Energy-Transfer Dynamics in the LHCII Complex of Higher Plants: Modified Redfield Approach

Probing the Effect of Mutations on Light Harvesting in CP29 by Transient Absorption and First-Principles Simulations

Natural light harvesting is exceptionally efficient thanks to the local energy funnel created within light-harvesting complexes (LHCs). To understand the design principles underlying energy transport in LHCs, ultrafast spectroscopy is often complemented by mutational studies that introduce perturbations into the excitonic structure of the natural complexes. However, such studies may fall short of identifying all excitation energy transfer (EET) pathways and their changes upon mutation. Here, we show that a synergistic combination of first-principles calculations and ultrafast spectroscopy can give unprecedented insight into the EET pathways occurring within LHCs. We measured the transient absorption spectra of the minor CP29 complex of plants and of two mutants, systematically mapping the kinetic components seen in experiments to the simulated exciton dynamics. With our combined strategy, we show that EET in CP29 is surprisingly robust to the changes in the exciton states induced by mutations, explaining the versatility of plant LHCs.

General framework for quantifying dissipation pathways in open quantum systems. I. Theoretical formulation

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.

Insights into Energy Transfer in Light-Harvesting Complex II Through Machine-Learning Assisted Simulations

Light-harvesting complex II (LHCII) is the major antenna of higher plants. Energy transfer processes taking place inside its aggregate of chlorophylls have been experimentally investigated with time-resolved techniques, but a complete understanding of the most relevant energy transfer pathways and relative characteristic times remains elusive. Theoretical models to disentangle experimental data in LHCII have long been challenged by the large size and complex nature of the system. Here, we show that a fully first-principles approach combining molecular dynamics and machine learning can be successfully used to reproduce transient absorption spectra and characterize the EET pathways and the involved times.

Protein Effects on the Excitation Energies and Exciton Dynamics of the CP24 Antenna Complex

In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales.

Electric Field Susceptibility of Chlorophyll c Leads to Unexpected Excitation Dynamics in the Major Light-Harvesting Complex of Diatoms

Diatoms are one of the most abundant photosynthetic organisms on earth and contribute largely to atmospheric oxygen production. They contain fucoxanthin and chlorophyll-a/c binding proteins (FCPs) as light-harvesting complexes with a remarkable adaptation to the fluctuating light on ocean surfaces. To understand the basis of the photosynthetic process in diatoms, the excitation energy funneling within FCPs must be probed. A state-of-the-art multiscale analysis within a quantum mechanics/molecular mechanics framework has been employed. To this end, the chlorophyll (Chl) excitation energies within the FCP complex from the diatom Phaeodactylum tricornutum have been determined. The Chl-c excitation energies were found to be 5-fold more susceptible to electric fields than those of Chl-a pigments and thus are significantly lower in FCP than in organic solvents. This finding challenges the general belief that the excitation energy of Chl-c is always higher than that of Chl-a in FCP proteins and reveals that Chl-c molecules are much more sensitive to electric fields within protein scaffolds than in Chl-a pigments. The analysis of the linear absorption spectrum and the two-dimensional electronic spectra of the FCP complex strongly supports these findings and allows us to study the excitation transfer within the FCP complex.

Unravelling the fluorescence kinetics of light-harvesting proteins with simulated measurements

The plant light-harvesting pigment-protein complex LHCII is the major antenna sub-unit of PSII and is generally (though not universally) accepted to play a role in photoprotective energy dissipation under high light conditions, a process known Non-Photochemical Quenching (NPQ). The underlying mechanisms of energy trapping and dissipation within LHCII are still debated. Various models have been proposed for the underlying molecular detail of NPQ, but they are often based on different interpretations of very similar transient absorption measurements of isolated complexes. Here we present a simulated measurement of the fluorescence decay kinetics of quenched LHCII aggregates to determine whether this relatively simple measurement can discriminate between different potential NPQ mechanisms. We simulate not just the underlying physics (excitation, energy migration, quenching and singlet-singlet annihilation) but also the signal detection and typical experimental data analysis. Comparing this to a selection of published fluorescence decay kinetics we find that: (1) Different proposed quenching mechanisms produce noticeably different fluorescence kinetics even at low (annihilation free) excitation density, though the degree of difference is dependent on pulse width. (2) Measured decay kinetics are consistent with most LHCII trimers becoming relatively slow excitation quenchers. A small sub-population of very fast quenchers produces kinetics which do not resemble any observed measurement. (3) It is necessary to consider at least two distinct quenching mechanisms in order to accurately reproduce experimental kinetics, supporting the idea that NPQ is not a simple binary switch.

Mapping electronic decoherence pathways in molecules

Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in [Formula: see text]30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it.

