Quest for spatially correlated fluctuations in the FMO light-harvesting complex

Predicting Mutation-Induced Changes in the Electronic Properties of Photosynthetic Proteins from First Principles: The Fenna-Matthews-Olson Complex Example

Multiscale molecular modeling is utilized to predict optical absorption and circular dichroism spectra of two single-point mutants of the Fenna-Matthews-Olson photosynthetic pigment-protein complex. The modeling approach combines classical molecular dynamics simulations with structural refinement of photosynthetic pigments and calculations of their excited states in a polarizable protein environment. The only experimental input to the modeling protocol is the X-ray structure of the wild-type protein. The first-principles modeling reproduces changes in the experimental optical spectra of the considered mutants, Y16F and Q198V. Interestingly, the Q198V mutation has a negligible effect on the electronic properties of the targeted bacteriochlorophyll a pigment. Instead, the electronic properties of several other pigments respond to this mutation. The molecular modeling demonstrates that a single-point mutation can induce long-range effects on the protein structure, while extensive structural changes near a pigment do not necessarily lead to significant changes in the electronic properties of that pigment.

Recent progress in atomistic modeling of light-harvesting complexes: a mini review

In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as site energies, excitonic couplings, and spectral densities are key quantities which usually need to be extracted to be able to determine the exciton dynamics and spectroscopic properties. The recently developed multiscale approach based on the numerically efficient density functional tight-binding framework followed by excited state calculations has been shown to be superior to the scheme based on pure classical molecular dynamics simulations. The enhanced approach, which improves the description of the internal vibrational dynamics of the pigment molecules, yields spectral densities in good agreement with the experimental counterparts for various bacterial and plant LH systems. Here, we provide a brief overview of those results and described the theoretical foundation of the multiscale protocol.

Manifestation of Hydrogen Bonding and Exciton Delocalization on the Absorption and Two-Dimensional Electronic Spectra of Chlorosomes

Chlorosomes are supramolecular aggregates that contain thousands of bacteriochlorophyll molecules. They perform the most efficient ultrafast excitation energy transfer of all natural light-harvesting complexes. Their broad absorption band optimizes light capture. In this study, we identify the microscopic sources of the disorder causing the spectral width and reveal how it affects the excited state properties and the optical response of the system. We combine molecular dynamics, quantum chemical calculations, and response function calculations to achieve this goal. The predicted linear and two-dimensional electronic spectra are found to compare well with experimental data reproducing all key spectral features. Our analysis of the microscopic model reveals the interplay of static and dynamic disorder from the molecular perspective. We find that hydrogen bonding motifs are essential for a correct description of the spectral line shape. Furthermore, we find that exciton delocalization over tens to hundreds of molecules is consistent with the two-dimensional electronic spectra.

Local Phonon Environment as a Design Element for Long-Lived Excitonic Coherence: Dithia-anthracenophane Revisited

The purpose of this study is to investigate the role of a structured immediate phonon environment in determining the exciton dynamics and the possibility of using it as an optimal design element. Through the case study of dithia-anthracenophane, a bichromophore using the Hierarchical Equations Of Motion formalism, we show that the experimentally observed coherent exciton dynamics can be reproduced only by considering the actual structure of the phonon environment. While the slow dephasing of quantum coherence in dithia-anthracenophane can be attributed to strong vibronic coupling to high-frequency modes, vibronic quenching is the source of long oscillation periods in population transfer. This study sheds light on the crucial role of the structure of the immediate phonon environment in determining the exciton dynamics. We conclude by proposing some design principles for sustaining long-lived coherence in molecular systems.

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.

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.

