How solvent controls electronic energy transfer and light harvesting: toward a quantum-mechanical description of reaction field and screening effects

This paper presents a quantum-mechanical study of electronic energy transfer (EET) coupling on over 100 pairs of chromophores taken from photosynthetic light-harvesting antenna proteins. Solvation effects due to the protein, intrinsic waters, and surrounding medium are analyzed in terms of screening and reaction field contributions using a model developed recently that combines a linear response approach with the polarizable continuum model (PCM). We find that the screening of EET interactions is quite insensitive to the quantum-mechanical treatment adopted. In contrast, it is greatly dependent on the geometrical details (distance, shape, and orientation) of the chromophore pair considered. We demonstrate that implicit (reaction field) as well as screening effects are dictated mainly by the optical dielectric properties of the host medium, while the effect of the static properties is substantially less important. The empirical distance-dependent screening function we proposed in a recent letter (Scholes, G. D.; Curutchet, C.; Mennucci, B.; Cammi, R.; Tomasi, J. J. Phys. Chem. B 2007, 111, 6978-6982) is analyzed and compared to other commonly used screening factors. In addition, we show that implicit medium effects on the coupling, resulting from changes in the transition densities upon solvation, are strongly dependent on the particular system considered, thus preventing the possibility of defining a general empirical expression for such an effect.     

Energy and charge transfer dynamics in fully decorated benzyl ether dendrimers and their disubstituted analogues

We examine the photophysics of a series of molecules consisting of a benzthiadiazole core surrounded by a network of benzyl ether arms terminated by aminopyrene chromophores, which function as both energy and electron donors. Three classes of molecules are studied: dendrimers whose peripheries are fully decorated with aminopyrene donors (F), disubstituted dendrimers whose peripheries contain only two donors (D), and linear analogues in which a pair of benzyl ether arms link two donors to the central core (L). The electronic energy transfer (EET) and charge transfer (CT) rates are determined by fluorescence lifetime measurements on the energy donors and electron acceptors, respectively. In all three types of molecules, the EET time scales as the square root of the generation number G, consistent with the flexible nature of the benzyl ether framework. Transient anisotropy measurements confirm that donor-donor energy hopping does not play a major role in determining the EET times. The CT dynamics occur on the nanosecond time scale and lead to stretched exponential decays, probably due to conformational disorder. Measurements at 100 degrees C confirm that conformational fluctuations play a role in the CT dynamics. The average CT time increases with G in the L and D molecules but decreases for the F dendrimers. This divergent behavior as G increases is attributed to the competing effects of larger donor-acceptor distances (which lengthen the CT time) versus a larger number of donors (which shorten the average CT time). This work illustrates two important points about light-harvesting and charge-separation dendrimers. First, the use of a flexible dendrimer framework can lead to a more favorable scaling of the EET time (and thus the light-harvesting efficiency) with dendrimer size, relative to what would be expected for a fully extended dendrimer. Second, fully decorated dendrimers can compensate for the distance-dependent slowdown in CT rate as G increases by providing additional pathways for the CT reaction to occur.     

Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory

A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.     

Towards a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems. II. The through-bond contribution

In this paper we present a quantum-mechanical investigation on the mechanisms which promote intramolecular EET coupling. This investigation is done by using a new computational strategy in which we combine a configuration-interaction and a linear response approach. The combined use of these two methods allows a direct identification and a quantification of both "direct" (coulomb and exchange) and through-bond (superexchange and charge-transfer) contributions. In addition, solvent effects are introduced using the polarizable continuum model. The method is applied to a family of naphthalene-bridge-naphthalene and naphthalene-bridge-anthracene systems, and the results obtained are compared with experiments. The results found suggest that the through-bond charge-transfer effects are not significant when the EET goes through permitted excitations on distant chromophores (see DN4 and DN6) while they become as important as (or even more important than) the covalent terms for EETs involving weakly allowed excitations (see A6N). By contrast, the presence of a very short bridge (in DN2) allows a very efficient delocalization of the excitation energy which is also largely modified by the presence of a solvent.     