First-principles simulation of excitation energy transfer and transient absorption spectroscopy in the CP29 light-harvesting complex

The dynamics of delocalized excitons in light-harvesting complexes (LHCs) can be investigated using different experimental techniques, and transient absorption (TA) spectroscopy is one of the most valuable methods for this purpose. A careful interpretation of TA spectra is essential for the clarification of excitation energy transfer (EET) processes occurring during light-harvesting. However, even in the simplest LHCs, a physical model is needed to interpret transient spectra as the number of EET processes occurring at the same time is very large to be disentangled from measurements alone. Physical EET models are commonly built by fittings of the microscopic exciton Hamiltonians and exciton-vibrational parameters, an approach that can lead to biases. Here, we present a first-principles strategy to simulate EET and transient absorption spectra in LHCs, combining molecular dynamics and accurate multiscale quantum chemical calculations to obtain an independent estimate of the excitonic structure of the complex. The microscopic parameters thus obtained are then used in EET simulations to obtain the population dynamics and the related spectroscopic signature. We apply this approach to the CP29 minor antenna complex of plants for which we follow the EET dynamics and transient spectra after excitation in the chlorophyll b region. Our calculations reproduce all the main features observed in the transient absorption spectra and provide independent insight on the excited-state dynamics of CP29. The approach presented here lays the groundwork for the accurate simulation of EET and unbiased interpretation of transient spectra in multichromophoric systems.

The location of the low-energy states in Lhca1 favors excitation energy transfer to the core in the plant PSI-LHCI supercomplex

Lhca1 is one of the four pigment-protein complexes composing the outer antenna of plant Photosystem I-light-havesting I supercomplex (PSI-LHCI). It forms a functional dimer with Lhca4 but, differently from this complex, it does not contain 'red-forms,' i.e., pigments absorbing above 700 nm. Interestingly, the recent PSI-LHCI structures suggest that Lhca1 is the main point of delivering the energy harvested by the antenna to the core. To identify the excitation energy pathways in Lhca1, we developed a structure-based exciton model based on the simultaneous fit of the low-temperature absorption, linear dichroism, and fluorescence spectra of wild-type Lhca1 and two mutants, lacking chlorophylls contributing to the long-wavelength region of the absorption. The model enables us to define the locations of the lowest energy pigments in Lhca1 and estimate pathways and timescales of energy transfer within the complex and to the PSI core. We found that Lhca1 has a particular energy landscape with an unusual (compared to Lhca4, LHCII, and CP29) configuration of the low-energy states. Remarkably, these states are located near the core, facilitating direct energy transfer to it. Moreover, the low-energy states of Lhca1 are also coupled to the red-most state (red forms) of the neighboring Lhca4 antenna, providing a pathway for effective excitation energy transfer from Lhca4 to the core.

Revealing Intermolecular Electronic and Vibronic Coherence with Polarization-Dependent Two-Dimensional Beating Maps

Two-dimensional electronic spectroscopy (2DES) has been widely employed as an efficient tool to reveal the impact of intermolecular electronic and/or vibronic quantum coherence on excitation energy transfer in light-harvesting complexes. However, intramolecular vibrational coherence would also contribute to oscillating signals in 2D spectra, along with the intermolecular coherence signals that are directly related to energy transfer. In this work, the possibility of screening the vibrational coherence signals is explored through polarization-dependent 2DES. The all-parallel (AP) and double-crossed (DC) polarization-dependent two-dimensional rephasing spectra (2DRS) are simulated for a minimalist heterodimer model with vibrational coupling. By combining the DC-2DRS and the 2D beating maps, we demonstrate that the population and vibrational coherence signals can be largely suppressed, resulting in highlighted intermolecular electronic and vibronic coherence signals. Moreover, the AP- and DC-2DBMs show rather different patterns at the vibrational frequency, indicating a possible way to identify pure vibrational coherence.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Enhancing the spectral range of plant and bacterial light-harvesting pigment-protein complexes with various synthetic chromophores incorporated into lipid vesicles

