Two-dimensional electronic spectroscopy reveals ultrafast energy diffusion in chlorosomes

Chlorosomes are light-harvesting antennae that enable exceptionally efficient light energy capture and excitation transfer. They are found in certain photosynthetic bacteria, some of which live in extremely low-light environments. In this work, chlorosomes from the green sulfur bacterium Chlorobaculum tepidum were studied by coherent electronic two-dimensional (2D) spectroscopy. Previously uncharacterized ultrafast energy transfer dynamics were followed, appearing as evolution of the 2D spectral line-shape during the first 200 fs after excitation. Observed initial energy flow through the chlorosome is well explained by effective exciton diffusion on a sub-100 fs time scale, which assures efficiency and robustness of the process. The ultrafast incoherent diffusion-like behavior of the excitons points to a disordered energy landscape in the chlorosome, which leads to a rapid loss of excitonic coherences between its structural subunits. This disorder prevents observation of excitonic coherences in the experimental data and implies that the chlorosome as a whole does not function as a coherent light-harvester.     

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.     

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.     

Influence of Higher Excited Singlet States on Ultrafast Exciton Motion in Pigment-Protein Complexes

Abstract— Numerical simulations of the ultrafast exciton motion in photosynthetic antenna complexes are used to reproduce measured data of optical pump-probe experiments. Emphasis is put on a chlorophyll aL/chlorophyll b dimer of the light-harvesting complex of the photosystem II of higher plants (LHC-II). To account for intramolecular excited-state absorption the standard exciton theory is extended to the inclusion of a second higher excited singlet state per chlorophyll molecule. The density matrix theory is applied to describe the dissipative dynamics of excitons. Different mechanisms for energy relaxation and dephasing including pure dephasing processes are discussed. As a result, a further refinement of earlier calculations on the one-color pump-probe spectra at the LHC-II can be presented. In particular, the presence of non-Markovian effects with respect to the exciton-vibrational interaction in the LHC-II, discovered previously in the two-color pump-probe spectrum, is demonstrated here for the one-color pump-probe case.     

Excitonic energy transfer in light-harvesting complexes in purple bacteria

Two distinct approaches, the Frenkel-Dirac time-dependent variation and the Haken-Strobl model, are adopted to study energy transfer dynamics in single-ring and double-ring light-harvesting (LH) systems in purple bacteria. It is found that the inclusion of long-range dipolar interactions in the two methods results in significant increase in intra- or inter-ring exciton transfer efficiency. The dependence of exciton transfer efficiency on trapping positions on single rings of LH2 (B850) and LH1 is similar to that in toy models with nearest-neighbor coupling only. However, owing to the symmetry breaking caused by the dimerization of BChls and dipolar couplings, such dependence has been largely suppressed. In the studies of coupled-ring systems, both methods reveal an interesting role of dipolar interactions in increasing energy transfer efficiency by introducing multiple intra/inter-ring transfer paths. Importantly, the time scale (4 ps) of inter-ring exciton transfer obtained from polaron dynamics is in good agreement with previous studies. In a double-ring LH2 system, non-nearest neighbor interactions can induce symmetry breaking, which leads to global and local minima of the average trapping time in the presence of a non-zero dephasing rate, suggesting that environment dephasing helps preserve quantum coherent energy transfer when the perfect circular symmetry in the hypothetic system is broken. This study reveals that dipolar coupling between chromophores may play an important role in the high energy transfer efficiency in the LH systems of purple bacteria and many other natural photosynthetic systems.     

Characterizing quantum-sharing of electronic excitation in molecular aggregates

A key and long standing question regarding the function of photosynthetic systems concerns the advantages that delocalized electronic excitations and their coherent dynamics could offer to robust and efficient energy transfer within and between photosynthetic light-harvesting complexes. Here we discuss how the framework of entanglement can be used to characterize the strength and spatial distribution of electronic coherences in biomolecular aggregates, why this is interesting, and how one can go about investigating possible relations between non-vanishing electronic coherences and efficient excitation transfer from donors to acceptors. As an example we discuss how certain coherences may correlate to efficient energy transfer in the Fenna-Mathews-Olson complex. Perspectives about understanding advantages of coherence-assisted energy transfer are discussed.     