Theory and calculation for the electronic coupling in excitation energy transfer

Excitation energy transfer (EET) is a process where the electronically excitation is transferred from a donor to an acceptor. EET is widely seen in both natural and in artificial systems, such as light‐harvesting in photosynthesis, the fluorescence resonance energy transfer technique, and the design of light‐emitting molecular devices. In this work, we outline the theories describing both singlet and triplet EET (SEET and TEET) rates, with a focus on the physical nature and computational methods for the electronic coupling factor, an important parameter in predicting EET rates. The SEET coupling is dominated by the Coulomb coupling, and the remaining short‐range coupling is very similar to the TEET coupling. The magnitude of the Coulomb coupling in SEET can vary much, but the contribution of short‐range coupling has been found to be similar across different excited states in naphthalene. The exchange coupling has been believed to be the major physical contribution to the short‐range coupling, but it has been pointed out that other contribution, such as the orbital overlap effect is similar or even larger in strength. The computational aspects and the subsequent physical implication for both SEET and TEET coupling values are summarized in this work. © 2013 The Authors. International Journal of Quantum Chemistry Published by Wiley Periodicals, Inc.     

Reconstitution of bacterial photosynthetic unit in a lipid bilayer studied by single-molecule spectroscopy at 5 K

As a model of photosynthetic unit (PSU), self-assembled aggregates of pigment-protein complexes from photosynthetic bacteria were prepared in a lipid bilayer by reconstitution of the light-harvesting 2 (LH2) complex and light-harvesting 1-reaction center (LH1-RC) complex through detergent removal of their micelles in the presence of lipids. By performing polarization-controlled fluorescence and fluorescence-excitation spectroscopy on single aggregates at a temperature of 5 K, the composition of individual aggregates was determined and excitation energy transfer (EET) between constituent complexes was observed. LH2 and LH1-RC from a bacterium, Rhodobacter (Rb.) sphaeroides, were found to form a trimeric aggregate in which EET takes place from one LH2 to two LH1-RCs. In contrast, a heterodimer of LH2 and LH1-RC in which EET works was found to assemble from a combination of complexes of different bacterial species, that is, LH2 from Rb. sphaeroides and LH1-RC from Rhodopseudomonas (Rps.) palustris.     

Self-assembly of supramolecular light-harvesting arrays from covalent multi-chromophore perylene-3,4:9,10-bis(dicarboximide) building blocks

We report on two multi-chromophore building blocks that self-assemble in solution and on surfaces into supramolecular light-harvesting arrays. Each building block is based on perylene-3,4:9,10-bis(dicarboximide) (PDI) chromophores. In one building block, N-phenyl PDI chromophores are attached at their para positions to both nitrogens and the 3 and 6 carbons of pyromellitimide to form a cross-shaped molecule (PI-PDI(4)). In the second building block, N-phenyl PDI chromophores are attached at their para positions to both nitrogens and the 1 and 7 carbons of a fifth PDI to produce a saddle-shaped molecule (PDI(5)). These molecules self-assemble into partially ordered dimeric structures (PI-PDI(4))(2) and (PDI(5))(2) in toluene and 2-methyltetrahydrofuran solutions with the PDI molecules approximately parallel to one another primarily due to pi-pi interactions between adjacent PDI chromophores. On hydrophobic surfaces, PDI(5) grows into rod-shaped nanostructures of average length 130 nm as revealed by atomic force microscopy. Photoexcitation of these supramolecular dimers in solution gives direct evidence of strong pi-pi interactions between the excited PDI chromophore and other PDI molecules nearby based on the observed formation of an excimer-like state in <130 fs with a lifetime of about 20 ns. Multiple photoexcitations of the supramolecular dimers lead to fast singlet-singlet annihilation of the excimer-like state, which occurs with exciton hopping times of about 5 ps, which are comparable to those observed in photosynthetic light-harvesting proteins from green plants.     

Excitation energy transport processes of porphyrin monomer,dimer, cyclic trimer,and hexamer probed by ultrafast fluorescence anisotropy decay

Femtosecond fluorescence anisotropy measurements for a variety of cyclic porphyrin arrays such as Zn(II)porphyrin m-trimer and hexamer are reported along with o-dimer and monomer as reference molecules. In the porphyrin arrays, a pair of porphyrin moieties are joined together via triphenyl linkage to ensure cyclic and rigid structures. Anisotropy decay times of the porphyrin arrays can be well described by the F?rster incoherent excitation hopping process between the porphyrin units. Exciton coupling strengths of 74 and 264 cm(-1) for the m-trimer and hexamer estimated from the observed excitation energy hopping rates are close to those of B800 and B850, respectively, in the LH2 bacterial light-harvesting antenna. Thus, these cyclic porphyrin array systems have proven to be useful in understanding energy migration processes in a relatively weak interaction regime in light of the similarity in overall structures and constituent chromophores to natural light-harvesting arrays.     