The Light-Harvesting (LH) pigment-protein complexes found in photosynthetic organisms have the role of absorbing solar energy with high efficiency and transferring it to reaction centre complexes. LH complexes contain a suite of pigments that each absorb light at specific wavelengths, however, the natural combinations of pigments within any one protein complex do not cover the full range of solar radiation. Here, we provide an in-depth comparison of the relative effectiveness of five different organic "dye" molecules (Texas Red, ATTO, Cy7, DiI, DiR) for enhancing the absorption range of two different LH membrane protein complexes (the major LHCII from plants and LH2 from purple phototrophic bacteria). Proteoliposomes were self-assembled from defined mixtures of lipids, proteins and dye molecules and their optical properties were quantified by absorption and fluorescence spectroscopy. Both lipid-linked dyes and alternative lipophilic dyes were found to be effective excitation energy donors to LH protein complexes, without the need for direct chemical or generic modification of the proteins. The Förster theory parameters (e.g., spectral overlap) were compared between each donor-acceptor combination and found to be good predictors of an effective dye-protein combination. At the highest dye-to-protein ratios tested (over 20:1), the effective absorption strength integrated over the full spectral range was increased to ∼180% of its natural level for both LH complexes. Lipophilic dyes could be inserted into pre-formed membranes although their effectiveness was found to depend upon favourable physicochemical interactions. Finally, we demonstrated that these dyes can also be effective at increasing the spectral range of surface-supported models of photosynthetic membranes, using fluorescence microscopy. The results of this work provide insight into the utility of self-assembled lipid membranes and the great flexibility of LH complexes for interacting with different dyes.

Controlling photosynthetic energy conversion by small conformational changes

Control phenomena in biology usually refer to changes in gene expression and protein translation and modification. In this paper, another mode of regulation is highlighted; we propose that photosynthetic organisms can harness the interplay between localization and delocalization of energy transfer by utilizing small conformational changes in the structure of light-harvesting complexes. We examine the mechanism of energy transfer in photosynthetic pigment-protein complexes, first through the scope of theoretical work and then by in vitro studies of these complexes. Next, the biological relevance to evolutionary fitness of this localization-delocalization switch is explored by in vivo experiments on desert crust and marine cyanobacteria, which are both exposed to rapidly changing environmental conditions. These examples demonstrate the flexibility and low energy cost of this mechanism, making it a competitive survival strategy.

Fingerprint and Universal Markovian Closure of Structured Bosonic Environments

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely, a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speedup with respect to standard chain mapping techniques and makes the memory requirement independent of the simulation time, while preserving all the information on the fingerprint modes. We illustrate the application of the Markovian closure to the computation of linear spectra but also to nonlinear spectral response, a relevant experimentally accessible many body coherence witness for which efficient numerically exact calculations in realistic environments are currently lacking.

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 pigments are moderately coupled (∼15 cm-1), but ctR spectra may differ significantly from exact spectra when strong interpigment coupling (>100 cm-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.

Bethe-Salpeter equation insights into the photo-absorption function and exciton structure of chlorophyll a and b in light-harvesting complex II

The photo-absorption process and the excitation of chlorophyll (Chl) is the primary and essential step of photosynthesis in green plants. By solving the Bethe-Salpeter equation (BSE) on top of the GW approximation within ab initio many-body perturbation theory, we calculate the photo-absorption function and the excitons structure of Chl a and b in their in vivo conformations as measured by X-ray diffraction in the light-harvesting complex (LHC) II. BSE optical absorption spectra are in good agreement with the experiment and we discuss residual discrepancies. The experimental evidence of multiple Chla forms in vivo is explained by BSE. The Chla and Chlb BSE exciton wavefunctions present important charge-transfer differences on the Soret band. Q excitons are almost identical, apart from charge (both electron and hole) localization on the Chlb C7 aldheide formyl group, absent on the Chla methyl C7, that is exactly the group where the two chlorophylls differ.

Spectral densities and absorption spectra of the core antenna complex CP43 from photosystem II

Besides absorbing light, the core antenna complex CP43 of photosystem II is of great importance in transferring excitation energy from the antenna complexes to the reaction center. Excitation energies, spectral densities, and linear absorption spectra of the complex have been evaluated by a multiscale approach. In this scheme, quantum mechanics/molecular mechanics molecular dynamics simulations are performed employing the parameterized density functional tight binding (DFTB) while the time-dependent long-range-corrected DFTB scheme is applied for the excited state calculations. The obtained average spectral density of the CP43 complex shows a very good agreement with experimental results. Moreover, the excitonic Hamiltonian of the system along with the computed site-dependent spectral densities was used to determine the linear absorption. While a Redfield-like approximation has severe shortcomings in dealing with the CP43 complex due to quasi-degenerate states, the non-Markovian full second-order cumulant expansion formalism is able to overcome the drawbacks. Linear absorption spectra were obtained, which show a good agreement with the experimental counterparts at different temperatures. This study once more emphasizes that by combining diverse techniques from the areas of molecular dynamics simulations, quantum chemistry, and open quantum systems, it is possible to obtain first-principle results for photosynthetic complexes, which are in accord with experimental findings.

