Coherent versus Incoherent Energy Transfer and Trapping in Photosynthetic Antenna Complexes

Coherent Charge Transfer Reveals a Different Theoretical Limit of Power Conversion Efficiency in Organic Solar Cells

The hopping charge transfer (CT) theory is used to explain the dynamics of traditional donor-acceptor (D-A) devices in organic solar cells (OSCs). But it is not applicable to the unconventional OSCs inspired by photosynthesis, referred to as Z-devices. In this study, we establish a universal heterojunction CT model in OSCs, based on the reported coherent CT in photosynthesis. Compared to the trade-off between energy loss and charge generation efficiency in the D-A device, we analyze its change in the Z-device. We introduce the "avalanche-like" CT of the Z-device induced by many-body Coulomb interaction and relevant experimental support. Combining with the Shockley-Queisser theory, we evaluate the theory limit power conversion efficiency of a D-A device and a Z-device. The Z-device has the potential to surpass the Shockley-Queisser limit of 33%.

Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment

Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.

Optimized excitonic transport mediated by local energy defects: Survival of optimization laws in the presence of dephasing

In an extended star with peripheral defects and a core occupied by a trap, it has been shown that exciton-mediated energy transport from the periphery to the core can be optimized [S. Yalouz et al., Phys. Rev. E 106, 064313 (2022)2470-004510.1103/PhysRevE.106.064313]. If the defects are judiciously chosen, then the exciton dynamics is isomorphic to that of an asymmetric chain and a speedup of the excitonic propagation is observed. Here we extend this previous work by considering that the exciton in both an extended star and an asymmetric chain is perturbed by the presence of a dephasing environment. Simulating the dynamics using a Lindblad master equation, two questions are addressed: How does the environment affect the energy transport on these two networks? and Do the two systems still behave equivalently in the presence of dephasing? Our results reveal that the timescale for the exciton dynamics strongly depends on the nature of the network. But quite surprisingly, the two networks behave similarly regarding the survival of their optimization law. In both cases, the energy transport can be improved using the same original optimal tuning of energy defects as long as the dephasing remains weak. However, for moderate or strong dephasing, the optimization law is lost due to quantum Zeno effect.

Environment-Assisted Modulation of Heat Flux in a Bio-Inspired System Based on Collision Model

The high energy transfer efficiency of photosynthetic complexes has been a topic of research across many disciplines. Several attempts have been made in order to explain this energy transfer enhancement in terms of quantum mechanical resources such as energetic and vibration coherence and constructive effects of environmental noise. The developments in this line of research have inspired various biomimetic works aiming to use the underlying mechanisms in biological light harvesting complexes for the improvement of synthetic systems. In this article, we explore the effect of an auxiliary hierarchically structured environment interacting with a system on the steady-state heat transport across the system. The cold and hot baths are modeled by a series of identically prepared qubits in their respective thermal states, and we use a collision model to simulate the open quantum dynamics of the system. We investigate the effects of system-environment, inter-environment couplings and coherence of the structured environment on the steady state heat flux and find that such a coupling enhances the energy transfer. Our calculations reveal that there exists a non-monotonic and non-trivial relationship between the steady-state heat flux and the mentioned parameters.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Redox conditions correlated with vibronic coupling modulate quantum beats in photosynthetic pigment-protein complexes

Quantum coherences, observed as time-dependent beats in ultrafast spectroscopic experiments, arise when light-matter interactions prepare systems in superpositions of states with differing energy and fixed phase across the ensemble. Such coherences have been observed in photosynthetic systems following ultrafast laser excitation, but what these coherences imply about the underlying energy transfer dynamics remains subject to debate. Recent work showed that redox conditions tune vibronic coupling in the Fenna-Matthews-Olson (FMO) pigment-protein complex in green sulfur bacteria, raising the question of whether redox conditions may also affect the long-lived (>100 fs) quantum coherences observed in this complex. In this work, we perform ultrafast two-dimensional electronic spectroscopy measurements on the FMO complex under both oxidizing and reducing conditions. We observe that many excited-state coherences are exclusively present in reducing conditions and are absent or attenuated in oxidizing conditions. Reducing conditions mimic the natural conditions of the complex more closely. Further, the presence of these coherences correlates with the vibronic coupling that produces faster, more efficient energy transfer through the complex under reducing conditions. The growth of coherences across the waiting time and the number of beating frequencies across hundreds of wavenumbers in the power spectra suggest that the beats are excited-state coherences with a mostly vibrational character whose phase relationship is maintained through the energy transfer process. Our results suggest that excitonic energy transfer proceeds through a coherent mechanism in this complex and that the coherences may provide a tool to disentangle coherent relaxation from energy transfer driven by stochastic environmental fluctuations.

