to‐meso tetramer possess relatively short excitation energy transfer (EET) times (1.28 and 2.48 ps, respectively) due to their good planarity and rigidity. In contrast, the EET time for the trimeric zinc(II)–porphyrin array (6.9 ps) is relatively long due to its nonradiative decay pathway (i.e., cis/trans isomerization of azobenzene). Both di‐ and tetramers exhibit relatively high fluorescence quantum yields, whereas the trimers show weak emission because of structural differences.     

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.     

Efficient excitation energy transfer in long meso-meso linked Zn(II) porphyrin arrays bearing a 5,15-bisphenylethynylated Zn(II) porphyrin acceptor

Electronically coupled porphyrin arrays are suitable for artificial light harvesting antenna in light of a large absorption cross-section and fast excitation energy transfer (EET). Along this line, an artificial energy transfer model system has been synthesized, comprising of an energy donating meso-meso linked Zn(II) porphyrin array and an energy accepting 5,15-bisphenylethynylated Zn(II) porphyrin linked via a 1,4-phenylene spacer. This includes an increasing number of porphyrins in the meso-meso linked Zn(II) porphyrin array, 1, 2, 3, 6, 12, and 24 (Z1A, Z2A, Z3A, Z6A, Z12A, and Z24A). The intramolecular singlet-singlet EET processes have been examined by means of the steady-state and time-resolved spectroscopic techniques. The steady-state fluorescence comes only from the acceptor moiety in Z1A-Z12A, indicating nearly the quantitative EET. In Z24A that has a molecular length of ca. 217 A, the fluorescence comes largely from the acceptor moiety but partly from the long donor array, indicating that the intramolecular EET is not quantitative. The transient absorption spectroscopy has provided the EET rates in real time scale: (2.5 ps)(-1) for Z1A, (3.3 ps)(-1) for Z2A, (5.5 ps)(-1) for Z3A, (21 ps)(-1) for Z6A, (63 ps)(-1) for Z12A, and (108 ps)(-1) for Z24A. These results have been well explained by a revised F?rster equation (Sumi formula), which takes into account an exciton extending coherently over several porphyrin pigments in the donor array, whose length is not much shorter than the average donor-acceptor distance. Advantages of such strongly coupled porphyrin arrays in light harvesting and transmission are emphasized in terms of fast EET and a large absorption cross-section for incident light.     

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.     

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.     

Bioenergetics and extracellular electron transfer in microbial fuel cells and microbial corrosion

Bioenergetics can be used to analyze the theoretical voltage output of a microbial fuel cell (MFC) and the thermodynamic driving force in microbiologically influenced corrosion (MIC). MFCs involve both inward and outward extracellular electron transfer (EET), whereas only inward EET is behind EET–MIC caused by an electroactive biofilm's harvest of energy from a metal. EET is often rate-limiting, and it is an important process in microbial energy metabolism. EET is critical to the understanding of MFCs and EET–MIC bioelectrochemical processes. Many advances have been made in the past decade on EET by MFC and MIC researchers. Gene manipulations have been used to improve EET in MFCs, leading to enhanced energy output. They have also been used to elucidate the EET processes for better understanding of EET–MIC, which aids in MIC analysis and decision-making of biocide treatment and its efficacy assessment. Researchers are starting to integrate EET knowledge from both fields.     

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.     

Excitation energy transfer in ion pairs of polymethine cyanine dyes: efficiency and dynamics

The present work deals with singlet excitation energy transfer (EET) occurring in contact ion pairs (CIPs) of several anionic oxonol analogues (acting as EE donors) and cationic cyanines (acting as acceptors) characterized by off resonance individual transitions. Combining conductometric and spectroscopic measurements with decreasing solvent polarity, we were able to observe a progressive ion pairing leading first to solvent-separated ion pairs (SSIPs) and then to CIPs. Analysis of the absorption spectra of three selected salts (A2,C1, A2,C2, and A1,C4) in chloroform-toluene mixtures showed that the transformation of SSIP into CIP involves the appearance of a certain exciton coupling, the extent of which decreases regularly with increasing gap between the local excitation energies. Fluorescence excitation spectra showed that EET occurs in CIP, and EET efficiencies were evaluated with a procedure expressly devised for weakly emitting donors. These were between 0.2 and 0.65 for the examined ion pairs involving anions A1 and A2. The spectroscopic study was complemented by a theoretical investigation aimed at establishing the dynamic regime of the observed EET. From classical MD simulations and local full geometry optimizations, A2,C1 and A2,C2 were found to form rather stable sandwich-type CIP structures with interchromophore distances (R) of about 0.45-0.50 nm. The donor-acceptor electronic coupling was calculated in terms of Coulombic interactions between atomic transition charges. For CIP, the electronic coupling was decidedly beyond the limit of the weak coupling required for an incoherent F?rster-type mechanism. Thus, we tried to arrange the EET dynamics within the theory developed by Kimura, Kakitani, and Yamato (J. Phys. Chem. B 2000, 104, 9276) for the intermediate coupling case, which provides analytical expressions of time-dependent occupation probability, EET rate, and coherency in terms of two basic quantities: the electronic coupling and a correlation time related to the Franck-Condon factor. The latter was shown to be primarily modulated by F?rster's spectral overlap integral (related in turn to the excitation energy gap). Calculations were carried out for the three sample systems using three values of the electronic coupling roughly corresponding to CIP, 1.0, and 2.0 nm interchromophore distances. At the CIP distance, EET in both A2,C1 and A2,C2 was predicted to occur with a partial exciton mechanism, very short transfer times (about 10 fs), and high degree of coherence. In A1,C4 (having the largest energy gap), EET was found to occur with a hot-transfer mechanism. More or less hot-transfer dynamics appeared to be retained by all three systems at R = 1.0 nm. Fully incoherent EET appeared to become operative only at distances larger than 2.0 nm.     