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.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Theoretical Study of the Spectral Differences of the Fenna-Matthews-Olson Protein from Different Species and Their Mutants

The structural basis for the spectral differences between the Fenna-Matthews-Olson (FMO) proteins from Chlorobaculum tepidum (C. tepidum) and Prosthecochloris aestuarii 2K (P. aestuarii) is yet to be fully understood. Mutation-induced perturbation to the exciton structure and the optical spectra of the complex provide a suitable means to investigate the critical role played by the protein scaffold. In this work, we have performed quantum-mechanics/molecular-mechanics calculations over the molecular dynamics simulation trajectories with the polarized protein-specific charge scheme for both wild-type FMOs and two mutants. Our result reveals that a single-point mutation in the vicinity of BChl 6, namely, W183F of C. tepidum, significantly affects the absorption spectrum, resulting in a switch of the absorption spectrum from type 2, for which the 806 nm band is more pronounced than the 815 nm band, to type 1, for which the 815 nm band is pronounced. Our observations agree with the single-point mutation experiments reported by Saer et al. (Biochim. Biophys. Acta, Bioenerg. 2017, 1858, 288-296) and Khmelnitskiy et al. (J. Phys. Chem. Lett. 2018, 9, 3378-3386). In contrast, the absorption spectrum of the P. aestuarii experiences the opposite transition (from type 1 to type 2) upon the same mutation. Furthermore, by comparing the contributions of individual pigments to the spectra in the wild type and its mutant, we find that a single-point mutation near BChl 6 not only induces changes in excitation energy of BChl 6 per se but also affects the excitonic structures of the neighboring BChls 5 and 7 through strong interpigment electronic couplings, resulting in a significant change in the absorption spectra.

Modeling and Simulating the Excited-State Dynamics of a System with Condensed Phases: A Machine Learning Approach

Simulating the irreversible quantum dynamics of exciton- and electron-transfer problems poses a nontrivial challenge. Because the irreversibility of the system dynamics is a result of quantum thermal activation and dissipation caused by the surrounding environment, it is necessary to include infinite environmental degrees of freedom in the simulation. Because the capabilities of full quantum dynamics simulations that include the surrounding molecular degrees of freedom are limited, employing a system-bath model is a practical approach. In such a model, the dynamics of excitons or electrons are described by a system Hamiltonian, while the other degrees of freedom that arise from the environmental molecules are described by a harmonic oscillator bath (HOB) and system-bath interaction parameters. By extending on a previous study of molecular liquids [ J. Chem. Theory Comput. 2020, 16, 2099], here, we construct a system-bath model for exciton- and electron-transfer problems by means of a machine learning approach. We determine both the system and system-bath interaction parameters, including the spectral distribution of the bath, using the electronic excitation energies obtained from a quantum mechanics/molecular mechanics (QM/MM) simulation that is conducted as a function of time. Using the analytical expressions of optical response functions, we calculate linear and two-dimensional electronic spectra (2DES) for indocarbocyanine dimers in methanol. From these results, we demonstrate the capability of our approach to elucidate the nonequilibrium exciton dynamics of a quantum system in a nonintuitive manner.

Exciton Lifetime Distributions and Population Dynamics in the FMO Protein Complex from Prosthecochloris aestuarii

Significant protein rearrangement upon excitation and energy transfer in Fenna-Matthews-Olson protein of Prosthecochloris aestuarii results in a modified energy landscape, which induces more changes in pigment site energies than predicted by the "standard" hole-burning theory. The energy changes are elucidated by simulations while investigating the effects of site-dependent disorder, both static (site-energy distribution widths) and dynamic (spectral density shapes). The resulting optimized site energies and their fluctuations are consistent with relative differences observed in inhomogeneous widths calculated by recent molecular dynamic simulations. Two sets of different spectral densities reveal how their shapes affect the population dynamics and distribution of exciton lifetimes. Calculations revealed the wavelength-dependent distributions of exciton lifetimes (T ₁) in the femtosecond to picosecond time frame. We suggest that the calculated multimodal and asymmetric wavelength-dependent T ₁ distributions offer more insight into the interpretation of resonant hole-burned (HB) spectra, kinetic traces in two-dimensional (2D) electronic spectroscopy experiments, and widely used global analyses in fitting data from transient absorption experiments.