Both electronic and vibrational coherences are involved in primary electron transfer in bacterial reaction center

Understanding the mechanism behind the near-unity efficiency of primary electron transfer in reaction centers is essential for designing performance-enhanced artificial solar conversion systems to fulfill mankind’s growing demands for energy. One of the most important challenges is distinguishing electronic and vibrational coherence and establishing their respective roles during charge separation. In this work we apply two-dimensional electronic spectroscopy to three structurally-modified reaction centers from the purple bacterium Rhodobacter sphaeroides with different primary electron transfer rates. By comparing dynamics and quantum beats, we reveal that an electronic coherence with dephasing lifetime of ~190 fs connects the initial excited state, P*, and the charge-transfer intermediate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}PA+PB-; this \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ \ast \to {\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}P*→PA+PB- step is associated with a long-lived quasi-resonant vibrational coherence; and another vibrational coherence is associated with stabilizing the primary photoproduct, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ + {\mathrm{B}}_{\mathrm{A}}^ -$$\end{document}P+BA-. The results show that both electronic and vibrational coherences are involved in primary electron transfer process and they correlate with the super-high efficiency.

Distinguishing electronic and vibrational coherences helps to clarify the near-unity efficiency of primary electron transfer in reaction centres. Here, the authors report their respective correlation with the electron transfer rate by comparing the 2D electronic spectra of three mutant reaction centres.

fs–ps Exciton dynamics in a stretched tetraphenylsquaraine polymer

A squaraine polymer shows surprisingly fast light induced energy transfer between two different structural sections on the ps/fs time scale.

Robust and Fragile Quantum Effects in the Transfer Kinetics of Delocalized Excitons between B850 Units of LH2 Complexes

Aggregates of light harvesting 2 (LH2) complexes form the major exciton-relaying domain in the photosynthetic unit of purple bacteria. Application of a generalized master equation to pairs of the B850 units of LH2 complexes, where excitons predominantly reside, provides quantitative information on how the inter-LH2 exciton transfer depends on the distance, relative rotational angle, and the relative energies of the two LH2s. The distance dependence demonstrates significant enhancement of the rate due to quantum delocalization of excitons, the qualitative nature of which remains robust against the disorder. The angle dependence reflects isotropic nature of exciton transfer, which remains similar for the ensemble of disorder. The variation of the rate on relative excitation energies of LH2 exhibits resonance peaks, which, however, is fragile as the disorder becomes significant. Overall, the average transfer times between two LH2s are estimated to be in the range of 4-25 ps for physically plausible inter-LH2 distances.

Chimera: enabling hierarchy based multi-objective optimization for self-driving laboratories

Finding the ideal conditions satisfying multiple pre-defined targets simultaneously is a challenging decision-making process, which impacts science, engineering, and economics. Additional complexity arises for tasks involving experimentation or expensive computations, as the number of evaluated conditions must be kept low. We propose Chimera as a general purpose achievement scalarizing function for multi-target optimization where evaluations are the limiting factor. Chimera combines concepts of a priori scalarizing with lexicographic approaches and is applicable to any set of n unknown objectives. Importantly, it does not require detailed prior knowledge about individual objectives. The performance of Chimera is demonstrated on several well-established analytic multi-objective benchmark sets using different single-objective optimization algorithms. We further illustrate the applicability and performance of Chimera with two practical examples: (i) the auto-calibration of a virtual robotic sampling sequence for direct-injection, and (ii) the inverse-design of a four-pigment excitonic system for an efficient energy transport. The results indicate that Chimera enables a wide class of optimization algorithms to rapidly find ideal conditions. Additionally, the presented applications highlight the interpretability of Chimera to corroborate design choices for tailoring system parameters.