紫色光合细菌ThermochromatiumTepidum捕光天线复合物2的激发态动力学

Thermochromatium (Tch.) tepidum是一种中等嗜热的紫色光合细菌, 最佳生长温度为48-50 ℃; 其捕光天线复合物2 (LH2)含有非均一性脱辅基蛋白和类胡萝卜素(Car), 且高分辨率晶体结构未知. 我们通过超快光谱研究了分别采用去垢剂n-dodecyl-β-D-maltoside (DDM)和lauryldimethylamine oxide (LDAO)制备的LH2的激发态动力学, 观测到由细菌叶绿素(BChl)的Qy态介导的B800-to-B850单重态能量传递过程(时间尺度~1.2 ps, 用DDM制备的LH2), 以及由类胡萝卜素S2态介导的Car-to-Car和Car-to-BChl 单重态能量传递过程(~100 fs). 结果表明C=C共轭双键数目(NC=C)为11和12的两类Car共处于同一LH2复合物中; 相对于源自其它菌种、构成组分相对简单的LH2, Tch. tepidum的LH2中B800-B850的相对取向有较大差异. 本工作发现LH2中低含量类胡萝卜素组分anhydrorhodovibrin (NC=C=12)起着高效“能量陷阱”的作用, 可能是一种重要的光保护机制; 基于类胡萝卜素的超快谱带位移现象提出(OH-)spirilloxanthin(NC=C=13)距BChl分子可能比其它类胡萝卜素更近. 这些研究结果有助于进一步理解苛刻自然条件下生长的Tch. tepidum的捕光和光保护机制.     

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.     

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.     

Light-harvesting in carbonyl-terminated phenylacetylene dendrimers: The role of delocalized excited States and the scaling of light-harvesting efficiency with dendrimer size

The photophysics of a family of conjugated phenylacetylene (PA) light-harvesting dendrimers are studied using steady-state and time-resolved optical spectroscopy. The dendrimers consist of a substituted PA core surrounded by meta-branched PA arms. The total number of PA moieties ranges from 3 (first generation) to 63 (fifth generation). By using an alcohol/ketone substituent at the dendrimer core, we avoid through-space Forster transfer from the peripheral PA donors to the core acceptor (in this case, the carbonyl group), which simplifies the analysis of these molecules relative to the perylene-terminated molecules studied previously. The delocalized excited states previously identified in smaller dendrons are seen in these larger dendrimers as well, and their influence on the intersite electronic energy transfer (EET) is analyzed in terms of a point-dipole Forster model. We find that these new delocalized states can both enhance EET (by decreasing the spatial separation between donor and acceptor) and degrade it (by lowering the emission cross section and shifting the energy, resulting in poorer spectral overlap between donor and acceptor). The combination of these two effects leads to a calculated intersite transfer time of 6 ps, in reasonable agreement with the 5-17 ps range obtained from experiment. In addition to characterizing the electronic states and intersite energy transfer times, we also examine how the overall light-harvesting efficiency scales with dendrimer size. After taking the size dependence of other nonradiative processes, such as excimer formation, into account, the overall dendrimer quenching rate k(Q) is found to decrease exponentially with dendrimer size over the first four generations. This exponential decrease is predicted by simple theoretical considerations and by kinetic models, but the dependence on generation is steeper than expected based on those models, probably due to increased disorder in the larger dendrimers. We discuss the implications of these results for dendrimeric light-harvesting structures based on PA and other chemical motifs.     

Structural induced control of energy transfer within Zn(II)-porphyrin dendrimers

We report on a study of singlet-singlet annihilation kinetics in a series of Zn(II)-porphyrin-appended dendrimers, where the energy transfer efficiency is significantly improved by extending the molecular chain that connects the light-harvesting chromophores to the dendrimeric backbone with one additional carbon. For the largest dendrimer having 64 Zn(II)-porphyrins, only approximately 10% of the excitation intensity is needed in order to observe the same extent of annihilation in the dendrimers with the additional carbon in the connecting chain as compared to those without. Complete annihilation, until only one chromophore remains excited, now occurs within subunits of seven chromophores, when half of the chromophores are excited. The improvement of the annihilation efficiency in the largest dendrimer with 64 porphyrins can be explained by the presence of a the two-step delayed annihilation process, involving energy hopping from excited to nonexcited chromophores prior to annihilation. In the smallest dendrimer with only four chromophores, delayed annihilation is not present, since the direct annihilation process is more efficient than the two-step delayed annihilation process. As the dendrimer size increases and the chances of originally exciting two neighboring chromophores decreases, the delayed annihilation process becomes more visible. The additional carbon, added to the connecting chain, results in more favorable chromophore distances and orientations for energy hopping. Hence, the improved energy transfer properties makes the Zn(II)-porphyrin-appended dendrimers with the additional carbon promising candidates as light-harvesting antennas for artificial photosynthesis.     