Static Disorder in Excitation Energies of the Fenna-Matthews-Olson Protein: Structure-Based Theory Meets Experiment

Inhomogeneous broadening of optical lines of the Fenna-Matthews-Olson (FMO) light-harvesting protein is investigated by combining a Monte Carlo sampling of low-energy conformational substates of the protein with a quantum chemical/electrostatic calculation of local transition energies (site energies) of the pigments. The good agreement between the optical spectra calculated for the inhomogeneous ensemble and the experimental data demonstrates that electrostatics is the dominant contributor to static disorder in site energies. Rotamers of polar amino acid side chains are found to cause bimodal distribution functions of site energy shifts, which can be probed by hole burning and single-molecule spectroscopy. When summing over the large number of contributions, the resulting distribution functions of the site energies become Gaussians, and the correlations in site energy fluctuations at different sites practically average to zero. These results demonstrate that static disorder in the FMO protein is in the realm of the central limit theorem of statistics.

Stochastically Realized Observables for Excitonic Molecular Aggregates

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

On the role of non-diagonal system-environment interactions in bridge-mediated electron transfer

Bridge-mediated electron transfer (ET) between a donor and an acceptor is prototypical for the description of numerous most important ET scenarios. While multi-step ET and the interplay of sequential and direct superexchange transfer pathways in the donor-bridge-acceptor (D-B-A) model are increasingly understood, the influence of off-diagonal system-bath interactions on the transfer dynamics is less explored. Off-diagonal interactions account for the dependence of the ET coupling elements on nuclear coordinates (non-Condon effects) and are typically neglected. Here, we numerically investigate with quasi-adiabatic propagator path integral simulations the impact of off-diagonal system-environment interactions on the transfer dynamics for a wide range of scenarios in the D-B-A model. We demonstrate that off-diagonal system-environment interactions can have profound impact on the bridge-mediated ET dynamics. In the considered scenarios, the dynamics itself does not allow for a rigorous assignment of the underlying transfer mechanism. Furthermore, we demonstrate how off-diagonal system-environment interaction mediates anomalous localization by preventing long-time depopulation of the bridge B and how coherent transfer dynamics between donor D and acceptor A can be facilitated. The arising non-exponential short-time dynamics and coherent oscillations are interpreted within an equivalent Hamiltonian representation of a primary reaction coordinate model that reveals how the complex vibronic interplay of vibrational and electronic degrees of freedom underlying the non-Condon effects can impose donor-to-acceptor coherence transfer on short timescales.

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.

Predictive First-Principles Modeling of a Photosynthetic Antenna Protein: The Fenna-Matthews-Olson Complex

High efficiency of light harvesting in photosynthetic pigment-protein complexes is governed by evolutionary-perfected protein-assisted tuning of individual pigment properties and interpigment interactions. Due to the large number of spectrally overlapping pigments in a typical photosynthetic complex, experimental methods often fail to unambiguously identify individual chromophore properties. Here, we report a first-principles-based modeling protocol capable of predicting properties of pigments in protein environment to a high precision. The technique was applied to successfully uncover electronic properties of the Fenna-Matthews-Olson (FMO) pigment-protein complex. Each of the three subunits of the FMO complex contains eight strongly coupled bacteriochlorophyll a (BChl a) pigments. The excitonic structure of FMO can be described by an electronic Hamiltonian containing excitation (site) energies of BChl a pigments and electronic couplings between them. Several such Hamiltonians have been developed in the past based on the information from various spectroscopic measurements of FMO; however, fine details of the excitonic structure and energy transfer in FMO, especially assignments of short-lived high-energy sites, remain elusive. Utilizing polarizable embedding quantum mechanics/molecular mechanics with the effective fragment potentials, we computed the electronic Hamiltonian of FMO that is in general agreement with previously reported empirical Hamiltonians and quantitatively reproduces experimental absorption and circular dichroism spectra of the FMO protein. The developed computational protocol is sufficiently simple and can be utilized for predictive modeling of other wild-type and mutated photosynthetic pigment-protein complexes.