Exact simulation of pigment-protein complexes unveils vibronic renormalization of electronic parameters in ultrafast spectroscopy

The primary steps of photosynthesis rely on the generation, transport, and trapping of excitons in pigment-protein complexes (PPCs). Generically, PPCs possess highly structured vibrational spectra, combining many discrete intra-pigment modes and a quasi-continuous of protein modes, with vibrational and electronic couplings of comparable strength. The intricacy of the resulting vibronic dynamics poses significant challenges in establishing a quantitative connection between spectroscopic data and underlying microscopic models. Here we show how to address this challenge using numerically exact simulation methods by considering two model systems, namely the water-soluble chlorophyll-binding protein of cauliflower and the special pair of bacterial reaction centers. We demonstrate that the inclusion of the full multi-mode vibronic dynamics in numerical calculations of linear spectra leads to systematic and quantitatively significant corrections to electronic parameter estimation. These multi-mode vibronic effects are shown to be relevant in the longstanding discussion regarding the origin of long-lived oscillations in multidimensional nonlinear spectra.

Multimode vibronic mixing in model photosynthetic systems revealed by numerically exact simulations is shown to strongly modify linear and non-linear optical responses and facilitate the persistence of coherent dynamics.

The atomistic modeling of light-harvesting complexes from the physical models to the computational protocol

The function of light-harvesting complexes is determined by a complex network of dynamic interactions among all the different components: the aggregate of pigments, the protein, and the surrounding environment. Complete and reliable predictions on these types of composite systems can be only achieved with an atomistic description. In the last few decades, there have been important advances in the atomistic modeling of light-harvesting complexes. These advances have involved both the completeness of the physical models and the accuracy and effectiveness of the computational protocols. In this Perspective, we present an overview of the main theoretical and computational breakthroughs attained so far in the field, with particular focus on the important role played by the protein and its dynamics. We then discuss the open problems in their accurate modeling that still need to be addressed. To illustrate an effective computational workflow for the modeling of light harvesting complexes, we take as an example the plant antenna complex CP29 and its H111N mutant.

Structure of the stress-related LHCSR1 complex determined by an integrated computational strategy

Light-harvesting complexes (LHCs) are pigment-protein complexes whose main function is to capture sunlight and transfer the energy to reaction centers of photosystems. In response to varying light conditions, LH complexes also play photoregulation and photoprotection roles. In algae and mosses, a sub-family of LHCs, light-harvesting complex stress-related (LHCSR), is responsible for photoprotective quenching. Despite their functional and evolutionary importance, no direct structural information on LHCSRs is available that can explain their unique properties. In this work, we propose a structural model of LHCSR1 from the moss P. patens, obtained through an integrated computational strategy that combines homology modeling, molecular dynamics, and multiscale quantum chemical calculations. The model is validated by reproducing the spectral properties of LHCSR1. Our model reveals the structural specificity of LHCSR1, as compared with the CP29 LH complex, and poses the basis for understanding photoprotective quenching in mosses.

The structure of the moss P. patens light-harvesting complex stress-related 1 (LHCSR1) is determined using a multi-scale computational approach for investigations of its photoprotective function.

Stark absorption and Stark fluorescence spectroscopies: Theory and simulations

Stark spectroscopy experiments are widely used to study the properties of molecular systems, particularly those containing charge-transfer (CT) states. However, due to the small transition dipole moments and large static dipole moments of the CT states, the standard interpretation of the Stark absorption and Stark fluorescence spectra in terms of the Liptay model may be inadequate. In this work, we provide a theoretical framework for calculations of Stark absorption and Stark fluorescence spectra and propose new methods of simulations that are based on the quantum-classical theory. In particular, we use the forward-backward trajectory solution and a variant of the Poisson bracket mapping equation, which have been recently adapted for the calculation of conventional (field-free) absorption and fluorescence spectra. For comparison, we also apply the recently proposed complex time-dependent Redfield theory, while exact results are obtained using the hierarchical equations of motion approach. We show that the quantum-classical methods produce accurate results for a wide range of systems, including those containing CT states. The CT states contribute significantly to the Stark spectra, and the standard Liptay formalism is shown to be inapplicable for the analysis of spectroscopic data in those cases. We demonstrate that states with large static dipole moments may cause a pronounced change in the total fluorescence yield of the system in the presence of an external electric field. This effect is correctly captured by the quantum-classical methods, which should therefore prove useful for further studies of Stark spectra of real molecular systems. As an example, we calculate the Stark spectra for the Fenna-Matthews-Olson complex of green sulfur bacteria.

Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes

Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.

Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications

Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum-classical theory─it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum-classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum-classical Liouville equation, namely, the forward-backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna-Matthews-Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [Gelzinis, A.; J. Chem. Phys. 2020, 152, 051103] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.

