All-Atom Semiclassical Dynamics Study of Quantum Coherence in Photosynthetic Fenna–Matthews–Olson Complex

A size-consistent multi-state mapping approach to surface hopping

We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.

A Linearized Semiclassical Dynamics Study of the Multiquantum Vibrational Relaxation of NO Scattering from a Au(111) Surface

The vibrational relaxation of NO molecules scattering from a Au(111) surface has served as the focus of efforts to understand nonadiabatic energy transfer at metal-molecule interfaces. Experimental measurements and previous theoretical efforts suggest that multiquantal NO vibrational energy relaxation occurs via electron-hole pair excitations in the metal. Here, using a linearized semiclassical approach, we accurately predict the vibrational relaxation of NO from the νi = 3 state for different incident translational energies. We also accurately capture the central role of transient electron transfer from the metal to the molecule in mediating the vibrational relaxation process but fall short of quantitatively predicting the full extent of multiquantum relaxation for high incident vibrational excitations (νi = 16).

Effects of Heterogeneous Protein Environment on Excitation Energy Transfer Dynamics in the Fenna-Matthews-Olson Complex

The Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has been serving as a prototypical light-harvesting protein for studying excitation energy transfer (EET) dynamics in photosynthesis. The most widely used Frenkel exciton model for FMO complex assumes that each excited bacteriochlorophyll site couples to an identical and isolated harmonic bath, which does not account for the heterogeneous local protein environment. To better describe the realistic environment, we propose to use the recently developed multistate harmonic (MSH) model, which contains a globally shared bath that couples to the different pigment sites according to the atomistic quantum mechanics/molecular mechanics simulations with explicit protein scaffold and solvent. In this work, the effects of heterogeneous protein environment on EET in FMO complexes from Prosthecochloris aestuarii and Chlorobium tepidum, specifically including realistic spectral density, site-dependent reorganization energies, and system-bath couplings are investigated. Semiclassical and mixed quantum-classical mapping dynamics were applied to obtain the nonadiabatic EET dynamics in several models ranging from the Frenkel exciton model to the MSH model and their variants. The MSH model with realistic spectral density and site-dependent system-bath couplings displays slower EET dynamics than the Frenkel exciton model. Our comparative study shows that larger average reorganization energy, heterogeneity in spectral densities, and low-frequency modes could facilitate energy dissipation, which is insensitive to the static disorder in reorganization energies. The effects of the spectral densities and system-bath couplings along with the MSH model can be used to optimize EET dynamics for artificial light-harvesting systems.

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.

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.

Two-oscillator mapping modification of the Poisson bracket mapping equation formulation of the quantum-classical Liouville equation

Mapping basis solutions provide efficient ways for simulating mixed quantum-classical (MQC) dynamics in complex systems by matching multiple quantum states of interest to some fictitious physical states. Recently, various MQC methods were devised such that two harmonic oscillators are employed to represent each electronic state, showing improvements over one-oscillator-based methods. Here, we introduce and analyze newly modified mapping approximations of the quantum-classical Liouville equation (QCLE) using two oscillators for each electronic state. We design two separate mapping relations that we can adopt toward simulating dynamics and computing expectation values. Through the process, two MQC methods can be constructed, one of which actually reproduces the population dynamics of the forward and backward trajectory solution of QCLE. By applying the methods to spin-boson systems with a range of parameters, we find out that the choice of mapping relations greatly affects the simulation results. We also show that further improvement is possible through using modified identity operator formulations. Our findings may be helpful in constructing improved MQC methods in the future.

On the proper derivation of the Floquet-based quantum classical Liouville equation and surface hopping describing a molecule or material subject to an external field

We investigate different approaches to derive the proper Floquet-based quantum-classical Liouville equation (F-QCLE) for laser-driven electron-nuclear dynamics. The first approach projects the operator form of the standard QCLE onto the diabatic Floquet basis and then transforms to the adiabatic representation. The second approach directly projects the QCLE onto the Floquet adiabatic basis. Both approaches yield a form that is similar to the usual QCLE with two modifications: (1) The electronic degrees of freedom are expanded to infinite dimension and (2) the nuclear motion follows Floquet quasi-energy surfaces. However, the second approach includes an additional cross derivative force due to the dual dependence on time and nuclear motion of the Floquet adiabatic states. Our analysis and numerical tests indicate that this cross derivative force is a fictitious artifact, suggesting that one cannot safely exchange the order of Floquet state projection with adiabatic transformation. Our results are in accord with similar findings by Izmaylov et al., [J. Chem. Phys. 140, 084104 (2014)] who found that transforming to the adiabatic representation must always be the last operation applied, although now we have extended this result to a time-dependent Hamiltonian. This paper and the proper derivation of the F-QCLE should lay the basis for further improvements of Floquet surface hopping.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Improved population operators for multi-state nonadiabatic dynamics with the mixed quantum-classical mapping approach

