Distinguishing the roles of energy funnelling and delocalization in photosynthetic light harvesting

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Large Scale Simulations of Photosynthetic Antenna Systems: Interplay of Cooperativity and Disorder

Large-scale simulations of light-matter interaction in natural photosynthetic antenna complexes containing more than one hundred thousands of chlorophyll molecules, comparable with natural size, have been performed. Photosynthetic antenna complexes present in Green sulfur bacteria and Purple bacteria have been analyzed using a radiative non-Hermitian Hamiltonian, well-known in the field of quantum optics, instead of the widely used dipole-dipole Frenkel Hamiltonian. This approach allows us to study ensembles of emitters beyond the small volume limit (system size much smaller than the absorbed wavelength), where the Frenkel Hamiltonian fails. When analyzed on a large scale, such structures display superradiant states much brighter than their single components. An analysis of the robustness to static disorder and dynamical (thermal) noise shows that exciton coherence in the whole photosynthetic complex is larger than the coherence found in its parts. This provides evidence that the photosynthetic complex as a whole plays a predominant role in sustaining coherences in the system even at room temperature. Our results allow a better understanding of natural photosynthetic antennae and could drive experiments to verify how the response to electromagnetic radiation depends on the size of the photosynthetic antenna.

Formally Exact Simulations of Mesoscale Exciton Diffusion in a Light-Harvesting 2 Antenna Nanoarray

The photosynthetic apparatus of plants and bacteria combine atomically precise pigment-protein complexes with dynamic membrane architectures to control energy transfer on the 10-100 nm length scales. Recently, synthetic materials have integrated photosynthetic antenna proteins to enhance exciton transport, though the influence of artificial packing on the excited-state dynamics in these biohybrid materials is not fully understood. Here, we use the adaptive hierarchy of pure states (adHOPS) to perform a formally exact simulation of excitation energy transfer within artificial aggregates of light-harvesting complex 2 (LH2) with a range of packing densities. We find that LH2 aggregates support a remarkable exciton diffusion length ranging from 100 nm at a biological packing density to 300 nm at the densest packing previously suggested in an artificial aggregate. The unprecedented scale of these formally exact calculations also underscores the efficiency with which adHOPS simulates excited-state processes in molecular materials.

Thermal site energy fluctuations in photosystem I: new insights from MD/QM/MM calculations

Cyanobacterial photosystem I (PSI) is one of the most efficient photosynthetic machineries found in nature. Due to the large scale and complexity of the system, the energy transfer mechanism from the antenna complex to the reaction center is still not fully understood. A central element is the accurate evaluation of the individual chlorophyll excitation energies (site energies). Such an evaluation must include a detailed treatment of site specific environmental influences on structural and electrostatic properties, but also their evolution in the temporal domain, because of the dynamic nature of the energy transfer process. In this work, we calculate the site energies of all 96 chlorophylls in a membrane-embedded model of PSI. The employed hybrid QM/MM approach using the multireference DFT/MRCI method in the QM region allows to obtain accurate site energies under explicit consideration of the natural environment. We identify energy traps and barriers in the antenna complex and discuss their implications for energy transfer to the reaction center. Going beyond previous studies, our model also accounts for the molecular dynamics of the full trimeric PSI complex. Via statistical analysis we show that the thermal fluctuations of single chlorophylls prevent the formation of a single prominent energy funnel within the antenna complex. These findings are also supported by a dipole exciton model. We conclude that energy transfer pathways may form only transiently at physiological temperatures, as thermal fluctuations overcome energy barriers. The set of site energies provided in this work sets the stage for theoretical and experimental studies on the highly efficient energy transfer mechanisms in PSI.

Environmentally Improved Coherent Light Harvesting

Coherence-enhanced light harvesting has not been directly observed experimentally, despite theoretical evidence that coherence can significantly enhance light-harvesting performance. The main experimental obstacle has been the difficulty in isolating the effect of coherence in the presence of confounding variables. Recent proposals for externally controlling coherence by manipulating the light's degree of polarization showed that coherent efficiency enhancements would be possible, but they were restricted to light-harvesting systems weakly coupled to their environment. Here, we show that increases in system-bath coupling strength can amplify coherent efficiency enhancements, rather than suppress them. This result dramatically broadens the range of systems that could be used to conclusively demonstrate coherence-enhanced light harvesting or to engineer coherent effects into artificial light-harvesting devices.