Time-dependent atomistic simulations of the CP29 light-harvesting complex

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Correlated vibration-solvent effects on the non-Condon exciton spectroscopy

Excitation energy transfer is crucially involved in a variety of systems. During the process, the non-Condon vibronic coupling and the surrounding solvent interaction may synergetically play important roles. In this work, we study the correlated vibration-solvent influences on the non-Condon exciton spectroscopy. Statistical analysis is elaborated for the overall vibration-plus-solvent environmental effects. Analytic solutions are derived for the linear absorption of monomer systems. General simulations are accurately carried out via the dissipaton-equation-of-motion approach. The resulted spectra in either the linear absorption or strong field regime clearly demonstrate the coherence enhancement due to the synergetic vibration-solvent correlation.

Fully Quantum Modeling of Exciton Diffusion in Mesoscale Light Harvesting Systems

It has long been a challenge to accurately and efficiently simulate exciton-phonon dynamics in mesoscale photosynthetic systems with a fully quantum mechanical treatment due to extensive computational resources required. In this work, we tackle this seemingly intractable problem by combining the Dirac-Frenkel time-dependent variational method with Davydov trial states and implementing the algorithm in graphic processing units. The phonons are treated on the same footing as the exciton. Tested with toy models, which are nanoarrays of the B850 pigments from the light harvesting 2 complexes of purple bacteria, the methodology is adopted to describe exciton diffusion in huge systems containing more than 1600 molecules. The superradiance enhancement factor extracted from the simulations indicates an exciton delocalization over two to three pigments, in agreement with measurements of fluorescence quantum yield and lifetime in B850 systems. With fractal analysis of the exciton dynamics, it is found that exciton transfer in B850 nanoarrays exhibits a superdiffusion component for about 500 fs. Treating the B850 ring as an aggregate and modeling the inter-ring exciton transfer as incoherent hopping, we also apply the method of classical master equations to estimate exciton diffusion properties in one-dimensional (1D) and two-dimensional (2D) B850 nanoarrays using derived analytical expressions of time-dependent excitation probabilities. For both coherent and incoherent propagation, faster energy transfer is uncovered in 2D nanoarrays than 1D chains, owing to availability of more numerous propagating channels in the 2D arrangement.

Multiscale QM/MM molecular dynamics simulations of the trimeric major light-harvesting complex II

Photosynthetic processes are driven by sunlight. Too little of it and the photosynthetic machinery cannot produce the reductive power to drive the anabolic pathways. Too much sunlight and the machinery can get damaged. In higher plants, the major Light-Harvesting Complex (LHCII) efficiently absorbs the light energy, but can also dissipate it when in excess (quenching). In order to study the dynamics related to the quenching process but also the exciton dynamics in general, one needs to accurately determine the so-called spectral density which describes the coupling between the relevant pigment modes and the environmental degrees of freedom. To this end, Born-Oppenheimer molecular dynamics simulations in a quantum mechanics/molecular mechanics (QM/MM) fashion utilizing the density functional based tight binding (DFTB) method have been performed for the ground state dynamics. Subsequently, the time-dependent extension of the long-range-corrected DFTB scheme has been employed for the excited state calculations of the individual chlorophyll-a molecules in the LHCII complex. The analysis of this data resulted in spectral densities showing an astonishing agreement with the experimental counterpart in this rather large system. This consistency with an experimental observable also supports the accuracy, robustness, and reliability of the present multi-scale scheme. To the best of our knowledge, this is the first theoretical attempt on this large complex system is ever made to accurately simulate the spectral density. In addition, the resulting spectral densities and site energies were used to determine the exciton transfer rate within a special pigment pair consisting of a chlorophyll-a and a carotenoid molecule which is assumed to play a role in the balance between the light harvesting and quenching modes.

Absence of far-red emission band in aggregated core antenna complexes

Reported herein is a Stark fluorescence spectroscopy study performed on photosystem II core antenna complexes CP43 and CP47 in their native and aggregated states. The systematic mathematical modeling of the Stark fluorescence spectra with the aid of conventional Liptay formalism revealed that induction of aggregation in both the core antenna complexes via detergent removal results in a single quenched species characterized by a remarkably broad and inhomogenously broadened emission lineshape peaking around 700 nm. The quenched species possesses a fairly large magnitude of charge-transfer character. From the analogy with the results from aggregated peripheral antenna complexes, the quenched species is thought to originate from the enhanced chlorophyll-chlorophyll interaction due to aggregation. However, in contrast, aggregation of both core antenna complexes did not produce a far-red emission band at ∼730 nm, which was identified in most of the aggregated peripheral antenna complexes. The 730-nm emission band of the aggregated peripheral antenna complexes was attributed to the enhanced chlorophyll-carotenoid (lutein1) interaction in the terminal emitter locus. Therefore, it is very likely that the no occurrence of the far-red band in the aggregated core antenna complexes is directly related to the absence of lutein1 in their structures. The absence of the far-red band also suggests the possibility that aggregation-induced conformational change of the core antenna complexes does not yield a chlorophyll-carotenoid interaction associated energy dissipation channel.