Successes & challenges in the atomistic modeling of light-harvesting and its photoregulation

Light-harvesting is a crucial step of photosynthesis. Its mechanisms and related energetics have been revealed by a combination of experimental investigations and theoretical modeling. The success of theoretical modeling is largely due to the application of atomistic descriptions combining quantum chemistry, classical models and molecular dynamics techniques. Besides the important achievements obtained so far, a complete and quantitative understanding of how the many different light-harvesting complexes exploit their structural specificity is still missing. Moreover, many questions remain unanswered regarding the mechanisms through which light-harvesting is regulated in response to variable light conditions. Here we show that, in both fields, a major role will be played once more by atomistic descriptions, possibly generalized to tackle the numerous time and space scales on which the regulation takes place: going from the ultrafast electronic excitation of the multichromophoric aggregate, through the subsequent conformational changes in the embedding protein, up to the interaction between proteins.

Identification and characterization of diverse coherences in the Fenna-Matthews-Olson complex

The idea that excitonic (electronic) coherences are of fundamental importance to natural photosynthesis gained popularity when slowly dephasing quantum beats (QBs) were observed in the two-dimensional electronic spectra of the Fenna-Matthews-Olson (FMO) complex at 77 K. These were assigned to superpositions of excitonic states, a controversial interpretation, as the strong chromophore-environment interactions in the complex suggest fast dephasing. Although it has been pointed out that vibrational motion produces similar spectral signatures, a concrete assignment of these oscillatory signals to distinct physical processes is still lacking. Here we revisit the coherence dynamics of the FMO complex using polarization-controlled two-dimensional electronic spectroscopy, supported by theoretical modelling. We show that the long-lived QBs are exclusively vibrational in origin, whereas the dephasing of the electronic coherences is completed within 240 fs even at 77 K. We further find that specific vibrational coherences are produced via vibronically coupled excited states. The presence of such states suggests that vibronic coupling is relevant for photosynthetic energy transfer.

Exciton transport in the PE545 complex: insight from atomistic QM/MM-based quantum master equations and elastic network models

In this paper, we work out a parameterization of environmental noise within the Haken-Strobl-Reinenker (HSR) model for the PE545 light-harvesting complex, based on atomic-level quantum mechanics/molecular mechanics (QM/MM) simulations. We use this approach to investigate the role of various auto- and cross-correlations in the HSR noise tensor, confirming that site-energy autocorrelations (pure dephasing) terms dominate the noise-induced exciton mobility enhancement, followed by site energy-coupling cross-correlations for specific triplets of pigments. Interestingly, several cross-correlations of the latter kind, together with coupling-coupling cross-correlations, display clear low-frequency signatures in their spectral densities in the 30-70 [Formula: see text] region. These slow components lie at the limits of validity of the HSR approach, which requires that environmental fluctuations be faster than typical exciton transfer time scales. We show that a simple coarse-grained elastic-network-model (ENM) analysis of the PE545 protein naturally spotlights collective normal modes in this frequency range that represent specific concerted motions of the subnetwork of cysteines covalenty linked to the pigments. This analysis strongly suggests that protein scaffolds in light-harvesting complexes are able to express specific collective, low-frequency normal modes providing a fold-rooted blueprint of exciton transport pathways. We speculate that ENM-based mixed quantum classical methods, such as Ehrenfest dynamics, might be promising tools to disentangle the fundamental designing principles of these dynamical processes in natural and artificial light-harvesting structures.