Do photosynthetic complexes use quantum coherence to increase their efficiency? Probably not

Answering the titular question has become a central motivation in the field of quantum biology, ever since the idea was raised following a series of experiments demonstrating wave-like behavior in photosynthetic complexes. Here, we report a direct evaluation of the effect of quantum coherence on the efficiency of three natural complexes. An open quantum systems approach allows us to simultaneously identify their level of "quantumness" and efficiency, under natural physiological conditions. We show that these systems reside in a mixed quantum-classical regime, characterized by dephasing-assisted transport. Yet, we find that the change in efficiency at this regime is minute at best, implying that the presence of quantum coherence does not play a substantial role in enhancing efficiency. However, in this regime, efficiency is independent of any structural parameters, suggesting that evolution may have driven natural complexes to their parameter regime to "design" their structure for other uses.

The dark side of energy transport along excitonic wires: On-site energy barriers facilitate efficient, vibrationally mediated transport through optically dark subspaces

We present a novel, counter-intuitive method, based on dark-state protection, for significantly improving exciton transport efficiency through "wires" comprising a chain of molecular sites with an intrinsic energy gradient. Specifically, by introducing "barriers" to the energy landscape at regular intervals along the transport path, we find that undesirable radiative recombination processes are suppressed due to a clear separation of sub-radiant and super-radiant eigenstates in the system. This, in turn, can lead to an improvement in transmitted power by many orders of magnitude, even for very long chains. From there, we analyze the robustness of this phenomenon to changes in both system and environment properties to show that this effect can be beneficial over a range of different thermal and optical environment regimes. Finally, we show that the novel energy landscape presented here may provide a useful foundation for overcoming the short length scales over which exciton diffusion typically occurs in organic photo-voltaics and other nanoscale transport scenarios, thus leading to considerable potential improvements in the efficiency of such devices.

Structure-based Hamiltonian model for IsiA uncovers a highly robust pigment-protein complex

The iron stress-induced protein A (IsiA) is a source of interest and debate in biological research. The IsiA supercomplex, binding over 200 chlorophylls, assembles in multimeric rings around photosystem I (PSI). Recently, the IsiA-PSI structure from Synechocystis sp. PCC 6803 was resolved to 3.48 Å. Based on this structure, we created a model simulating a single excitation event in an IsiA monomer. This model enabled us to calculate the fluorescence and the localization of the excitation in the IsiA structure. To further examine this system, noise was introduced to the model in two forms-thermal and positional. Introducing noise highlights the functional differences in the system between cryogenic temperatures and biologically relevant temperatures. Our results show that the energetics of the IsiA pigment-protein complex are very robust at room temperature. Nevertheless, shifts in the position of specific chlorophylls lead to large changes in their optical and fluorescence properties. Based on these results, we discuss the implication of highly robust structures, with potential for serving different roles in a context-dependent manner, on our understanding of the function and evolution of photosynthetic processes.

Classification of Coherent Enhancements of Light-Harvesting Processes

Several kinds of coherence have recently been shown to affect the performance of light-harvesting systems, in some cases significantly improving their efficiency. Here, we classify the possible mechanisms of coherent efficiency enhancements, based on the types of coherence that can characterize a light-harvesting system and the types of processes these coherences can affect. We show that enhancements are possible only when coherences and dissipative effects are best described in different bases of states. Our classification allows us to predict a previously unreported coherent enhancement mechanism, where coherence between delocalized eigenstates can be used to localize excitons away from dissipation, thus reducing the rate of recombination and increasing efficiency.

Why are photosynthetic reaction centres dimeric?