Application to the 7-state Frenkel-exciton Hamiltonian for the Fenna–Matthews–Olson complex shows that using a different representation of the electronic population operators can drastically improve the accuracy of the quasiclassical mapping approach without increasing the computational effort.

Study of the exciton dynamics in perylene bisimide (PBI) aggregates with symmetrical quasiclassical dynamics based on the Meyer–Miller mapping Hamiltonian

The exciton dynamics in one-dimensional stacked PBI (Perylene Bisimide) aggregates was studied with SQC-MM dynamics (Symmetrical Quasiclassical Dynamics based on the Meyer–Miller mapping Hamiltonian).

Excited state energy fluctuations in the Fenna-Matthews-Olson complex from molecular dynamics simulations with interpolated chromophore potentials

We analyze the environment-induced fluctuation of pigment excitation energies in the Fenna-Matthews-Olson (FMO) complex from various perspectives, by employing an interpolation-based all-atom potential energy model for describing realistic pigment vibrations. We conduct molecular dynamics simulations on a 100 ns timescale, which is an extent that can enclose the effect of static disorder, and demonstrate its timescale separation from fast dynamic disorder. We extract the spectral densities of the complex by considering both the site and the exciton bases. We show that exciton delocalization reduces the effective environmental fluctuation and rationalize this aspect based on a model of fluctuating molecular aggregates. We also obtained the spectral density of the lowest exciton state under low temperature conditions and show that it reasonably well reproduces the experimental result. Finally, by additionally performing non-equilibrium excited state trajectory simulations, we show that the system lies well within the linear response regime after photo-absorption and that the pigments do not visit anharmonic regions of the potential surface to a significant extent. This indicates that methodologies based on harmonic bath models are indeed reasonable approaches for describing the excited state dynamics of the FMO complex.

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Exciton states and optical properties of the CP26 photosynthetic protein

The photosynthetic complex CP26, one of the minor antennae of the photosystem II, plays an important role in regulation of the excitation energy transfer in the PSII. Due to instability during isolation and purification, it remained poorly studied from the viewpoint of theoretical chemistry because of the absence of X-ray crystallography data. In this work, using the recently determined three-dimensional structure of the complex we apply the quantum chemical approach to study the properties of exciton states in it. Spectral properties, structure of exciton states and roles of the pigments in the complex and photosystem II are discussed.

Photosynthesis, pigment-protein complexes and electronic energy transport: simple models for complicated processes

In this review, we discuss our recent work on modelling biological pigment-protein complexes, such as the Fenna-Matthews-Olson complex and light-harvesting complex-II, to explain their electronic energy transport properties. In particular, we highlight how a network-based analysis approach, where the light-absorbing pigments are treated as a network of interconnected nodes, can provide a qualitative picture of quantum dynamic energy transport. With this in mind, we demonstrate how other properties such as robustness to environmental changes can be assessed in a simple and computationally tractable manner. Such analyses could prove useful for the design of artificial energy transport networks such as those which might find application in solar cells.

Evidence of Correlated Static Disorder in the Fenna-Matthews-Olson Complex

Observation of excitonic quantum beats in photosynthetic antennae has prompted wide debate regarding the function of excitonic coherence in pigment-protein complexes. Much of this work focuses on the interactions of excitons with the femto-to-picosecond dynamical fluctuations of their environment. However, in experiments these effects can be masked by static disorder of the excited-state energies across ensembles, whose microscopic origins are challenging to predict. Here the excited-state properties of ∼2000 atom clusters of the Fenna-Matthews-Olson complex are simulated using a unique combination of linear-scaling density functional theory and constrained geometric dynamics. While slow, large amplitude protein motion leads to large variations in the Q_y transitions of two pigments, we identify pigment-protein correlations that greatly reduce variations in the energy gap across the ensemble, which is consistent with experimental observations of suppressed inhomogeneous dephasing of quantum beats.