Trivial Excitation Energy Transfer to Carotenoids Is an Unlikely Mechanism for Non-photochemical Quenching in LHCII

Higher plants defend themselves from bursts of intense light via the mechanism of Non-Photochemical Quenching (NPQ). It involves the Photosystem II (PSII) antenna protein (LHCII) adopting a conformation that favors excitation quenching. In recent years several structural models have suggested that quenching proceeds via energy transfer to the optically forbidden and short-lived S ₁ states of a carotenoid. It was proposed that this pathway was controlled by subtle changes in the relative orientation of a small number of pigments. However, quantum chemical calculations of S ₁ properties are not trivial and therefore its energy, oscillator strength and lifetime are treated as rather loose parameters. Moreover, the models were based either on a single LHCII crystal structure or Molecular Dynamics (MD) trajectories about a single minimum. Here we try and address these limitations by parameterizing the vibronic structure and relaxation dynamics of lutein in terms of observable quantities, namely its linear absorption (LA), transient absorption (TA) and two-photon excitation (TPE) spectra. We also analyze a number of minima taken from an exhaustive meta-dynamical search of the LHCII free energy surface. We show that trivial, Coulomb-mediated energy transfer to S ₁ is an unlikely quenching mechanism, with pigment movements insufficiently pronounced to switch the system between quenched and unquenched states. Modulation of S ₁ energy level as a quenching switch is similarly unlikely. Moreover, the quenching predicted by previous models is possibly an artifact of quantum chemical over-estimation of S ₁ oscillator strength and the real mechanism likely involves short-range interaction and/or non-trivial inter-molecular states.

The role of mixed vibronic Qy-Qx states in green light absorption of light-harvesting complex II

The importance of green light for driving natural photosynthesis has long been underappreciated, however, under the presence of strong illumination, green light actually drives photosynthesis more efficiently than red light. This green light is absorbed by mixed vibronic Q_y-Q_x states, arising from chlorophyll (Chl)-Chl interactions, although almost nothing is known about these states. Here, we employ polarization-dependent two-dimensional electronic-vibrational spectroscopy to study the origin and dynamics of the mixed vibronic Q_y-Q_x states of light-harvesting complex II. We show the states in this region dominantly arise from Chl b and demonstrate how it is possible to distinguish between the degree of vibronic Q_y versus Q_x character. We find that the dynamics for states of predominately Chl b Q_y versus Chl b Q_x character are markedly different, as excitation persists for significantly longer in the Q_x states and there is an oscillatory component to the Q_x dynamics, which is discussed. Our findings demonstrate the central role of electronic-nuclear mixing in efficient light-harvesting and the different functionalities of Chl a and Chl b.

The green component of the solar spectrum can efficiently drive natural photosynthesis, but the process has been little investigated due to the complexity of the excited states involved. Here the authors utilize polarization-dependent two-dimensional electronic-vibrational spectroscopy to define the origin and dynamics of these states in light-harvesting complex II.

Delocalization Effects in Chlorophyll Fluorescence: Nonperturbative Line Shape Analysis of a Vibronically Coupled Dimer

Non-adiabatic vibrational/electronic (vibronic) interactions in photosynthetic pigment/protein complexes (PPCs) have recently attracted considerable interest as a potential source for long-lived dynamic coherence and optimized light harvesting. The analysis of such effects is limited, however, by the complexity of the vibrational spectrum of biological pigments such as chlorophyll (Chl) molecules, which often makes numerical calculations prohibitively expensive and complicates the interpretation of experimental spectroscopic data. This work contributes to both challenges by using numerically exact computational methods to systematically examine vibronic mixing effects in the low-temperature fluorescence spectra of a Chl dimer possessing a full complement of local vibrations, using parameters extracted from experimental data. The results highlight the varying roles local vibrations can play in energy-transfer dynamics, both enhancing delocalization through vibronic resonance and, conversely, inducing dynamic localization by acting as a "self-bath" for local electronic transitions. In the specific context of line-narrowed fluorescence, the results indicate that, while low-frequency features are strongly suppressed by delocalization, high-frequency modes are likely to be dynamically localized in the parameter regime relevant to most photosynthetic complexes.

DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum-classical description. To this end, Born-Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna-Matthews-Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

An investigation into the energy transfer efficiency of a two-pigment photosynthetic system using a macroscopic quantum model

Despite several different measures of efficiency that are applicable to the photosynthetic systems, a precise degree of efficiency of these systems is not completely determined. Introducing an efficient model for the dynamics of light-harvesting complexes in biological environments is a major purpose in investigating such systems. Here, we investigate the effect of macroscopic quantum behavior of a system of two pigments on the transport phenomena in this system model which interacts with an oscillating environment. We use the second-order perturbation theory to calculate the time-dependent population of excitonic states of a two-dimensional Hamiltonian using a non-master equation approach. Our results demonstrate that the quantum efficiency is robust with respect to the macroscopicity parameter h˜ solely, but the ratio of macroscopicity over the pigment-pigment interaction energy can be considered as a parameter that may control the energy transfer efficiency at a given time. So, the dynamical behavior and the quantum efficiency of the supposed photosynthetic system may be influenced by a change in the macroscopic behavior of the system.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

Vibronic mixing enables ultrafast energy flow in light-harvesting complex II

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps.

Coherently and fluorescence-detected two-dimensional electronic spectroscopy: direct comparison on squaraine dimers

Optical two-dimensional electronic spectroscopy (2DES) is now widely utilized to study excitonic structure and dynamics of a broad range of systems, from molecules to solid state. Besides the traditional experimental implementation using phase matching and coherent signal field detection, action-based approaches that detect incoherent signals such as fluorescence have been gaining popularity in recent years. While incoherent detection extends the range of applicability of 2DES, the observed spectra are not equivalent to the coherently detected ones. This raises questions about their interpretation and the sensitivity of the technique. Here we directly compare, both experimentally and theoretically, four-wave mixing coherently and fluorescence-detected 2DES of a series of squaraine dimers of increasing electronic coupling. All experiments are qualitatively well reproduced by a Frenkel exciton model with secular Redfield theory description of excitation dynamics. We contrast the spectral features and the sensitivities of both techniques with respect to exciton energies, delocalization, coherent and dissipative dynamics, and exciton-exciton annihilation. Discussing the fundamental and practical differences, we demonstrate the degree of complementarity of the techniques.

Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy

During the past two decades, two-dimensional electronic spectroscopy (2DES) and related techniques have emerged as a potent experimental toolset to study the ultrafast elementary steps of photosynthesis. Apart from the highly engaging albeit controversial analysis of the role of quantum coherences in the photosynthetic processes, 2DES has been applied to resolve the dynamics and pathways of energy and electron transport in various light-harvesting antenna systems and reaction centres, providing unsurpassed level of detail. In this paper we discuss the main technical approaches and their applicability for solving specific problems in photosynthesis. We then recount applications of 2DES to study the exciton dynamics in plant and photosynthetic light-harvesting complexes, especially light-harvesting complex II (LHCII) and the fucoxanthin-chlorophyll proteins of diatoms, with emphasis on the types of unique information about such systems that 2DES is capable to deliver. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.

Light harvesting complexes in chlorophyll c-containing algae

Besides the so-called 'green lineage' of eukaryotic photosynthetic organisms that include vascular plants, a huge variety of different algal groups exist that also harvest light by means of membrane intrinsic light harvesting proteins (Lhc). The main taxa of these algae are the Cryptophytes, Haptophytes, Dinophytes, Chromeridae and the Heterokonts, the latter including diatoms, brown algae, Xanthophyceae and Eustigmatophyceae amongst others. Despite the similarity in Lhc proteins between vascular plants and these algae, pigmentation is significantly different since no Chl b is bound, but often replaced by Chl c, and a large diversity in carotenoids functioning in light harvesting and/or photoprotection is present. Due to the presence of Chl c in most of the taxa the name 'Chl c-containing organisms' has become common, however, Chl b-less is more precise since some harbour Lhc proteins that only bind one type of Chl, Chl a. In recent years huge progress has been made about the occurrence and function of Lhc in diatoms, so-called fucoxanthin chlorophyll proteins (FCP), where also the first molecular structure became available recently. In addition, especially energy transfer amongst the unusual pigments bound was intensively studied in many of these groups. This review summarises the present knowledge about the molecular structure, the arrangement of the different Lhc in complexes, the excitation energy transfer abilities and the involvement in photoprotection of the different Lhc systems in the so-called Chl c-containing organisms. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.

Anisotropic Circular Dichroism of Light-Harvesting Complex II in Oriented Lipid Bilayers: Theory Meets Experiment

Anisotropic circular dichroism (ACD) spectroscopy of macroscopically aligned molecules reveals additional information about their excited states that is lost in the CD of randomly oriented solutions. ACD spectra of light-harvesting complex II (LHCII)-the main peripheral antenna of photosystem II in plants-in oriented lipid bilayers were recorded from the far-UV to the visible wavelength region. ACD spectra show a drastically enhanced magnitude and level of detail compared to the isotropic CD spectra, resolving a greater number of bands and weak optical transitions. Exciton calculations show that the spectral features in the chlorophyll Q _y region are well-reproduced by an existing Hamiltonian for LHCII, providing further evidence for the identity of energy sinks at chlorophylls a603 and a610 in the stromal layer and chlorophylls a604 and a613 in the luminal layer. We propose ACD spectroscopy to be a valuable tool linking the three-dimensional structure and the photophysical properties of pigment-protein complexes.