Non-equilibrium stationary coherences in photosynthetic energy transfer under weak-field incoherent illumination

We present a theoretical study of the quantum dynamics of energy transfer in a model photosynthetic dimer excited by incoherent light and show that the interplay between incoherent pumping and phonon-induced relaxation, dephasing, and trapping leads to the emergence of non-equilibrium stationary states characterized by substantial stationary coherences in the energy basis. We obtain analytic expressions for these coherences in the limits of rapid dephasing of electronic excitations and of small excitonic coupling between the chromophores. The stationary coherences are maximized in the regime where the excitonic coupling is small compared to the trapping rate. We further show that the non-equilibrium coherences anti-correlate with the energy transfer efficiency in the regime of localized coupling to the reaction center and that no correlation exists under delocalized (Förster) trapping conditions.

Optimal dephasing for ballistic energy transfer in disordered linear chains

We study the interplay between dephasing, disorder, and coupling to a sink on transport efficiency in a one-dimensional chain of finite length N, and in particular the beneficial or detrimental effect of dephasing on transport. The excitation moves along the chain by coherent nearest-neighbor hopping Ω, under the action of static disorder W and dephasing γ. The last site is coupled to an external acceptor system (sink), where the excitation can be trapped with a rate Γ_{trap}. While it is known that dephasing can help transport in the localized regime, here we show that dephasing can enhance energy transfer even in the ballistic regime. Specifically, in the localized regime we recover previous results, where the optimal dephasing is independent of the chain length and proportional to W or W^{2}/Ω. In the ballistic regime, the optimal dephasing decreases as 1/N or 1/sqrt[N], respectively, for weak and moderate static disorder. When focusing on the excitation starting at the beginning of the chain, dephasing can help excitation transfer only above a critical value of disorder W^{cr}, which strongly depends on the sink coupling strength Γ_{trap}. Analytic solutions are obtained for short chains.

Quantum modeling of ultrafast photoinduced charge separation

Phenomena involving electron transfer are ubiquitous in nature, photosynthesis and enzymes or protein activity being prominent examples. Their deep understanding thus represents a mandatory scientific goal. Moreover, controlling the separation of photogenerated charges is a crucial prerequisite in many applicative contexts, including quantum electronics, photo-electrochemical water splitting, photocatalytic dye degradation, and energy conversion. In particular, photoinduced charge separation is the pivotal step driving the storage of sun light into electrical or chemical energy. If properly mastered, these processes may also allow us to achieve a better command of information storage at the nanoscale, as required for the development of molecular electronics, optical switching, or quantum technologies, amongst others. In this Topical Review we survey recent progress in the understanding of ultrafast charge separation from photoexcited states. We report the state-of-the-art of the observation and theoretical description of charge separation phenomena in the ultrafast regime mainly focusing on molecular- and nano-sized solar energy conversion systems. In particular, we examine different proposed mechanisms driving ultrafast charge dynamics, with particular regard to the role of quantum coherence and electron-nuclear coupling, and link experimental observations to theoretical approaches based either on model Hamiltonians or on first principles simulations.

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.

Opening-assisted coherent transport in the semiclassical regime

We study quantum enhancement of transport in open systems in the presence of disorder and dephasing. Quantum coherence effects may significantly enhance transport in open systems even in the semiclassical regime (where the decoherence rate is greater than the intersite hopping amplitude), as long as the disorder is sufficiently strong. When the strengths of disorder and dephasing are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected in the Fenna-Matthews-Olson (FMO) photosynthetic complex, which may be viewed as intermediate between these paradigmatic models.

