Fluorographene with impurities as a biomimetic light-harvesting medium.

We investigate the prospect of using a two-dimensional material, fluorographene, to mimic the light-harvesting function of natural photosynthetic antennas. We show by quantum chemical calculations that isles of graphene in a fluorographene sheet can act as quasi-molecules similar to natural pigments from which the structures similar in function to photosynthetic antennas can be built. The graphene isles retain enough identity so that they can be used as building blocks to which intuitive design principles of natural photosynthetic antennas can be applied. We examine the excited state properties, stability, and interactions of these building blocks. Constraints put on the antenna structure by the two-dimensionality of the material as well as the discrete nature of fluorographene sheet are studied. We construct a hypothetical energetic funnel out of two types of quasi-molecules to show how a limited number of building blocks can be arranged to bridge the energy gap and spatial separation in excitation energy transfer. Energy transfer rates for a wide range of the system-environment interaction strengths are predicted. We conclude that conditions for the near unity quantum efficiency of energy transfer are likely to be fulfilled in fluorographene with the controlled arrangement of quasi-molecules.

Accuracy of approximate methods for the calculation of absorption-type linear spectra with a complex system-bath coupling.

The accuracy of approximate methods for calculating linear optical spectra depends on many variables. In this study, we fix most of these parameters to typical values found in photosynthetic light-harvesting complexes of plants and determine the accuracy of approximate spectra with respect to exact calculation as a function of the energy gap and interpigment coupling in a pigment dimer. We use a spectral density with the first eight intramolecular modes of chlorophyll a and include inhomogeneous disorder for the calculation of spectra. We compare the accuracy of absorption, linear dichroism, and circular dichroism spectra calculated using the Full Cumulant Expansion (FCE), coherent time-dependent Redfield (ctR), and time-independent Redfield and modified Redfield methods. As a reference, we use spectra calculated with the exact stochastic path integral evaluation method. We find the FCE method to be the most accurate for the calculation of all spectra. The ctR method performs well for the qualitative calculation of absorption and linear dichroism spectra when the pigments are moderately coupled (∼15cm-1), but ctR spectra may differ significantly from exact spectra when strong interpigment coupling (>100cm-1) is present. The dependence of the quality of Redfield and modified Redfield spectra on molecular parameters is similar, and these methods almost always perform worse than ctR, especially when the interpigment coupling is strong or the excitonic energy gap is small (for a given coupling). The accuracy of approximate spectra is not affected by resonance with intramolecular modes for typical system-bath coupling and disorder values found in plant light-harvesting complexes.

Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD2 ansatz.

Effects of non-linear coupling between the system and the bath vibrational modes on the system internal conversion dynamics are investigated using the Dirac-Frenkel variational approach with a newly defined sD2 ansatz. It explicitly accounts for the entangled system electron-vibrational states, while the bath quantum harmonic oscillator states are expanded in a superposition of quantum coherent states. Using a non-adiabatically coupled three-level model, we show that efficient irreversible internal conversion due to quadratic vibrational-bath coupling occurs when the initially populated system vibrational levels are in resonance with the vibrational levels of a lower energy electronic state, also, a non-Gaussian bath wavepacket representation is required. The quadratic system-bath couplings result in broadened and asymmetrically squeezed bath quantum harmonic oscillator wavepackets in the coordinate-momentum phase space.

Exact description of excitonic dynamics in molecular aggregates weakly driven by light.

We present a rigorous theoretical description of excitonic dynamics in molecular light-harvesting aggregates photoexcited by weak-intensity radiation of arbitrary properties. While the interaction with light is included up to the second order, the treatment of the excitation-environment coupling is exact and results in an exact expression for the reduced excitonic density matrix that is manifestly related to the spectroscopic picture of the photoexcitation process. This expression takes fully into account the environmental reorganization processes triggered by the two interactions with light. This is particularly important for slow environments and/or strong excitation-environment coupling. Within the exponential decomposition scheme, we demonstrate how our result can be recast as the hierarchy of equations of motion (HEOM) that explicitly and consistently includes the photoexcitation step. We analytically describe the environmental reorganization dynamics triggered by a delta-like excitation of a single chromophore and demonstrate how our HEOM, in appropriate limits, reduces to the Redfield equations comprising a pulsed photoexcitation and the nonequilibrium Förster theory. We also discuss the relation of our formalism to the combined Born-Markov-HEOM approaches in the case of excitation by thermal light.

Nonequilibrium steady-state picture of incoherent light-induced excitation harvesting.