All photosynthetic organisms convert solar energy into chemical energy through charge separation in dimeric reaction centres. It is unknown why early reaction centres dimerised and completely displaced their monomeric ancestors. Here, we discuss several proposed explanations for reaction-centre dimerism and conclude-with only weak assumptions about the primordial dimerisation event-that the most probable explanation for the dimerism is that it arose because it enhanced light-harvesting efficiency by deepening the excitonic trap, i.e., by enhancing the rate of exciton transfer from an antenna complex and decreasing the rate of back transfer. This effect would have outweighed the negative effect dimerisation would have had on charge transfer within the reaction centre. Our argument implies that dimerisation likely occurred after the evolution of the first antennas, and it explains why the lower-energy state of the special pair is bright.

Quantum dissipative systems beyond the standard harmonic model: Features of linear absorption and dynamics

Current simulations of ultraviolet-visible absorption lineshapes and dynamics of condensed phase systems largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have the same curvature. Although convenient, for many realistic molecular systems, this approximation no longer suffices. We elucidate nonstandard harmonic and anharmonic effects on linear absorption and dynamics using a stochastic Schrödinger equation approach to account for the environment. First, a harmonic oscillator model with ground and excited potentials that differ in curvature is utilized. Using this model, it is shown that curvature difference gives rise to an additional substructure in the vibronic progression of absorption spectra. This effect is explained and subsequently quantified via a derived expression for the Franck-Condon coefficients. Subsequently, anharmonic features in dissipative systems are studied, using a Morse potential and parameters that correspond to the diatomic molecule H₂ for differing displacements and environment interaction. Finally, using a model potential, the population dynamics and absorption spectra for the stiff-stilbene photoswitch are presented and features are explained by a combination of curvature difference and anharmonicity in the form of potential energy barriers on the excited potential.

Theory for polariton-assisted remote energy transfer

Strong-coupling between light and matter produces hybridized states (polaritons) whose delocalization and electromagnetic character allow for novel modifications in spectroscopy and chemical reactivity of molecular systems. Recent experiments have demonstrated remarkable distance-independent long-range energy transfer between molecules strongly coupled to optical microcavity modes. To shed light on the mechanism of this phenomenon, we present the first comprehensive theory of polariton-assisted remote energy transfer (PARET) based on strong-coupling of donor and/or acceptor chromophores to surface plasmons. Application of our theory demonstrates that PARET up to a micron is indeed possible. In particular, we report two regimes for PARET: in one case, strong-coupling to a single type of chromophore leads to transfer mediated largely by surface plasmons while in the other case, strong-coupling to both types of chromophores creates energy transfer pathways mediated by vibrational relaxation. Importantly, we highlight conditions under which coherence enhances or deteriorates these processes. For instance, while exclusive strong-coupling to donors can enhance transfer to acceptors, the reverse turns out not to be true. However, strong-coupling to acceptors can shift energy levels in a way that transfer from acceptors to donors can occur, thus yielding a chromophore role-reversal or "carnival effect". This theoretical study demonstrates the potential for confined electromagnetic fields to control and mediate PARET, thus opening doors to the design of remote mesoscale interactions between molecular systems.

Generalised Marcus theory for multi-molecular delocalised charge transfer

Transfer of charges delocalised over multiple molecules can be described using the properties of the component molecules.

Although Marcus theory is widely used to describe charge transfer in molecular systems, in its usual form it is restricted to transfer from one molecule to another. If a charge is delocalised across multiple donor molecules, this approach requires us to treat the entire donor aggregate as a unified supermolecule, leading to potentially expensive quantum-chemical calculations and making it more difficult to understand how the aggregate components contribute to the overall transfer. Here, we show that it is possible to describe charge transfer between groups of molecules in terms of the properties of the constituent molecules and couplings between them, obviating the need for expensive supermolecular calculations. We use the resulting theory to show that charge delocalisation between molecules in either the donor or acceptor aggregates can enhance the rate of charge transfer through a process we call supertransfer (or suppress it through subtransfer). The rate can also be enhanced above what is possible with a single donor and a single acceptor by judiciously tuning energy levels and reorganisation energies. We also describe bridge-mediated charge transfer between delocalised molecular aggregates. The equations of generalised Marcus theory are in closed form, providing qualitative insight into the impact of delocalisation on charge dynamics in molecular systems.