Photosynthetic pigment-protein complexes as highly connected networks: implications for robust energy transport

Photosynthetic pigment-protein complexes (PPCs) are a vital component of the light-harvesting machinery of all plants and photosynthesizing bacteria, enabling efficient transport of the energy of absorbed light towards the reaction centre, where chemical energy storage is initiated. PPCs comprise a set of chromophore molecules, typically bacteriochlorophyll species, held in a well-defined arrangement by a protein scaffold; this relatively rigid distribution leads to a viewpoint in which the chromophore subsystem is treated as a network, where chromophores represent vertices and inter-chromophore electronic couplings represent edges. This graph-based view can then be used as a framework within which to interrogate the role of structural and electronic organization in PPCs. Here, we use this network-based viewpoint to compare excitation energy transfer (EET) dynamics in the light-harvesting complex II (LHC-II) system commonly found in higher plants and the Fenna-Matthews-Olson (FMO) complex found in green sulfur bacteria. The results of our simple network-based investigations clearly demonstrate the role of network connectivity and multiple EET pathways on the efficient and robust EET dynamics in these PPCs, and highlight a role for such considerations in the development of new artificial light-harvesting systems.

Constructing an Interpolated Potential Energy Surface of a Large Molecule: A Case Study with Bacteriochlorophyll a Model in the Fenna-Matthews-Olson Complex

Constructing a reliable potential energy surface (PES) is a key step toward computationally studying the chemical dynamics of any molecular system. The interpolation scheme is a useful tool that can closely follow the accuracy of quantum chemical means at a dramatically reduced computational cost. However, applying interpolation to building a PES of a large molecule is not a straightforward black-box approach, as it frequently encounters practical difficulties associated with its large dimensionality. Here, we present detailed courses of applying interpolation toward building a PES of a large chromophore molecule. We take the example of S₀ and S₁ electronic states of bacteriochlorophyll a (BChla) molecules in the Fenna-Matthews-Olson light harvesting complex. With a reduced model molecule that bears BChla's main π-conjugated ring, various practical approaches are designed for improving the PES quality in a stable manner and for fine-tuning the final surface such that the surface can be adopted for long time molecular dynamics simulations. Combined with parallel implementation, we show that interpolated mechanics/molecular mechanics (IM/MM) simulations of the entire complex in the nanosecond time scale can be conducted readily without any practical issues. With 1500 interpolation data points for each chromophore unit, the PES error relative to the reference quantum chemical calculation is found to be ∼0.15 eV in the thermally accessible region of the conformational space, together with ∼0.01 eV error in S₀ - S₁ transition energies. The performance issue related to the use of a large interpolation database within the framework of our parallel routines is also discussed.

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.

Hybrid QM/MM study of FMO complex with polarized protein-specific charge

The Fenna-Matthews-Olson (FMO) light-harvesting complex is now one of the primary model systems for the study of excitation energy transfer (EET). However, the mechanism of the EET in this system is still controversial. In this work, molecular dynamics simulations and the electrostatic-embedding quantum-mechanics/molecular-mechanics single-point calculations have been employed to predict the energy transfer pathways utilizing the polarized protein-specific charge (PPC), which provides a more realistic description of Coulomb interaction potential in the protein than conventional mean-field charge scheme. The recently discovered eighth pigment has also been included in this study. Comparing with the conventional mean-field charges, more stable structures of FMO complex were found under PPC scheme during molecular dynamic simulation. Based on the electronic structure calculations, an exciton model was constructed to consider the couplings during excitation. The results show that pigments 3 and 4 dominate the lowest exciton levels whereas the highest exciton level are mainly constituted of pigments 1 and 6. This observation agrees well with the assumption based on the spatial distribution of the pigments. Moreover, the obtained spectral density in this study gives a reliable description of the diverse local environment embedding each pigment.

Effect of Chromophore Potential Model on the Description of Exciton-Phonon Interactions

System-bath interactions in nonadiabatic simulations are often depicted by first performing molecular dynamics calculations and then by evaluating excitation energies at the trajectory snapshots. Usually, molecular mechanics models and quantum chemical calculations are used in a mixed manner toward a trade-off between efficiency and accuracy. Here we investigate how this mixing scheme affects that depiction by using various potential energy surfaces (PESs) of coumarin-153 chromophore, with the help of interpolated PESs that can closely match the accuracies of quantum chemical calculations. We find that although spectral densities are computed only with second stage data the PES characteristics during the first sampling stage can still prevail in the densities, with limited influences on related reorganization energies. Our results suggest that using the mixed scheme can be acceptable when dynamics is mainly governed by the integrated effect of all phonon modes, but care must be taken for understanding detailed effects from individual modes.