Exciton-Coupled Electron Transfer Process Controlled by Non-Markovian Environments

We theoretically investigate an exciton-coupled electron transfer (XCET) process that is conversion of an exciton into a charge transfer state. This conversion happens in an exciton transfer (XT) process, and the electron moves away in an electron transfer (ET) process in multiple environments (baths). This XCET process plays an essential role in the harvesting of solar energy in biological and photovoltaic materials. We develop a practical theoretical model to study the efficiency of the XCET process that occurs either in consecutive or concerted processes under the influence of non-Markovian baths. The role of quantum coherence in the XT-ET system and the baths is investigated using reduced hierarchal equations of motion (HEOM). This model includes independent baths for each XT and ET state, in addition to a XCET bath for the conversion process. We found that, while quantum system-bath coherence is important in the XT and ET processes, coherence between the XT and ET processes must be suppressed in order to realize that an efficient irreversible XCET process through the weak off-diagonal interaction between the XT and ET bridge sites arises from an XCET bath.

Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex

Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.

Modeling Electronic-Nuclear Interactions for Excitation Energy Transfer Processes in Light-Harvesting Complexes

An accurate approach for computing intermolecular and intrachromophore contributions to spectral densities to describe the electronic-nuclear interactions relevant for modeling excitation energy transfer processes in light harvesting systems is presented. The approach is based on molecular dynamics (MD) calculations of classical correlation functions of long-range contributions to excitation energy fluctuations and a separate harmonic analysis and single-point gradient quantum calculations for electron-intrachromophore vibrational couplings. A simple model is also presented that enables detailed analysis of the shortcomings of standard MD-based excitation energy fluctuation correlation function approaches. The method introduced here avoids these problems, and its reliability is demonstrated in accurate predictions for bacteriochlorophyll molecules in the Fenna-Matthews-Olson pigment-protein complex, where excellent agreement with experimental spectral densities is found. This efficient approach can provide instantaneous spectral densities for treating the influence of fluctuations in environmental dissipation on fast electronic relaxation.

Machine learning exciton dynamics

Obtaining the exciton dynamics of large photosynthetic complexes by using mixed quantum mechanics/molecular mechanics (QM/MM) is computationally demanding. We propose a machine learning technique, multi-layer perceptrons, as a tool to reduce the time required to compute excited state energies. With this approach we predict time-dependent density functional theory (TDDFT) excited state energies of bacteriochlorophylls in the Fenna-Matthews-Olson (FMO) complex. Additionally we compute spectral densities and exciton populations from the predictions. Different methods to determine multi-layer perceptron training sets are introduced, leading to several initial data selections. In addition, we compute spectral densities and exciton populations. Once multi-layer perceptrons are trained, predicting excited state energies was found to be significantly faster than the corresponding QM/MM calculations. We showed that multi-layer perceptrons can successfully reproduce the energies of QM/MM calculations to a high degree of accuracy with prediction errors contained within 0.01 eV (0.5%). Spectral densities and exciton dynamics are also in agreement with the TDDFT results. The acceleration and accurate prediction of dynamics strongly encourage the combination of machine learning techniques with ab initio methods.

Light Absorption and Energy Transfer in the Antenna Complexes of Photosynthetic Organisms

The process of photosynthesis is initiated by the capture of sunlight by a network of light-absorbing molecules (chromophores), which are also responsible for the subsequent funneling of the excitation energy to the reaction centers. Through evolution, genetic drift, and speciation, photosynthetic organisms have discovered many solutions for light harvesting. In this review, we describe the underlying photophysical principles by which this energy is absorbed, as well as the mechanisms of electronic excitation energy transfer (EET). First, optical properties of the individual pigment chromophores present in light-harvesting antenna complexes are introduced, and then we examine the collective behavior of pigment-pigment and pigment-protein interactions. The description of energy transfer, in particular multichromophoric antenna structures, is shown to vary depending on the spatial and energetic landscape, which dictates the relative coupling strength between constituent pigment molecules. In the latter half of the article, we focus on the light-harvesting complexes of purple bacteria as a model to illustrate the present understanding of the synergetic effects leading to EET optimization of light-harvesting antenna systems while exploring the structure and function of the integral chromophores. We end this review with a brief overview of the energy-transfer dynamics and pathways in the light-harvesting antennas of various photosynthetic organisms.