Dynamics of the mixed exciton and charge-transfer states in light-harvesting complex Lhca4: Hierarchical equation approach

We model the energy transfer dynamics in the Lhca4 peripheral antenna of photosystem I from higher plants. Equilibration between the bulk exciton levels of the antenna and the red-shifted charge-transfer (CT) states is described using the numerically inexpensive Redfield-Förster approach and exact hierarchical equation (HEOM) method. We propose a compartmentalization scheme allowing a quantitatively correct description of the dynamics with the Redfield-Förster theory, including the exciton-type relaxation within strongly coupled compartments and hopping-type migration between them. The Redfield-Förster method gives the kinetics close to the HEOM solution when treating the CT state as dynamically localized. We also demonstrate that the excited states strongly coupled with the CT should be considered as localized as well.

Local protein solvation drives direct down-conversion in phycobiliprotein PC645 via incoherent vibronic transport

The mechanisms controlling excitation energy transport (EET) in light-harvesting complexes remain controversial. Following the observation of long-lived beats in 2D electronic spectroscopy of PC645, vibronic coherence, the delocalization of excited states between pigments supported by a resonant vibration, has been proposed to enable direct excitation transport from the highest-energy to the lowest-energy pigments, bypassing a collection of intermediate states. Here, we instead show that for phycobiliprotein PC645 an incoherent vibronic transport mechanism is at play. We quantify the solvation dynamics of individual pigments using ab initio quantum mechanics/molecular mechanics (QM/MM) nuclear dynamics. Our atomistic spectral densities reproduce experimental observations ranging from absorption and fluorescence spectra to the timescales and selectivity of down-conversion observed in transient absorption measurements. We construct a general model for vibronic dimers and establish the parameter regimes of coherent and incoherent vibronic transport. We demonstrate that direct down-conversion in PC645 proceeds incoherently, enhanced by large reorganization energies and a broad collection of high-frequency vibrations. We suggest that a similar incoherent mechanism is appropriate across phycobiliproteins and represents a potential design principle for nanoscale control of EET.

Simple Quantum Dynamics with Thermalization

In this paper, we introduce two simple quantum dynamics methods. One is based on the popular surface-hopping method, and the other is based on rescaling of the propagation on the bath ground-state potential surface. The first method is special, as it avoids specific feedback from the simulated quantum system to the bath and can be applied for precalculated classical trajectories. It is based on the equipartition theorem to determine if hops between different potential energy surfaces are allowed. By comparing with the formally exact Hierarchical Equations Of Motion approach for four model systems we find that the method generally approximates the quantum dynamics toward thermal equilibrium very well. The second method is based on rescaling of the nonadiabatic coupling and also neglect the effect of the state of the quantum system on the bath. By the nature of the approximations, they cannot reproduce the effect of bath relaxation following excitation. However, the methods are both computationally more tractable than the conventional fewest switches surface hopping, and we foresee that the methods will be powerful for simulations of quantum dynamics in systems with complex bath dynamics, where the system-bath coupling is not too strong compared to the thermal energy.

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.

Long-range energy transport in photosystem II

We simulate the long-range inter-complex electronic energy transfer in photosystem II-from the antenna complex, via a core complex, to the reaction center-using a non-Markovian (ZOFE) quantum master equation description that allows the electronic coherence involved in the energy transfer to be explicitly included at all length scales. This allows us to identify all locations where coherence is manifested and to further identify the pathways of the energy transfer in the full network of coupled chromophores using a description based on excitation probability currents. We investigate how the energy transfer depends on the initial excitation-localized, coherent initial excitation versus delocalized, incoherent initial excitation-and find that the overall energy transfer is remarkably robust with respect to such strong variations of the initial condition. To explore the importance of vibrationally enhanced transfer and to address the question of optimization in the system parameters, we systematically vary the strength of the coupling between the electronic and the vibrational degrees of freedom. We find that the natural parameters lie in a (broad) region that enables optimal transfer efficiency and that the overall long-range energy transfer on a ns time scale appears to be very robust with respect to variations in the vibronic coupling of up to an order of magnitude. Nevertheless, vibrationally enhanced transfer appears to be crucial to obtain a high transfer efficiency, with the latter falling sharply for couplings outside the optimal range. Comparison of our full quantum simulations to results obtained with a "classical" rate equation based on a modified-Redfield/generalized-Förster description previously used to simulate energy transfer dynamics in the entire photosystem II complex shows good agreement for the overall time scales of excitation energy transport.