Proposal for probing energy transfer pathway by single-molecule pump-dump experiment

The structure of Fenna-Matthews-Olson (FMO) light-harvesting complex had long been recognized as containing seven bacteriochlorophyll (BChl) molecules. Recently, an additional BChl molecule was discovered in the crystal structure of the FMO complex, which may serve as a link between baseplate and the remaining seven molecules. Here, we investigate excitation energy transfer (EET) process by simulating single-molecule pump-dump experiment in the eight-molecules complex. We adopt the coherent modified Redfield theory and non-Markovian quantum jump method to simulate EET dynamics. This scheme provides a practical approach of detecting the realistic EET pathway in BChl complexes with currently available experimental technology. And it may assist optimizing design of artificial light-harvesting devices.

Towards quantification of vibronic coupling in photosynthetic antenna complexes

Photosynthetic antenna complexes harvest sunlight and efficiently transport energy to the reaction center where charge separation powers biochemical energy storage. The discovery of existence of long lived quantum coherence during energy transfer has sparked the discussion on the role of quantum coherence on the energy transfer efficiency. Early works assigned observed coherences to electronic states, and theoretical studies showed that electronic coherences could affect energy transfer efficiency--by either enhancing or suppressing transfer. However, the nature of coherences has been fiercely debated as coherences only report the energy gap between the states that generate coherence signals. Recent works have suggested that either the coherences observed in photosynthetic antenna complexes arise from vibrational wave packets on the ground state or, alternatively, coherences arise from mixed electronic and vibrational states. Understanding origin of coherences is important for designing molecules for efficient light harvesting. Here, we give a direct experimental observation from a mutant of LH2, which does not have B800 chromophores, to distinguish between electronic, vibrational, and vibronic coherence. We also present a minimal theoretical model to characterize the coherences both in the two limiting cases of purely vibrational and purely electronic coherence as well as in the intermediate, vibronic regime.

Optimal efficiency of quantum transport in a disordered trimer

Disordered quantum networks, such as those describing light-harvesting complexes, are often characterized by the presence of peripheral ringlike structures, where the excitation is initialized, and inner structures and reaction centers (RCs), where the excitation is trapped and transferred. The peripheral rings often display distinguished coherent features: Their eigenstates can be separated, with respect to the transfer of excitation, into two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In the absence of disorder, superradiant states have an enhanced coupling strength to the RC, while the subradiant ones are basically decoupled from it. Static on-site disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. The problem of finding the optimal transfer conditions, as a function of both the RC energy and the disorder strength, is very complex even in the simplest network, namely, a three-level system. In this paper we analyze such trimeric structure, choosing as the initial condition an excitation on a subradiant state, rather than the more common choice of an excitation localized on a single site. We show that, while the optimal disorder is of the order of the superradiant coupling, the optimal detuning between the initial state and the RC energy strongly depends on system parameters: When the superradiant coupling is much larger than the energy gap between the superradiant and the subradiant levels, optimal transfer occurs if the RC energy is at resonance with the subradiant initial state, whereas we find an optimal RC energy at resonance with a virtual dressed state when the superradiant coupling is smaller than or comparable to the gap. The presence of dynamical noise, which induces dephasing and decoherence, affects the resonance structure of energy transfer producing an additional incoherent resonance peak, which corresponds to the RC energy being equal to the energy of the superradiant state.

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.

A Structural Model for a Self-Assembled Nanotube Provides Insight into Its Exciton Dynamics

The design and synthesis of functional self-assembled nanostructures is frequently an empirical process fraught with critical knowledge gaps about atomic-level structure in these noncovalent systems. Here, we report a structural model for a semiconductor nanotube formed via the self-assembly of naphthalenediimide-lysine (NDI-Lys) building blocks determined using experimental 13C-13C and 13C-15N distance restraints from solid-state nuclear magnetic resonance supplemented by electron microscopy and X-ray powder diffraction data. The structural model reveals a two-dimensional-crystal-like architecture of stacked monolayer rings each containing ∼50 NDI-Lys molecules, with significant π-stacking interactions occurring both within the confines of the ring and along the long axis of the tube. Excited-state delocalization and energy transfer are simulated for the nanotube based on time-dependent density functional theory and an incoherent hopping model. Remarkably, these calculations reveal efficient energy migration from the excitonic bright state, which is in agreement with the rapid energy transfer within NDI-Lys nanotubes observed previously using fluorescence spectroscopy.