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.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Towards an ab initio description of the optical spectra of light-harvesting antennae: application to the CP29 complex of photosystem II

Light-harvesting pigment-protein complexes (PPC) represent the fundamental units through which the photosynthetic organisms absorb sunlight and funnel the energy to the reaction centre for carrying out the primary energy conversion reactions of photosynthesis. Here we apply a multiscale computational strategy to a specific PPC present in the photosystem II of plants and algae (CP29) to investigate in what detail should the environment effects due to protein and membrane/solvent be included for an accurate description of optical spectra. We find that a refinement of the crystal structure is needed before any meaningful quantum chemical calculations of pigment transition energies can be performed. For this purpose we apply classical molecular dynamics simulations of the PPC within its natural environment and we perform ab initio computations of the exciton Hamiltonian of the complex, including the environment either implicitly by the polarizable continuum model (PCM) or explicitly using the polarizable QM/MM methodology (MMPol). However, PCM essentially leads to an unspecific redshift of all transition energies, and MMPol is able to reveal site-specific changes in the optical properties of the pigments. Based on the latter and the excitonic couplings obtained within a polarizable QM/MM methodology, optical spectra are calculated, which are in good qualitative agreement with experimental data. A weakness of the approach is however found in the overestimation of the fluctuations of the excitonic parameters of the pigments along the MD trajectory. An explanation for such a finding in terms of the limits of the force fields commonly used for protein cofactors is presented and discussed.

Energy transfer efficiency in the chromophore network strongly coupled to a vibrational mode

Using methods from condensed matter and statistical physics, we examine the transport of excitons through the photosynthetic complex from a receiving antenna to a reaction center. Writing the equations of motion for the exciton creation-annihilation operators, we are able to describe the exciton dynamics, even in the regime when the reorganization energy is of the order of the intrasystem couplings. We determine the exciton transfer efficiency in the presence of a quenching field and protein environment. While the majority of the protein vibrational modes are treated as a heat bath, we address the situation when specific modes are strongly coupled to excitons and examine the effects of these modes on the energy transfer efficiency in the steady-state regime. Using the structural parameters of the Fenna-Matthews-Olson complex, we find that, for vibrational frequencies below 16 meV, the exciton transfer is drastically suppressed. We attribute this effect to the formation of a "mixed exciton-vibrational mode" where the exciton is transferred back and forth between the two pigments with the absorption or emission of vibrational quanta, instead of proceeding to the reaction center. The same effect suppresses the quantum beating at the vibrational frequency of 25 meV. We also show that the efficiency of the energy transfer can be enhanced when the vibrational mode strongly couples to the third pigment only, instead of coupling to the entire system.

Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review

For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.

Effects of Different Quantum Coherence on the Pump-Probe Polarization Anisotropy of Photosynthetic Light-Harvesting Complexes: A Computational Study

Observations of oscillatory features in the 2D spectra of several photosynthetic complexes have led to diverged opinions on their origins, including electronic coherence, vibrational coherence, and vibronic coherence. In this work, effects of these different types of quantum coherence on ultrafast pump-probe polarization anisotropy are investigated and distinguished. We first simulate the isotropic pump-probe signal and anisotropy decay of the Fenna-Matthews-Olson (FMO) complex using a model with only electronic coherence at low temperature and obtain the same coherence time as in the previous experiment. Then, three model dimer systems with different prespecified quantum coherence are simulated, and the results show that their different spectral characteristics can be used to determine the type of coherence during the spectral process. Finally, we simulate model systems with different electronic-vibrational couplings and reveal the condition in which long time vibronic coherence can be observed in systems like the FMO complex.

Open quantum system parameters for light harvesting complexes from molecular dynamics

We elucidate the difference between various parameter extraction methods and demonstrate sensitivity to molecular dynamics equilibration.