We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is developed to compute the nonequilibrium steady state (NESS) arising from the interplay between excitation generation, excitation relaxation, dephasing, trapping at the load, and recombination. The NESS is most conveniently described in the so-called preferred basis in which the steady-state excitonic density matrix is diagonal. The NESS properties are examined by relating the preferred-basis description to the descriptions in the site or excitonic bases. Focusing on a model photosynthetic dimer, we find that the NESS in the limit of long trapping time is quite similar to the excited-state equilibrium in which the stationary coherences originate from the excitation-environment entanglement. For shorter trapping times, we demonstrate how the properties of the NESS can be extracted from the time-dependent description of an incoherently driven but unloaded dimer. This relation between stationary and time-dependent pictures is valid, provided that the trapping time is longer than the decay time of dynamic coherences accessible in femtosecond spectroscopy experiments.

How reduced excitonic coupling enhances light harvesting in the main photosynthetic antennae of diatoms.

Strong excitonic interactions are a key design strategy in photosynthetic light harvesting, expanding the spectral cross-section for light absorption and creating considerably faster and more robust excitation energy transfer. These molecular excitons are a direct result of exceptionally densely packed pigments in photosynthetic proteins. The main light-harvesting complexes of diatoms, known as fucoxanthin-chlorophyll proteins (FCPs), are an exception, displaying surprisingly weak excitonic coupling between their chlorophyll (Chl) a's, despite a high pigment density. Here, we show, using single-molecule spectroscopy, that the FCP complexes of Cyclotella meneghiniana switch frequently into stable, strongly emissive states shifted 4-10 nm toward the red. A few percent of isolated FCPa complexes and ∼20% of isolated FCPb complexes, on average, were observed to populate these previously unobserved states, percentages that agree with the steady-state fluorescence spectra of FCP ensembles. Thus, the complexes use their enhanced sensitivity to static disorder to increase their light-harvesting capability in a number of ways. A disordered exciton model based on the structure of the main plant light-harvesting complex explains the red-shifted emission by strong localization of the excitation energy on a single Chl a pigment in the terminal emitter domain due to very specific pigment orientations. We suggest that the specific construction of FCP gives the complex a unique strategy to ensure that its light-harvesting function remains robust in the fluctuating protein environment despite limited excitonic interactions.

Ultrafast energy relaxation in single light-harvesting complexes.

Energy relaxation in light-harvesting complexes has been extensively studied by various ultrafast spectroscopic techniques, the fastest processes being in the sub-100-fs range. At the same time, much slower dynamics have been observed in individual complexes by single-molecule fluorescence spectroscopy (SMS). In this work, we use a pump-probe-type SMS technique to observe the ultrafast energy relaxation in single light-harvesting complexes LH2 of purple bacteria. After excitation at 800 nm, the measured relaxation time distribution of multiple complexes has a peak at 95 fs and is asymmetric, with a tail at slower relaxation times. When tuning the excitation wavelength, the distribution changes in both its shape and position. The observed behavior agrees with what is to be expected from the LH2 excited states structure. As we show by a Redfield theory calculation of the relaxation times, the distribution shape corresponds to the expected effect of Gaussian disorder of the pigment transition energies. By repeatedly measuring few individual complexes for minutes, we find that complexes sample the relaxation time distribution on a timescale of seconds. Furthermore, by comparing the distribution from a single long-lived complex with the whole ensemble, we demonstrate that, regarding the relaxation times, the ensemble can be considered ergodic. Our findings thus agree with the commonly used notion of an ensemble of identical LH2 complexes experiencing slow random fluctuations.

Robust light harvesting by a noisy antenna.

Photosynthetic light harvesting can be very efficient in solar energy conversion while taking place in a highly disordered and noisy physiological environment. This efficiency is achieved by the ultrafast speed of the primary photosynthetic processes, which is enabled by a delicate interplay of quantum effects, thermodynamics and environmental noise. The primary processes take place in light-harvesting antennas built from pigments bound to a fluctuating protein scaffold. Here, we employ ultrafast single-molecule spectroscopy to follow fluctuations of the femtosecond energy transfer times in individual LH2 antenna complexes of purple bacteria. By combining single molecule results with ensemble spectroscopy through a unified theoretical description of both, we show how the protein fluctuations alter the excitation energy transfer dynamics. We find that from the thirteen orders of magnitude of possible timescales from picoseconds to minutes, the relevant fluctuations occur predominantly on a biological timescale of seconds, i.e. in the domain of slow protein motion. The measured spectra and dynamics can be explained by the protein modulating pigment excitation energies only. Moreover, we find that the small spread of pigment mean energies allows for excitation delocalization between the coupled pigments to survive. These unique features provide fast energy transport even in the presence of disorder. We conclude that this is the mechanism that enables LH2 to operate as a robust light-harvester, in spite of its intrinsically noisy biological environment.