Theoretical investigation of electronic excitation energy transfer in bichromophoric assemblies

Electronic excitation energy transfer (EET) rates in rylene diimide dyads are calculated using second-order approximate coupled-cluster theory and time-dependent density functional theory. We investigate the dependence of the EET rates on the interchromophoric distance and the relative orientation and show that Forster theory works quantitatively only for donor-acceptor separations larger than roughly 5 nm. For smaller distances the EET rates are over- or underestimated by Forster theory depending on the respective orientation of the transition dipole moments of the chromophores. In addition to the direct transfer rates we consider bridge-mediated transfer originating from oligophenylene units placed between the chromophores. We find that the polarizability of the bridge significantly enhances the effective interaction. We compare our calculations to single molecule experiments on two types of dyads and find reasonable agreement between theory and experiment.     

A tightly coupled linear array of perylene, bis(porphyrin), and phthalocyanine units that functions as a photoinduced energy-transfer cascade

We have prepared a linear array of chromophores consisting of a perylene input unit, a bis(free base porphyrin) transmission unit, and a free base phthalocyanine output unit for studies in artificial photosynthesis and molecular photonics. The synthesis involved four stages: (1) a rational synthesis of trans-AB2C-porphyrin building blocks each bearing one meso-unsubstituted position, (2) oxidative, meso,meso coupling of the zinc porphyrin monomers to afford a bis(zinc porphyrin) bearing one phthalonitrile group and one iodophenyl group, (3) preparation of a bis(porphyrin)-phthalocyanine array via a mixed cyclization involving the bis(free base porphyrin) and 4-tert-butylphthalonitrile, and (4) Pd-mediated coupling of an ethynylperylene to afford a perylene-bis(porphyrin)-phthalocyanine linear array. The perylene-bis(porphyrin)-phthalocyanine array absorbs strongly across the visible spectrum. Excitation at 490 nm, where the perylene absorbs preferentially, results in fluorescence almost exclusively from the phthalocyanine (phi(f) = 0.78). The excited phthalocyanine forms with time constants of 2 ps (90%) and 13 ps (10%). The observed time constants resemble those of corresponding phenylethyne-linked dyads, including a perylene-porphyrin (< or = 0.5 ps) and a porphyrin-phthalocyanine (1.1 ps (70%) and 8 ps (30%)). The perylene-bis(porphyrin)-phthalocyanine architecture exhibits efficient light-harvesting properties and rapid funneling of energy in a cascade from perylene to bis(porphyrin) to phthalocyanine.     

Excited-state calculations with TD-DFT: from benchmarks to simulations in complex environments

In this perspective, we present an overview of recent progress on Time-Dependent Density Functional Theory (TD-DFT) with a specific focus on its accuracy and on models able to take into account environmental effects, including complex media. To this end, we first summarise recent benchmarks and define an average TD-DFT accuracy in reproducing excitation energies when a conventional approach is used. Next, coupling of TD-DFT with models able to account for different kinds of interactions between a central chromophore and nearby chemical objects (solvent, organic cage, metal as well as semi-conducting surface) is investigated. Examples of application to excitation properties are presented, allowing to briefly describe several recent computational strategies. In addition, an extension of TD-DFT to describe a phenomenon involving interacting chromophores, e.g. the electronic energy transfer (EET), is presented to illustrate that this methodology can be applied to processes beyond the vertical excitation. This perspective therefore aims to provide to non-specialists a flavour of recent trends in the field of simulations of excited states in "realistic" situations.     

Advanced theory of excitation energy transfer in dimers

Previously, we developed a unified theory of the excitation energy transfer (EET) in dimers, which is applicable to all of the cases of excitonic coupling strength (Kimura, A.; Kakitani, T.; Yamato, T. J. Phys. Chem. B 2000, 104, 9276). This theory was formulated only for the forward reaction of the EET. In the present paper, we advanced this theory so that it might include the backward reaction of the EET as well as the forward reaction. This new theory is formulated on the basis of the generalized master equation (GME), without using physically unclear assumptions. Comparing the present result with the previous one, we find that the excitonic coupling strengths of criteria between exciton and partial exciton and between hot transfer and hopping (F?rster) mechanisms are reduced by a factor of 2. The critical coherency eta c is also reduced significantly.     

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.