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.

Constructing polyatomic potential energy surfaces by interpolating diabatic Hamiltonian matrices with demonstration on green fluorescent protein chromophore

Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.

Quantum dynamics in open quantum-classical systems

Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence on the properties of the quantum system. In many instances the environment is well-approximated by classical mechanics, so that one is led to consider the dynamics of open quantum-classical systems. Since a full quantum dynamical description of large many-body systems is not currently feasible, mixed quantum-classical methods can provide accurate and computationally tractable ways to follow the dynamics of both the system and its environment. This review focuses on quantum-classical Liouville dynamics, one of several quantum-classical descriptions, and discusses the problems that arise when one attempts to combine quantum and classical mechanics, coherence and decoherence in quantum-classical systems, nonadiabatic dynamics, surface-hopping and mean-field theories and their relation to quantum-classical Liouville dynamics, as well as methods for simulating the dynamics.

Electronic coherence and the kinetics of inter-complex energy transfer in light-harvesting systems

Comparison of inter-complex excitation energy transfer rates obtained in a general system (original, red) and in an alternative parameterization of the system that preserves static coherence while eliminating dynamic coherence (SCP, black) reveals that static coherence largely governs the kinetics of incoherent inter-complex EET in model light-harvesting networks, whereas dynamic coherence plays only a minor role.

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.

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.

Atomistic study of energy funneling in the light-harvesting complex of green sulfur bacteria

Phototrophic organisms such as plants, photosynthetic bacteria, and algae use microscopic complexes of pigment molecules to absorb sunlight. Within the light-harvesting complexes, which frequently have several functional and structural subunits, the energy is transferred in the form of molecular excitations with very high efficiency. Green sulfur bacteria are considered to be among the most efficient light-harvesting organisms. Despite multiple experimental and theoretical studies of these bacteria, the physical origin of the efficient and robust energy transfer in their light-harvesting complexes is not well understood. To study excitation dynamics at the systems level, we introduce an atomistic model that mimics a complete light-harvesting apparatus of green sulfur bacteria. The model contains approximately 4000 pigment molecules and comprises a double wall roll for the chlorosome, a baseplate, and six Fenna-Matthews-Olson trimer complexes. We show that the fast relaxation within functional subunits combined with the transfer between collective excited states of pigments can result in robust energy funneling to the initial excitation conditions and temperature changes. Moreover, the same mechanism describes the coexistence of multiple time scales of excitation dynamics frequently observed in ultrafast optical experiments. While our findings support the hypothesis of supertransfer, the model reveals energy transport through multiple channels on different length scales.

Quantum coherent energy transfer over varying pathways in single light-harvesting complexes

The initial steps of photosynthesis comprise the absorption of sunlight by pigment-protein antenna complexes followed by rapid and highly efficient funneling of excitation energy to a reaction center. In these transport processes, signatures of unexpectedly long-lived coherences have emerged in two-dimensional ensemble spectra of various light-harvesting complexes. Here, we demonstrate ultrafast quantum coherent energy transfer within individual antenna complexes of a purple bacterium under physiological conditions. We find that quantum coherences between electronically coupled energy eigenstates persist at least 400 femtoseconds and that distinct energy-transfer pathways that change with time can be identified in each complex. Our data suggest that long-lived quantum coherence renders energy transfer in photosynthetic systems robust in the presence of disorder, which is a prerequisite for efficient light harvesting.

The FMO complex in a glycerol-water mixture

Experimental findings of long-lived quantum coherence in the Fenna-Matthews-Olson (FMO) complex and other photosynthetic complexes have led to theoretical studies searching for an explanation of this unexpected phenomenon. Extending in this regard our own earlier calculations, we performed simulations of the FMO complex in a glycerol-water mixture at 310 K as well as 77 K, matching the conditions of earlier 2D spectroscopic experiments by Engel et al. The calculations, based on an improved quantum procedure employed by us already, yielded spectral densities of each individual pigment of FMO, in water and glycerol-water solvents at ambient temperature that compare well to prior experimental estimates. Due to the slow solvent dynamics at 77 K, the present results strongly indicate the presence of static disorder, i.e., disorder on a time scale beyond that relevant for the construction of spectral densities.