On the relation of energy and electron transfer in multidimensional chromophores based on polychlorinated triphenylmethyl radicals and triarylamines

Chromophores with many donors and acceptors show electron transfer which is identical to energy transfer.

Intermolecular vibrational energy transfers in liquids and solids

Resonant and nonresonant intermolecular vibrational energy transfers in liquids and solids are measured and elucidated using two competing mechanisms.

Two-dimensional electronic spectroscopy of bacteriochlorophyll a in solution: Elucidating the coherence dynamics of the Fenna-Matthews-Olson complex using its chromophore as a control

Following the observation of long-lived coherences in the two-dimensional (2D) electronic spectra of the Fenna-Matthews-Olson (FMO) complex, many theoretical works suggest that coherences between excitons may play a role in the efficient energy transfer that occurs in photosynthetic antennae. This interpretation of the dynamics depends on the assignment of quantum beating signals to superpositions of excitons, which is complicated by the possibility of observing both electronic and vibrational coherences in 2D spectra. Here, we explore 2D spectra of bacteriochlorophyll a (BChla) in solution in an attempt to isolate vibrational beating signals in the absence of excitonic signals to identify the origin of the quantum beats in 2D spectra of FMO. Even at high laser power, our BChla spectra show strong beating only from the nonresonant response of the solvent. The beating signals that we can conclusively assign to vibrational modes of BChla are only slightly above the noise and at higher frequencies than those previously observed in spectra of FMO. Our results suggest that the beating observed in spectra of FMO is of a radically different character than the signals observed here and can therefore be attributed to electronic coherences or intermolecular degrees of freedom.

Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers

Calculating the evolution of an open quantum system, i.e., a system in contact with a thermal environment, has presented a theoretical and computational challenge for many years. With the advent of supercomputers containing large amounts of memory and many processors, the computational challenge posed by the previously intractable theoretical models can now be addressed. The hierarchy equations of motion present one such model and offer a powerful method that remained under-utilized so far due to its considerable computational expense. By exploiting concurrent processing on parallel computers the hierarchy equations of motion can be applied to biological-scale systems. Herein we introduce the quantum dynamics software PHI, that solves the hierarchical equations of motion. We describe the integrator employed by PHI and demonstrate PHI's scaling and efficiency running on large parallel computers by applying the software to the calculation of inter-complex excitation transfer between the light harvesting complexes 1 and 2 of purple photosynthetic bacteria, a 50 pigment system.

Measures and implications of electronic coherence in photosynthetic light-harvesting

We review various methods for measuring delocalization in light-harvesting complexes. Direct relations between inverse participation ratios (IPRs) and entanglement measures are derived. The B850 ring from the LH2 complex in Rhodopseudomonas acidophila is studied. By analysing electronic energy transfer dynamics in the B850 ring using different metrics for quantifying excitonic delocalization, we conclude that measures of entanglement are far more robust (in terms of time scale, temperature and level of decoherence) than IPRs, and are therefore more appropriate for the purpose of studying the time evolution of coherence in a system.

Microscopic quantum coherence in a photosynthetic-light-harvesting antenna

We briefly review the coherent quantum beats observed in recent two-dimensional electronic spectroscopy experiments in a photosynthetic-light-harvesting antenna. We emphasize that the decay of the quantum beats in these experiments is limited by ensemble averaging. The in vivo dynamics of energy transport depends upon the local fluctuations of a single photosynthetic complex during the energy transfer time (a few picoseconds). Recent analyses suggest that it remains possible that the quantum-coherent motion may be robust under individual realizations of the environment-induced fluctuations contrary to intuition obtained from condensed phase spectroscopic measurements and reduced density matrices. This result indicates that the decay of the observed quantum coherence can be understood as ensemble dephasing. We propose a fluorescence-detected single-molecule experiment with phase-locked excitation pulses to investigate the coherent dynamics at the level of a single molecule without hindrance by ensemble averaging. We discuss the advantages and limitations of this method. We report our initial results on bulk fluorescence-detected coherent spectroscopy of the Fenna-Mathews-Olson complex.

