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.

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.

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.

Anharmonic Molecular Motion Drives Resonance Energy Transfer in peri-Arylene Dyads.

Spectral and dynamical properties of molecular donor-acceptor systems strongly depend on the steric arrangement of the constituents with exciton coupling J as a key control parameter. In the present work we study two peri-arylene based dyads with orthogonal and parallel transition dipoles for donor and acceptor moieties, respectively. We show that the anharmonic multi-well character of the orthogonal dyad's intramolecular potential explains findings from both stationary and time-resolved absorption experiments. While for a parallel dyad, standard quantum chemical estimates of J at 0 K are in good agreement with experimental observations, J becomes vanishingly small for the orthogonal dyad, in contrast to its ultrafast experimental transfer times. This discrepancy is not resolved even by accounting for harmonic fluctuations along normal coordinates. We resolve this problem by supplementing quantum chemical approaches with dynamical sampling of fluctuating geometries. In contrast to the moderate Gaussian fluctuations of J for the parallel dyad, fluctuations for the orthogonal dyad are found to follow non-Gaussian statistics leading to significantly higher effective J in good agreement with experimental observations. In effort to apply a unified framework for treating the dynamics of optical coherence and excitonic populations of both dyads, we employ a vibronic approach treating electronic and selected vibrational degrees on an equal footing. This vibronic model is used to model absorption and fluorescence spectra as well as donor-acceptor transport dynamics and covers the more traditional categories of Förster and Redfield transport as limiting cases.

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.

Quantum biology revisited.

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.

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.

Quantum dissipation driven by electron transfer within a single molecule investigated with atomic force microscopy.

Intramolecular charge transfer processes play an important role in many biological, chemical and physical processes including photosynthesis, redox chemical reactions and electron transfer in molecular electronics. These charge transfer processes are frequently influenced by the dynamics of their molecular or atomic environments, and they are accompanied with energy dissipation into this environment. The detailed understanding of such processes is fundamental for their control and possible exploitation in future technological applications. Most of the experimental studies of the intramolecular charge transfer processes so far have been carried out using time-resolved optical spectroscopies on large molecular ensembles. This hampers detailed understanding of the charge transfer on the single molecular level. Here we build upon the recent progress in scanning probe microscopy, and demonstrate the control of mixed valence state. We report observation of single electron transfer between two ferrocene redox centers within a single molecule and the detection of energy dissipation associated with the single electron transfer.

Signatures of Exciton Delocalization and Exciton-Exciton Annihilation in Fluorescence-Detected Two-Dimensional Coherent Spectroscopy.

Incoherently detected coherent multidimensional spectroscopy is rapidly gaining popularity, promising a different application range and sensitivity than its traditional counterpart. While measuring the same response, the two methods are not equivalent. We present calculations of the fluorescence-detected coherent two-dimensional (F-2DES) spectra of a molecular heterodimer. We compare how the F-2DES technique differs from standard coherently detected two-dimensional (2DES) spectroscopy in measuring exciton delocalization. We analyze which processes contribute to cross-peaks in the zero-waiting-time spectra obtained by the two methods. Strictly on the basis of time-dependent perturbation theory, we study how in both methods the varying degree of cancellation between perturbative contributions gives rise to cross-peaks and we identify exciton annihilation and exciton relaxation contributions to the cross-peak in the zero-waiting-time F-2DES. We propose that time-gated fluorescence detection can be used to isolate the annihilation contribution to F-2DES both to retrieve information equivalent to 2DES spectroscopy and to study the annihilation contribution itself.

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.

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 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.

Polarization-controlled optimal scatter suppression in transient absorption spectroscopy.

Ultrafast transient absorption spectroscopy is a powerful technique to study fast photo-induced processes, such as electron, proton and energy transfer, isomerization and molecular dynamics, in a diverse range of samples, including solid state materials and proteins. Many such experiments suffer from signal distortion by scattered excitation light, in particular close to the excitation (pump) frequency. Scattered light can be effectively suppressed by a polarizer oriented perpendicular to the excitation polarization and positioned behind the sample in the optical path of the probe beam. However, this introduces anisotropic polarization contributions into the recorded signal. We present an approach based on setting specific polarizations of the pump and probe pulses, combined with a polarizer behind the sample. Together, this controls the signal-to-scatter ratio (SSR), while maintaining isotropic signal. We present SSR for the full range of polarizations and analytically derive the optimal configuration at angles of 40.5° between probe and pump and of 66.9° between polarizer and pump polarizations. This improves SSR by (or compared to polarizer parallel to probe). The calculations are validated by transient absorption experiments on the common fluorescent dye Rhodamine B. This approach provides a simple method to considerably improve the SSR in transient absorption spectroscopy.

Study of Electronic Structures and Pigment-Protein Interactions in the Reaction Center of Thermochromatium tepidum with a Dynamic Environment.

On the basis of the recently reported X-ray crystal structure of light-harvesting complex 1-reaction center (LH1-RC) complex from Thermochromatium tepidum, we investigate electronic structures and pigment-protein interactions in the RC complex from a theoretical perspective. Hybrid quantum-mechanics/molecular-mechanics methods in combination with molecular dynamics simulations are employed to study environmental effects on excitation energies of RC cofactors with the consideration of a dynamic environment. The environmental effects are found to be essential for electronic structure determination. The special pair, a dimer of bacteriochlorophylls which serves as the primary electron donor in the bacterial RC, is our focus in this work. The first excited state of the special pair is found to have the lowest excitation energy of all molecules in the system, making it the most likely populated site after the excitation transfer. The transition charges from electrostatic potentials and the point dipole approximation have been applied to calculate the electronic coupling between individual pigments and that between the special pair and other pigments. Stronger electronic coupling is obtained between the PM molecule and the L branch pigments than that between the PM and the pigments in the M branch. Quantum chemical calculations reveal charge transfer characteristics of the first excited state of the special pair. It follows that charge separation takes place along the L branch in the RC. Spectral densities for all the cofactors are also calculated.

Single Molecule Spectroscopy of Monomeric LHCII: Experiment and Theory.

We derive approximate equations of motion for excited state dynamics of a multilevel open quantum system weakly interacting with light to describe fluorescence-detected single molecule spectra. Based on the Frenkel exciton theory, we construct a model for the chlorophyll part of the LHCII complex of higher plants and its interaction with previously proposed excitation quencher in the form of the lutein molecule Lut 1. The resulting description is valid over a broad range of timescales relevant for single molecule spectroscopy, i.e. from ps to minutes. Validity of these equations is demonstrated by comparing simulations of ensemble and single-molecule spectra of monomeric LHCII with experiments. Using a conformational change of the LHCII protein as a switching mechanism, the intensity and spectral time traces of individual LHCII complexes are simulated, and the experimental statistical distributions are reproduced. Based on our model, it is shown that with reasonable assumptions about its interaction with chlorophylls, Lut 1 can act as an efficient fluorescence quencher in LHCII.

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.

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.

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.