Limits and potentials of quantum chemical methods in modelling photosynthetic antennae

A critical overview of quantum chemical approaches to simulate the light-harvesting process in photosynthetic antennae is presented together with a perspective on the developments that need to be introduced to reach a quantitative predictive power.

Constrained geometric dynamics of the Fenna-Matthews-Olson complex: the role of correlated motion in reducing uncertainty in excitation energy transfer

The trimeric Fenna-Mathews-Olson (FMO) complex of green sulphur bacteria is a well-studied example of a photosynthetic pigment-protein complex, in which the electronic properties of the pigments are modified by the protein environment to promote efficient excitonic energy transfer from antenna complexes to the reaction centres. By a range of simulation methods, many of the electronic properties of the FMO complex can be extracted from knowledge of the static crystal structure. However, the recent observation and analysis of long-lasting quantum dynamics in the FMO complex point to protein dynamics as a key factor in protecting and generating quantum coherence under laboratory conditions. While fast inter- and intra-molecular vibrations have been investigated extensively, the slow, conformational dynamics which effectively determine the optical inhomogeneous broadening of experimental ensembles has received less attention. The following study employs constrained geometric dynamics to study the flexibility in the protein network by efficiently generating the accessible conformational states from the published crystal structure. Statistical and principle component analyses reveal highly correlated low frequency motions between functionally relevant elements, including strong correlations between pigments that are excitonically coupled. Our analysis reveals a hierarchy of structural interactions which enforce these correlated motions, from the level of monomer-monomer interfaces right down to the α-helices, β-sheets and pigments. In addition to inducing strong spatial correlations across the conformational ensemble, we find that the overall rigidity of the FMO complex is exceptionally high. We suggest that these observations support the idea of highly correlated inhomogeneous disorder of the electronic excited states, which is further supported by the remarkably low variance (typically <5%) of the excitonic couplings of the conformational ensemble.

Different Types of Vibrations Interacting with Electronic Excitations in Phycoerythrin 545 and Fenna-Matthews-Olson Antenna Systems

The interest in the phycoerythrin 545 (PE545) photosynthetic antenna system of marine algae and the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has drastically increased since long-lived quantum coherences were reported for these complexes. For the PE545 complex, this phenomenon is clearly visible even at ambient temperatures, while for the FMO system it is more prominent at lower temperatures. The key to elucidate the role of the environment in these long-lived quantum effects is the spectral density. Here, we employ molecular dynamics simulations combined with quantum chemistry calculations to study the coupling between the biological environment and the vertical excitation energies of the bilin pigment molecules in PE545 and compare them to prior calculations on the FMO complex. It is found that the overall strength of the resulting spectral densities for the PE545 system is similar to the experiment-based counterpart but also to those in the FMO complex. Molecular analysis, however, reveals that the origin for the spectral densities in the low frequency range, which is most important for excitonic transitions, is entirely different. In the case of FMO, this part of the spectral density is due to environmental fluctuations, while, in case of PE545, it is essentially only due to internal modes of the bilin molecules. This finding sheds new light on possible explanations of the long-lived quantum coherences and that the reasons might actually be different in dissimilar systems.

Theoretical study on excited states of bacteriochlorophyll a in solutions with density functional assessment

The excited-state properties of bacteriochlorophyll (BChl) a in triethylamine, 1-propanol, and methanol are investigated with the time-dependent density functional theory by using the quantum mechanical and molecular mechanical reweighting free energy self-consistant field method. It is found that no prevalent density functionals can reproduce the experimental excited-state properties, i.e., the absorption and reorganization energies, of BChl a in the solutions. The parameter μ in the range-separated hybrid functional is therefore optimized to reproduce the differences of the absorption energies in the solutions. We examine the origin of the differences of the absorption energies in the solutions and find that sensitive balance between contributions of structural changes and solute-solvent interactions determines the differences. The accurate description of the excitation with the density functional with the adjusted parameter is therefore essential to the understanding of the excited-state properties of BChl a in proteins and also the mechanism of the photosynthetic systems.