How Quantum Coherence Assists Photosynthetic Light Harvesting

This perspective examines how hundreds of pigment molecules in purple bacteria cooperate through quantum coherence to achieve remarkable light harvesting efficiency. Quantum coherent sharing of excitation, which modifies excited state energy levels and combines transition dipole moments, enables rapid transfer of excitation over large distances. Purple bacteria exploit the resulting excitation transfer to engage many antenna proteins in light harvesting, thereby increasing the rate of photon absorption and energy conversion. We highlight here how quantum coherence comes about and plays a key role in the photosynthetic apparatus of purple bacteria.

Energy transfer and structure determination of porphyrin dimers linked via a phenylenebisvinylene bridge: A time-resolved triplet electron paramagnetic resonance study

The photoexcited triplet state in a series of homo and hetero dimers was examined by time resolved electron paramagnetic resonance (TREPR) spectroscopy. The systems studied here consist of free-base tetraxylylporphyrin ( H 2 TXP ) and Zn (II) tetraxylylporphyrin ( ZnTXP ) and held together covalently by phenylenebisvinylene bridge at different positions. Experiments were carried out on the dimers, dissolved in an isotropic matrix (toluene), and in an anisotropic matrix of a liquid crystal (LC). Analysis of the results demonstrates that the dimers exhibit different geometries, depending on the linkage. Specifically, the triplet line shape analysis indicates that the para-dimers have a planar structure, the meta-dimers reveal the existence of two structural conformers, i.e. planar and slightly bent, while the ortho-dimers are characterized by the strongly bent molecular structure. The dimers exhibit efficient intramolecular singlet energy transfer (EnT) from ZnTXP to H 2 TXP subunit. On the other hand, EnT in all hetero dimers studied here is incomplete and some contribution from ZnTXP subunit is present in all triplet spectra. Thus, the efficiency of the EnT in the present systems is determined by properties of the connecting spacer, and does not depend on specific conformation and geometry of the molecule.

High-Performance Solution of Hierarchical Equations of Motion for Studying Energy Transfer in Light-Harvesting Complexes

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the possibility of memory effects in this process and require one to consider time nonlocal propagation techniques. The hierarchical equations of motion (HEOM) were proposed by Ishizaki and Fleming to describe the site-dependent reorganization dynamics of protein environments ( J. Chem. Phys. 2009 , 130 , 234111 ), which plays a significant role in photosynthetic electronic energy transfer. HEOM are often used as a reference for other approximate methods but have been implemented only for small systems due to their adverse computational scaling with the system size. Here, we show that HEOM are also solvable for larger systems, since the underlying algorithm is ideally suited for the usage of graphics processing units (GPU). The tremendous reduction in computational time due to the GPU allows us to perform a systematic study of the energy-transfer efficiency in the Fenna-Matthews-Olson (FMO) light-harvesting complex at physiological temperature under full consideration of memory effects. We find that approximative methods differ qualitatively and quantitatively from the HEOM results and discuss the importance of finite temperature to achieving high energy-transfer efficiencies.

Multiphonon transitions in the biomolecular energy transfer dynamics

We show that the biomolecular exciton dynamics under the influence of slow polarization fluctuations in the solvent cannot be described by lowest order, one-phonon approaches which are perturbative in the system-bath coupling. Instead, nonperturbative multiphonon transitions induced by the slow bath yield significant contributions. This is shown by comparing results for the decoherence rate of the exciton dynamics of a resumed perturbation theory with numerically exact real-time path-integral data. The exact decoherence rate for realistically slow solvent environments is significantly modified by multiphonon processes even in the weak coupling regime, while a one-phonon description is satisfactory only for fast environmental noise. Slow environments inhibit bath modes that are resonant with the exciton dynamics, thereby suppressing one-phonon transitions and enhancing multiphonon processes, which are typically not captured by lowest order perturbative treatments, such as Redfield or Lindblad approaches, even in more refined variants.