Porphyrin‐Ryleneimide Hybrids: Low‐Bandgap Acceptors in Energy‐Transfer Cassettes

Energy‐transfer cassettes consisting of naphthaleneimide‐fused metalloporphyrin acceptors (M=Zn and Pd) and BODIPY donors have been designed and synthesized. These systems have rigid pseudo‐tetrahedral structures with a donor‐acceptor separation of ca. 17.5 Å. Spectroscopic investigations, including femtosecond transient absorption measurements, showed efficient excitation energy transfer (EET) occurring according to the Förster mechanism. Strong fluorescence of the donor units and significant spectral overlap of the donor and acceptor subunits are prerequisites for the efficient EET in these systems.     

Proton Transport in the Outer‐Membrane Flavocytochrome Complex Limits the Rate of Extracellular Electron Transport

The microbial transfer of electrons to extracellularly located solid compounds, termed extracellular electron transport (EET), is critical for microbial electrode catalysis. Although the components of the EET pathway in the outer membrane (OM) have been identified, the role of electron/cation coupling in EET kinetics is poorly understood. We studied the dynamics of proton transport associated with EET in an OM flavocytochrome complex in Shewanella oneidensis MR‐1. Using a whole‐cell electrochemical assay, a significant kinetic isotope effect (KIE) was observed following the addition of deuterated water (D₂O). The removal of a flavin cofactor or key components of the OM flavocytochrome complex significantly increased the KIE in the presence of D₂O to values that were significantly larger than those reported for proton channels and ATP synthase, thus indicating that proton transport by OM flavocytochrome complexes limits the rate of EET.     

When hydroquinone meets methoxy radical: Hydrogen abstraction reaction from the viewpoint of interacting quantum atoms

Interacting Quantum Atoms methodology is used for a detailed analysis of hydrogen abstraction reaction from hydroquinone by methoxy radical. Two pathways are analyzed, which differ in the orientation of the reactants at the corresponding transition states. Although the discrepancy between the two barriers amounts to only 2 kJ/mol, which implies that the two pathways are of comparable probability, the extent of intra‐atomic and inter‐atomic energy changes differs considerably. We thus demonstrated that Interacting Quantum Atoms procedure can be applied to unravel distinct energy transfer routes in seemingly similar mechanisms. Identification of energy components with the greatest contribution to the variation of the overall energy (intra‐atomic and inter‐atomic terms that involve hydroquinone's oxygen and the carbon atom covalently bound to it, the transferring hydrogen and methoxy radical's oxygen), is performed using the Relative energy gradient method. Additionally, the Interacting Quantum Fragments approach shed light on the nature of dominant interactions among selected fragments: both Coulomb and exchange‐correlation contributions are of comparable importance when considering interactions of the transferring hydrogen atom with all other atoms, whereas the exchange‐correlation term dominates interaction between methoxy radical's methyl group and hydroquinone's aromatic ring. This study represents one of the first applications of Interacting Quantum Fragments approach on first order saddle points. © 2018 Wiley Periodicals, Inc.     

Toward a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems

This paper presents a quantum-mechanical study of the intramolecular excitation energy transfer (EET) coupling in naphthalene-bridge-naphthalene systems in gas phase and in solution. ZINDO and TDDFT response schemes are compared using both an exact and an approximate solution. The approximate solution based on a perturbative approach uses the single chromophore properties to reconstruct the real system coupling thus neglecting possible through-bond effects which conversely are accounted for in the exact solution. The comparison of the results of the two approaches with the experiments allows a detailed analysis of the relative importance of through-bond and through-space effects as well as a more complete understanding of the modifications in the EET coupling with the size of the system, the chromophore-chromophore distance, and solvation.