Machine learning for quantum dynamics: deep learning of excitation energy transfer properties

Understanding the relationship between the structure of light-harvesting systems and their excitation energy transfer properties is of fundamental importance in many applications including the development of next generation photovoltaics. Natural light harvesting in photosynthesis shows remarkable excitation energy transfer properties, which suggests that pigment-protein complexes could serve as blueprints for the design of nature inspired devices. Mechanistic insights into energy transport dynamics can be gained by leveraging numerically involved propagation schemes such as the hierarchical equations of motion (HEOM). Solving these equations, however, is computationally costly due to the adverse scaling with the number of pigments. Therefore virtual high-throughput screening, which has become a powerful tool in material discovery, is less readily applicable for the search of novel excitonic devices. We propose the use of artificial neural networks to bypass the computational limitations of established techniques for exploring the structure-dynamics relation in excitonic systems. Once trained, our neural networks reduce computational costs by several orders of magnitudes. Our predicted transfer times and transfer efficiencies exhibit similar or even higher accuracies than frequently used approximate methods such as secular Redfield theory.

Structure-Dynamics Relation in Physically-Plausible Multi-Chromophore Systems

We study a large number of physically-plausible arrangements of chromophores, generated via a computational method involving stochastic real-space transformations of a naturally-occurring "reference" structure, illustrating our methodology using the well-studied Fenna-Matthews-Olson complex (FMO). To explore the idea that the natural structure has been tuned for efficient energy transport, we use an atomic transition charge method to calculate the excitonic couplings of each generated structure and a Lindblad master equation to study the quantum transport of an exciton from a "source" to a "drain" chromophore. We find significant correlations between structure and transport efficiency: High-performing structures tend to be more compact and, among those, the best structures display a certain orientation of the chromophores, particularly the chromophore closest to the source-to-drain vector. We conclude that, subject to reasonable, physically motivated constraints, the FMO complex is highly attuned to the purpose of energy transport, partly by exploiting these structural motifs.

Strong Impact of an Axial Ligand on the Absorption by Chlorophyll a and b Pigments Determined by Gas-Phase Ion Spectroscopy Experiments

The microenvironments in photosynthetic proteins affect the absorption by chlorophyll (Chl) pigments. It is, however, a challenge to disentangle the impact on the transition energies of different perturbations, for example, the global electrostatics of the protein (nonbonded environmental effects), exciton coupling between Chl's, conformational variations, and binding of an axial ligand to the magnesium center. This is needed to distinguish between the two most commonly proposed mechanisms for energy transport in photosynthetic proteins, relying on either weakly or strongly coupled pigments. Here, on the basis of photodissociation action spectroscopy, we establish that the redshift of the Soret absorption band due to binding of a negatively charged carboxylate (as present in aspartic acid and glutamic acid residues) is 0.1-0.2 eV for Chl a and b. This effect is almost enough to reproduce the well-known green color of plants and can account for the strong spectral variation between Chl's. The experimental data serve to benchmark future high-level calculations of excited-state energies. Finally, we demonstrate that complexes between Chl a and histidine, tagged by a quaternary ammonium ion, can be made in the gas phase by electrospray ionization, but more work is needed to produce enough ions for gas-phase spectroscopy.

Geometry, Supertransfer, and Optimality in the Light Harvesting of Purple Bacteria

The remarkable rotational symmetry of the photosynthetic antenna complexes of purple bacteria has long been thought to enhance their light harvesting and excitation energy transport. We study the role of symmetry by modeling hypothetical antennas whose symmetry is broken by altering the orientations of the bacteriochlorophyll pigments. We find that in both LH2 and LH1 complexes, symmetry increases energy transfer rates by enabling the cooperative, coherent process of supertransfer. The enhancement is particularly pronounced in the LH1 complex, whose natural geometry outperforms the average randomized geometry by 5.5 standard deviations, the most significant coherence-related enhancement found in a photosynthetic complex.