Could light harvesting complexes exhibit non-classical effects at room temperature?

Mounting experimental and theoretical evidence suggest that coherent quantum effects play a role in the efficient transfer of an excitation from a chlorosome antenna to a reaction centre in the Fenna–Matthews–Olson protein complex. However, it is conceivable that a satisfying alternate interpretation of the results is possible in terms of a classical theory. To address this possibility, we consider a class of classical theories satisfying the minimal postulates of macrorealism and frame Leggett–Garg-type tests that could rule them out. Our numerical simulations indicate that even in the presence of decoherence, several tests could exhibit the required violations of the Leggett–Garg inequality. Remarkably, some violations persist even at room temperature for our decoherence model.

Electromagnetic biostimulation of living cultures for biotechnology, biofuel and bioenergy applications

The surge of interest in bioenergy has been marked with increasing efforts in research and development to identify new sources of biomass and to incorporate cutting-edge biotechnology to improve efficiency and increase yields. It is evident that various microorganisms will play an integral role in the development of this newly emerging industry, such as yeast for ethanol and Escherichia coli for fine chemical fermentation. However, it appears that microalgae have become the most promising prospect for biomass production due to their ability to grow fast, produce large quantities of lipids, carbohydrates and proteins, thrive in poor quality waters, sequester and recycle carbon dioxide from industrial flue gases and remove pollutants from industrial, agricultural and municipal wastewaters. In an attempt to better understand and manipulate microorganisms for optimum production capacity, many researchers have investigated alternative methods for stimulating their growth and metabolic behavior. One such novel approach is the use of electromagnetic fields for the stimulation of growth and metabolic cascades and controlling biochemical pathways. An effort has been made in this review to consolidate the information on the current status of biostimulation research to enhance microbial growth and metabolism using electromagnetic fields. It summarizes information on the biostimulatory effects on growth and other biological processes to obtain insight regarding factors and dosages that lead to the stimulation and also what kind of processes have been reportedly affected. Diverse mechanistic theories and explanations for biological effects of electromagnetic fields on intra and extracellular environment have been discussed. The foundations of biophysical interactions such as bioelectromagnetic and biophotonic communication and organization within living systems are expounded with special consideration for spatiotemporal aspects of electromagnetic topology, leading to the potential of multipolar electromagnetic systems. The future direction for the use of biostimulation using bioelectromagnetic, biophotonic and electrochemical methods have been proposed for biotechnology industries in general with emphasis on an holistic biofuel system encompassing production of algal biomass, its processing and conversion to biofuel.

Correlation-dependent coherent to incoherent transitions in resonant energy transfer dynamics

I investigate energy transfer in a donor-acceptor pair beyond weak system-bath coupling. I identify a transition from coherent to incoherent dynamics with increasing temperature, due to multiphonon effects not captured by a standard weak-coupling treatment. The crossover temperature has a marked dependence on the degree of spatial correlation between fluctuations experienced at the two system sites. For strong correlations, this leads to the possibility of coherence surviving into a high-temperature regime.

Role of quantum coherence and environmental fluctuations in chromophoric energy transport

The role of quantum coherence in the dynamics of photosynthetic energy transfer in chromophoric complexes is not fully understood. In this work, we quantify the biological importance of fundamental physical processes, such as the excitonic Hamiltonian evolution and phonon-induced decoherence, by their contribution to the efficiency of the primary photosynthetic event. We study the effect of spatial correlations in the phonon bath and slow protein scaffold movements on the efficiency and the contributing processes. To this end, we develop two theoretical approaches based on a Green's function method and energy transfer susceptibilities. We investigate the Fenna-Matthews-Olson protein complex, in which we find a contribution of coherent dynamics of about 10% in the presence of uncorrelated phonons and about 30% in the presence of realistically correlated ones.