The Excitation Spectra of Naphthalene Dimers: Frenkel and Charge‐transfer Excitons

Vertical electronic excitation energies have been calculated at the second‐order approximate coupled‐cluster (CC2) level for a series of dimeric naphthalene systems. The calculated excitation energies are compared with values obtained for a single naphthalene molecule and provide information about the coupling between the naphthalene moieties in the dimers. The calculations show that the coupling between the naphthalenes depends on the distance and the energy of the exciton. At long distances and high energies the excitons on the two naphthalenes are strongly coupled, whereas the excitation energies of the few lowest states are almost unaffected by the presence of the neighboring molecules. We have also analyzed the composition of the dimeric states that consist of the individual monomer states, to investigate the charge‐transfer (CT) and the Frenkel character of the excitons. Our results indicate that the CT exciton exists at short distances, and that its population drops as the distance between the two naphthalene increases.     

DNA scaffold supports long-lived vibronic coherence in an indodicarbocyanine (Cy5) dimer

Vibronic coupling between pigment molecules is believed to prolong coherences in photosynthetic pigment–protein complexes. Reproducing long-lived coherences using vibronically coupled chromophores in synthetic DNA constructs presents a biomimetic route to efficient artificial light harvesting. Here, we present two-dimensional (2D) electronic spectra of one monomeric Cy5 construct and two dimeric Cy5 constructs (0 bp and 1 bp between dyes) on a DNA scaffold and perform beating frequency analysis to interpret observed coherences. Power spectra of quantum beating signals of the dimers reveal high frequency oscillations that correspond to coherences between vibronic exciton states. Beating frequency maps confirm that these oscillations, 1270 cm⁻¹ and 1545 cm⁻¹ for the 0-bp dimer and 1100 cm⁻¹ for the 1-bp dimer, are coherences between vibronic exciton states and that these coherences persist for ∼300 fs. Our observations are well described by a vibronic exciton model, which predicts the excitonic coupling strength in the dimers and the resulting molecular exciton states. The energy spacing between those states closely corresponds to the observed beat frequencies. MD simulations indicate that the dyes in our constructs lie largely internal to the DNA base stacking region, similar to the native design of biological light harvesting complexes. Observed coherences persist on the timescale of photosynthetic energy transfer yielding further parallels to observed biological coherences, establishing DNA as an attractive scaffold for synthetic light harvesting applications.

Dyes coupled to DNA display distance-dependent vibronic couplings that prolongs quantum coherences detected with 2D spectroscopy.     

Ab inito study on triplet excitation energy transfer in photosynthetic light-harvesting complexes

We have studied the triplet energy transfer (TET) for photosynthetic light-harvesting complexes, the bacterial light-harvesting complex II (LH2) of Rhodospirillum molischianum and Rhodopseudomonas acidophila, and the peridinin-chlorophyll a protein (PCP) from Amphidinium carterae. The electronic coupling factor was calculated with the recently developed fragment spin difference scheme (You and Hsu, J. Chem. Phys. 2010, 133, 074105), which is a general computational scheme that yields the overall coupling under the Hamiltonian employed. The TET rates were estimated based on the couplings obtained. For all light-harvesting complexes studied, there exist nanosecond triplet energy transfer from the chlorophylls to the carotenoids. This result supports a direct triplet quenching mechanism for the photoprotection function of carotenoids. The TET rates are similar for a broad range of carotenoid triplet state energy, which implies a general and robust TET quenching role for carotenoids in photosynthesis. This result is also consistent with the weak dependence of TET kinetics on the type or the number of π conjugation lengths in the carotenoids and their analogues reported in the literature. We have also explored the possibility of forming triplet excitons in these complexes. In B850 of LH2 or the peridinin cluster in PCP, it is unlikely to have triplet exciton since the energy differences of any two neighboring molecules are likely to be much larger than their TET couplings. Our results provide theoretical limits to the possible photophysics in the light-harvesting complexes.     