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories.

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in a strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

The Role of Resonant Vibrations in Electronic Energy Transfer.

Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.

The role of exciton delocalization in the major photosynthetic light-harvesting antenna of plants.

In the major peripheral plant light-harvesting complex LHCII, excitation energy is transferred between chlorophylls along an energetic cascade before it is transmitted further into the photosynthetic assembly to be converted into chemical energy. The efficiency of these energy transfer processes involves a complicated interplay of pigment-protein structural reorganization and protein dynamic disorder, and the system must stay robust within the fluctuating protein environment. The final, lowest energy site has been proposed to exist within a trimeric excitonically coupled chlorophyll (Chl) cluster, comprising Chls a610-a611-a612. We studied an LHCII monomer with a site-specific mutation resulting in the loss of Chls a611and a612, and find that this mutant exhibits two predominant overlapping fluorescence bands. From a combination of bulk measurements, single-molecule fluorescence characterization, and modeling, we propose the two fluorescence bands originate from differing conditions of exciton delocalization and localization realized in the mutant. Disruption of the excitonically coupled terminal emitter Chl trimer results in an increased sensitivity of the excited state energy landscape to the disorder induced by the protein conformations. Consequently, the mutant demonstrates a loss of energy transfer efficiency. On the contrary, in the wild-type complex, the strong resonance coupling and correspondingly high degree of excitation delocalization within the Chls a610-a611-a612 cluster dampens the influence of the environment and ensures optimal communication with neighboring pigments. These results indicate that the terminal emitter trimer is thus an essential design principle for maintaining the efficient light-harvesting function of LHCII in the presence of protein disorder.

Vibronic coupling explains the ultrafast carotenoid-to-bacteriochlorophyll energy transfer in natural and artificial light harvesters.

The initial energy transfer steps in photosynthesis occur on ultrafast timescales. We analyze the carotenoid to bacteriochlorophyll energy transfer in LH2 Marichromatium purpuratum as well as in an artificial light-harvesting dyad system by using transient grating and two-dimensional electronic spectroscopy with 10 fs time resolution. We find that Förster-type models reproduce the experimentally observed 60 fs transfer times, but overestimate coupling constants, which lead to a disagreement with both linear absorption and electronic 2D-spectra. We show that a vibronic model, which treats carotenoid vibrations on both electronic ground and excited states as part of the system's Hamiltonian, reproduces all measured quantities. Importantly, the vibronic model presented here can explain the fast energy transfer rates with only moderate coupling constants, which are in agreement with structure based calculations. Counterintuitively, the vibrational levels on the carotenoid electronic ground state play the central role in the excited state population transfer to bacteriochlorophyll; resonance between the donor-acceptor energy gap and the vibrational ground state energies is the physical basis of the ultrafast energy transfer rates in these systems.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion.

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Unraveling the nature of coherent beatings in chlorosomes.

Coherent two-dimensional (2D) spectroscopy at 80 K was used to study chlorosomes isolated from green sulfur bacterium Chlorobaculum tepidum. Two distinct processes in the evolution of the 2D spectrum are observed. The first being exciton diffusion, seen in the change of the spectral shape occurring on a 100-fs timescale, and the second being vibrational coherences, realized through coherent beatings with frequencies of 91 and 145 cm(-1) that are dephased during the first 1.2 ps. The distribution of the oscillation amplitude in the 2D spectra is independent of the evolution of the 2D spectral shape. This implies that the diffusion energy transfer process does not transfer coherences within the chlorosome. Remarkably, the oscillatory pattern observed in the negative regions of the 2D spectrum (dominated by the excited state absorption) is a mirror image of the oscillations found in the positive part (originating from the stimulated emission and ground state bleach). This observation is surprising since it is expected that coherences in the electronic ground and excited states are generated with the same probability and the latter dephase faster in the presence of fast diffusion. Moreover, the relative amplitude of coherent beatings is rather high compared to non-oscillatory signal despite the reported low values of the Huang-Rhys factors. The origin of these effects is discussed in terms of the vibronic and Herzberg-Teller couplings.

Vibronic and vibrational coherences in two-dimensional electronic spectra of supramolecular J-aggregates.