Dynamics of light harvesting in photosynthesis

We review recent theoretical and experimental advances in the elucidation of the dynamics of light harvesting in photosynthesis, focusing on recent theoretical developments in structure-based modeling of electronic excitations in photosynthetic complexes and critically examining theoretical models for excitation energy transfer. We then briefly describe two-dimensional electronic spectroscopy and its application to the study of photosynthetic complexes, in particular the Fenna-Matthews-Olson complex from green sulfur bacteria. This review emphasizes recent experimental observations of long-lasting quantum coherence in photosynthetic systems and the implications of quantum coherence in natural photosynthesis.

A Hexagonal Prismatic Porphyrin Array: Synthesis, STM Detection, and Efficient Energy Hopping in Near-Infrared Region

A belt-shaped hexagonal cyclic porphyrin array 2 that comprises of six meso-meso, beta-beta, beta-beta triply linked diporphyrins 3 bridged by 1,3-phenylene spacers is prepared by oxidation from cyclic dodecameric array 1 consisting of six meso-meso directly linked diporphyrins 4 with DDQ and Sc(OTf)3. The absorption spectrum of 2 is similar to that of the constituent subunit 3 but shows a slight red-shift for the Q-bands in near-infrared (NIR) region, indicating the exciton coupling between the neighboring diporphyrin chromophores. Observed total exciton coupling energies in the absorption spectra were largely matched with the calculated values based on point-dipole exciton coupling approximation. It was found that the experimental exciton coupling strength (292 cm(-1)) of the Q-band in 2 is slightly larger than the calculated one (99 cm(-1)), indicating that the electronic communications are enhanced through 1,3-phenylene linkers in hexameric macromolecule. A rate of the excitation energy hopping (EEH) that occurs in 2 at the lowest excited singlet state in the near-infrared region has been determined to be (1.8 ps)(-1) on the basis of the pump-power dependent femtosecond transient absorption (TA) and the transient absorption anisotropy (TAA) decay measurements. The 2 times faster EEH rate of 2 than that of 1 (4.0 ps)(-1) mainly comes from involving through-bond energy transfer among diporphyrin subunits via 1,3-phenylene bridges as well as Förster-type through-space EEH processes. STM measurement of 2 in the Cu(100) surface revealed that it takes several discrete conformations with respect to the relative orientation of neighboring diporphyrins. Collectively, an effective EEH in the NIR region is realized in 2 due largely to the intensified oscillator strength in the S(1) state (Q-band) and the close proximity held by 1,3-phenylene spacers.

Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems

Photosynthetic complexes are exquisitely tuned to capture solar light efficiently, and then transmit the excitation energy to reaction centres, where long term energy storage is initiated. The energy transfer mechanism is often described by semiclassical models that invoke 'hopping' of excited-state populations along discrete energy levels. Two-dimensional Fourier transform electronic spectroscopy has mapped these energy levels and their coupling in the Fenna-Matthews-Olson (FMO) bacteriochlorophyll complex, which is found in green sulphur bacteria and acts as an energy 'wire' connecting a large peripheral light-harvesting antenna, the chlorosome, to the reaction centre. The spectroscopic data clearly document the dependence of the dominant energy transport pathways on the spatial properties of the excited-state wavefunctions of the whole bacteriochlorophyll complex. But the intricate dynamics of quantum coherence, which has no classical analogue, was largely neglected in the analyses-even though electronic energy transfer involving oscillatory populations of donors and acceptors was first discussed more than 70 years ago, and electronic quantum beats arising from quantum coherence in photosynthetic complexes have been predicted and indirectly observed. Here we extend previous two-dimensional electronic spectroscopy investigations of the FMO bacteriochlorophyll complex, and obtain direct evidence for remarkably long-lived electronic quantum coherence playing an important part in energy transfer processes within this system. The quantum coherence manifests itself in characteristic, directly observable quantum beating signals among the excitons within the Chlorobium tepidum FMO complex at 77 K. This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path.