Energy transfer via guest excitons in isotopic mixed naphthalene crystals

The temperature dependence of the fluorescence spectra of aggregates in naphthalene-perdeuteronaphthalene mixed crystals has been investigated between 1.4 and 70 K and for concentrations up to 50% naphthalene. It is shown that the most abundant traps — the monomer guest molecules — transfer energy like a guest exciton band 48 cm^?1 below the host exciton band. With increasing temperature, the excitation energy is redistributed between the different aggregate traps by thermal activation into the monomer states. The energy transfer constant within the monomer exciton band is measured as a function of concentration. It is suggested that dipole-dipole interaction between the monomer guests is responsible for the energy transfer via guest excitons.     

Mapping the spatial overlap of excitons in a photosynthetic complex via coherent nonlinear frequency generation

We experimentally demonstrate a nonlinear spectroscopic method that is sensitive to exciton-exciton interactions in a Frenkel exciton system. Spatial overlap of one-exciton wavefunctions leads to coupling between them, resulting in two-exciton eigenstates that have the character of many single-exciton pairs. The mixed character of the two-exciton wavefunctions gives rise to a four-wave-mixing nonlinear frequency generation signal. When only part of the linear excitation spectrum of the complex is excited with three spectrally tailored pulses with separate spatial directions, a frequency-shifted third-order nonlinear signal emerges in the phase-matched direction. We employ the nonlinear response function formalism to show that the emergence of the signal is mediated by and carries information about the two-exciton eigenstates of the system. We report experimental results for nonlinear frequency generation in the Fenna-Matthews-Olson (FMO) photosynthetic pigment-protein complex. Our theoretical analysis of the signal from FMO confirms that the emergence of the frequency-shifted signal is due to the interaction of spatially overlapped excitons. In this method, the signal intensity is directly measured in the frequency domain and does not require scanning of pulse delays or signal phase retrieval. The wavefunctions of the two-exciton states contain information about the spatial overlap of excitons and can be helpful in identifying coupling strengths and relaxation pathways. We propose this method as a facile experimental means of studying exciton correlations in systems with complicated electronic structures.     

Excitation energy transfer between closely spaced multichromophoric systems: effects of band mixing and intraband relaxation

We theoretically analyze the excitation energy transfer between two closely spaced linear molecular J-aggregates, whose excited states are Frenkel excitons. The aggregate with the higher (lower) exciton band edge energy is considered as the donor (acceptor). The celebrated theory of F?rster resonance energy transfer (FRET), which relates the transfer rate to the overlap integral of optical spectra, fails in this situation. We point out that, in addition to the well-known fact that the point-dipole approximation breaks down (enabling energy transfer between optically forbidden states), also the perturbative treatment of the electronic interactions between donor and acceptor system, which underlies the F?rster approach, in general loses its validity due to overlap of the exciton bands. We therefore propose a nonperturbative method, in which donor and acceptor bands are mixed and the energy transfer is described in terms of a phonon-assisted energy relaxation process between the two new (renormalized) bands. The validity of the conventional perturbative approach is investigated by comparing to the nonperturbative one; in general, this validity improves for lower temperature and larger distances (weaker interactions) between the aggregates. We also demonstrate that the interference between intraband relaxation and energy transfer renders the proper definition of the transfer rate and its evaluation from experiment a complicated issue that involves the initial excitation condition. Our results suggest that the best way of determining this transfer rate between two J-aggregates is to measure the fluorescence kinetics of the acceptor J-band after resonant excitation of the donor J-band.     