In J-aggregates of cyanine dyes, closely packed molecules form mesoscopic tubes with nanometer-diameter and micrometer-length. Their efficient energy transfer pathways make them suitable candidates for artificial light harvesting systems. This great potential calls for an in-depth spectroscopic analysis of the underlying energy deactivation network and coherence dynamics. We use two-dimensional electronic spectroscopy with sub-10 fs laser pulses in combination with two-dimensional decay-associated spectra analysis to describe the population flow within the aggregate. Based on the analysis of Fourier-transform amplitude maps, we distinguish between vibrational or vibronic coherence dynamics as the origin of pronounced oscillations in our two-dimensional electronic spectra.

Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems.

Photosynthetic complexes are exquisitely tuned to capture solar light efficiently, and then transmit the excitation energy to reaction centres, where long term energy storage is initiated. The energy transfer mechanism is often described by semiclassical models that invoke 'hopping' of excited-state populations along discrete energy levels. Two-dimensional Fourier transform electronic spectroscopy has mapped these energy levels and their coupling in the Fenna-Matthews-Olson (FMO) bacteriochlorophyll complex, which is found in green sulphur bacteria and acts as an energy 'wire' connecting a large peripheral light-harvesting antenna, the chlorosome, to the reaction centre. The spectroscopic data clearly document the dependence of the dominant energy transport pathways on the spatial properties of the excited-state wavefunctions of the whole bacteriochlorophyll complex. But the intricate dynamics of quantum coherence, which has no classical analogue, was largely neglected in the analyses-even though electronic energy transfer involving oscillatory populations of donors and acceptors was first discussed more than 70 years ago, and electronic quantum beats arising from quantum coherence in photosynthetic complexes have been predicted and indirectly observed. Here we extend previous two-dimensional electronic spectroscopy investigations of the FMO bacteriochlorophyll complex, and obtain direct evidence for remarkably long-lived electronic quantum coherence playing an important part in energy transfer processes within this system. The quantum coherence manifests itself in characteristic, directly observable quantum beating signals among the excitons within the Chlorobium tepidum FMO complex at 77 K. This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path.

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.

Ultrafast photo-induced charge transfer unveiled by two-dimensional electronic spectroscopy.

The interaction of exciton and charge transfer (CT) states plays a central role in photo-induced CT processes in chemistry, biology, and physics. In this work, we use a combination of two-dimensional electronic spectroscopy (2D-ES), pump-probe measurements, and quantum chemistry to investigate the ultrafast CT dynamics in a lutetium bisphthalocyanine dimer in different oxidation states. It is found that in the anionic form, the combination of strong CT-exciton interaction and electronic asymmetry induced by a counter-ion enables CT between the two macrocycles of the complex on a 30 fs timescale. Following optical excitation, a chain of electron and hole transfer steps gives rise to characteristic cross-peak dynamics in the electronic 2D spectra, and we monitor how the excited state charge density ultimately localizes on the macrocycle closest to the counter-ion within 100 fs. A comparison with the dynamics in the radical species further elucidates how CT states modulate the electronic structure and tune fs-reaction dynamics. Our experiments demonstrate the unique capability of 2D-ES in combination with other methods to decipher ultrafast CT dynamics.

Hidden vibronic and excitonic structure and vibronic coherence transfer in the bacterial reaction center.

We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden vibronic and excitonic structure. Through analysis of the coherent dynamics of the BRC, we identify multiple quasi-resonances between pigment vibrations and excitonic energy gaps, and vibronic coherence transfer processes that are typically neglected in standard models of photosynthetic energy transfer and charge separation. We support our assignment with control experiments on bacteriochlorophyll and simulations of the coherent dynamics using a reduced excitonic model of the BRC. We find that specific vibronic coherence processes can readily reveal weak exciton transitions. While the functional relevance of such processes is unclear, they provide a spectroscopic tool that uses vibrations as a window for observing excited state structure and dynamics elsewhere in the BRC via vibronic coupling. Vibronic coherence transfer reveals the upper exciton of the "special pair" that was weakly visible in previous 2DES experiments.

Decoherence in weakly coupled excitonic complexes.

Equations of motion for weakly coupled excitonic complexes are derived. The description allows one to treat the system in the basis of electronic states localized on individual chromophores while at the same time accounting for experimentally observable delocalization effects in optical spectra. The equations are shown to be related to the well-known Förster type energy-transfer rate equations, but unlike Förster equations, they provide a description of the decoherence processes leading to suppression of the resonance coupling by bath fluctuations. Linear absorption and two-dimensional photon echo correlation spectra are calculated for simple model systems in the homogeneous limit, demonstrating a distinct delocalization effect and reduction of the resonance coupling due to interaction with the bath.