Two-dimensional spectroscopy can distinguish between decoherence and dephasing of zero-quantum coherences

Recent experiments on a variety of photosynthetic antenna systems have revealed that coherences among electronic states persist longer than previously anticipated. In an ensemble measurement, the observed dephasing of a coherent state can occur because of either disorder across the ensemble or decoherence from interactions with the bath. Distinguishing how much such disorder affects the experimentally observed dephasing rate is paramount for understanding the role that quantum coherence may play in energy transfer through these complexes. Here, we show that two-dimensional electronic spectra can distinguish between the limiting cases of homogeneous dephasing (decoherence) and inhomogeneous dephasing by examining how the quantum beat frequency changes within a cross peak. For the antenna complex LH2 isolated from Rhodobacter sphaeroides , we find that dephasing of the coherence between the B850 and B800 rings arises predominantly from inhomogeneity. In contrast, within the Fenna-Matthews-Olson (FMO) complex from Chlorobium tepidum , dephasing of the coherence between the first two excitons appears quite homogeneous. Thus, the observed dephasing rate sets an upper bound on decoherence for the LH2 complex while establishing both an upper and lower bound for the FMO complex.     

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.     

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.     

A molecular spectroscopic view of surface plasmon enhanced resonance Raman scattering

The enhancement of resonance Raman scattering by coupling to the plasmon resonance of a metal nanoparticle is developed by treating the molecule-metal interaction as transition dipole coupling between the molecular electronic transition and the much stronger optical transition of the nanoparticle. A density matrix treatment accounts for coupling of both transitions to the electromagnetic field, near-resonant energy transfer between the molecule-excited and nanoparticle-excited states, and dephasing processes. This fully quantum mechanical approach reproduces the interference effects observed in extinction spectra of J-aggregated dyes adsorbed to metal nanoparticles and makes testable predictions for surface-enhanced resonance Raman excitation profiles.     

Exciton migration by ultrafast Förster transfer in highly doped matrixes

The energy transfer between dye molecules and the mobility of the corresponding excitons are investigated in polymethyl methacrylate films highly doped with perylene bisimide dyes. The dynamics is measured by group delay corrected, femtosecond broad-band spectroscopy revealing the transfer route via absorption changes that are specific for the participating species. In films doped with 0.14 M perylene orange an ultrafast homotransfer between the dye molecules is found by analyzing the loss of the excitation-induced anisotropy. The process exhibits a stretched exponential time dependence which is characteristic for F?rster energy transfer between immobilized molecules. The transfer time is 1.5 ps for an average transfer distance of 2.3 nm and results in a high mobility of the optically generated excitons. In addition, we find that the excitons move to perylene orange dimers, which have formed in low concentration during the sample preparation. The observed energy transfer time is slightly shorter than expected for a direct F?rster transfer and indicates that exciton migration by multistep transfer between the monomers speeds up the transport to the dimers. In samples doped with perylene orange and perylene red heterotransfer to perylene red takes place with transfer times down to 600 fs. The mechanism is F?rster transfer as demonstrated by the agreement with calculations assuming electric dipole interaction between immobilized and statistically distributed donor and acceptor units. The model predicts the correct time dependence and concentration scaling for highly doped as well as diluted samples. The results show that ultrafast exciton migration between dye molecules in highly doped matrixes is an attractive and efficient mechanism to transport and collect energy in molecular systems and organic electronic devices. Further optimization should lead to a loss-free transport over distances typical for the thickness of active layers in these systems.     

Delayed-fluorescence ODMR and EPR studies of triplet excitons in charge-transfer molecular crystals

Triplet excitons in electron donor—acceptor charge-transfer (CT) molecular crystals are generated through the intersystem crossing process by excitation in the CT visible band and give rise to delayed fluorescence. Delayed-fluorescence optically detected magnetic resonance (DF ODMR) in magnetic field is analyzed in terms of microwave-induced transitions between energy levels of either the isolated triplet excitons or the annihilating triplet exciton pair. The spin polarization of the triplet excitons plays an important role in the described phenomena. A comparison between DF ODMR and EPR spectra of the anthracene—tetracyanobenzene and biphenyl—tetracyanobenzene systems is presented. In the former case the microwave transitions occurring between free exciton sublevels are predominantly responsible of the DF ODMR signal, whereas the transitions between energy levels of the exciton pair are the most important for biphenyl—TCNB.     

Mixed frequency/time domain optical analogues of heteronuclear multidimensional NMR

Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.     

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.