How Quantum Coherence Assists 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.

Bioinspired polymeric supramolecular columns as efficient yet controllable artificial light-harvesting platform

Light-harvesting is an indispensable process in photosynthesis, and researchers have been exploring various structural scaffolds to create artificial light-harvesting systems. However, achieving high donor/acceptor ratios for efficient energy transfer remains a challenge as excitons need to travel longer diffusion lengths within the donor matrix to reach the acceptor. Here, we report a polymeric supramolecular column-based light-harvesting platform inspired by the natural light-harvesting of purple photosynthetic bacteria to address this issue. The supramolecular column is designed as a discotic columnar liquid crystalline polymer and acts as the donor, with the acceptor intercalated within it. The modular columnar design enables an ultrahigh donor/acceptor ratio of 20000:1 and an antenna effect exceeding 100. Moreover, the spatial confinement within the supramolecular columns facilitates control over the energy transfer process, enabling dynamic full-color tunable emission for information encryption applications with spatiotemporal regulation security.

Pursuing excitonic energy transfer with programmable DNA-based optical breadboards

DNA nanotechnology has now enabled the self-assembly of almost any prescribed 3-dimensional nanoscale structure in large numbers and with high fidelity. These structures are also amenable to site-specific modification with a variety of small molecules ranging from drugs to reporter dyes. Beyond obvious application in biotechnology, such DNA structures are being pursued as programmable nanoscale optical breadboards where multiple different/identical fluorophores can be positioned with sub-nanometer resolution in a manner designed to allow them to engage in multistep excitonic energy-transfer (ET) via Förster resonance energy transfer (FRET) or other related processes. Not only is the ability to create such complex optical structures unique, more importantly, the ability to rapidly redesign and prototype almost all structural and optical analogues in a massively parallel format allows for deep insight into the underlying photophysical processes. Dynamic DNA structures further provide the unparalleled capability to reconfigure a DNA scaffold on the fly in situ and thus switch between ET pathways within a given assembly, actively change its properties, and even repeatedly toggle between two states such as on/off. Here, we review progress in developing these composite materials for potential applications that include artificial light harvesting, smart sensors, nanoactuators, optical barcoding, bioprobes, cryptography, computing, charge conversion, and theranostics to even new forms of optical data storage. Along with an introduction into the DNA scaffolding itself, the diverse fluorophores utilized in these structures, their incorporation chemistry, and the photophysical processes they are designed to exploit, we highlight the evolution of DNA architectures implemented in the pursuit of increased transfer efficiency and the key lessons about ET learned from each iteration. We also focus on recent and growing efforts to exploit DNA as a scaffold for assembling molecular dye aggregates that host delocalized excitons as a test bed for creating excitonic circuits and accessing other quantum-like optical phenomena. We conclude with an outlook on what is still required to transition these materials from a research pursuit to application specific prototypes and beyond.

Directed Gradients in the Excited-State Energy Landscape of Poly(3-hexylthiophene) Nanofibers

Funneling excitation energy toward lower energy excited states is a key concept in photosynthesis, which is often realized with at most two chemically different types of pigment molecules. However, current synthetic approaches to establish energy funnels, or gradients, typically rely on Förster-type energy-transfer cascades along many chemically different molecules. Here, we demonstrate an elegant concept for a gradient in the excited-state energy landscape along micrometer-long supramolecular nanofibers based on the conjugated polymer poly(3-hexylthiophene), P3HT, as the single component. Precisely aligned P3HT nanofibers within a supramolecular superstructure are prepared by solution processing involving an efficient supramolecular nucleating agent. Employing hyperspectral imaging, we find that the lowest-energy exciton band edge continuously shifts to lower energies along the nanofibers' growth direction. We attribute this directed excited-state energy gradient to defect fractionation during nanofiber growth. Our concept provides guidelines for the design of supramolecular structures with an intrinsic energy gradient for nanophotonic applications.

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.

Experimental and computational characterisation of an artificial light harvesting complex

Photosynthesis has been shown to be a highly efficient process for energy transfer in plants and bacteria. Like natural photosynthetic systems, the artificial light harvesting complex (LHC) BODIPY pillar[5]arene exhibits Förster resonance energy transfer (FRET). However, extensive characterisation of the BODIPY pillar[5]arene LHC to determine its suitability as an artificial LHC has yet to occur. In this paper we experimentally and computationally investigate the photophysical properties of the LHC by comparing the light absorption of the BODIPY LHC to individual BODIPY chromophores. Our results show evidence for quantum coherence, with oscillation frequencies of 100 cm^-1 and 600 cm^-1, which are attributable to vibronic, or exciton-phonon type coupling. Computational analysis suggests strong couplings of the molecular orbitals of the LHC resulting from the stacking of neighbouring BODIPY chromophore units. Interestingly, we find a 40% reduction in the absorbance of light for the BODIPY LHC compared to the individual chromophores which we attribute to electronic interactions between the conjugated π-systems of the BODIPY chromophores and the pillar[5]arene backbone.

Semiclassical Theory of Multistage Nonequilibrium Electron Transfer in Macromolecular Compounds in Polar Media with Several Relaxation Timescales

Many specific features of ultrafast electron transfer (ET) reactions in macromolecular compounds can be attributed to nonequilibrium configurations of intramolecular vibrational degrees of freedom and the environment. In photoinduced ET, nonequilibrium nuclear configurations are often produced at the stage of optical excitation, but they can also be the result of electron tunneling itself, i.e., fast redistribution of charges within the macromolecule. A consistent theoretical description of ultrafast ET requires an explicit consideration of the nuclear subsystem, including its evolution between electron jumps. In this paper, the effect of the multi-timescale nuclear reorganization on ET transitions in macromolecular compounds is studied, and a general theory of ultrafast ET in non-Debye polar environments with a multi-component relaxation function is developed. Particular attention is paid to designing the multidimensional space of nonequilibrium nuclear configurations, as well as constructing the diabatic free energy surfaces for the ET states. The reorganization energies of individual ET transitions, the equilibrium energies of ET states, and the relaxation properties of the environment are used as input data for the theory. The effect of the system-environment interaction on the ET kinetics is discussed, and mechanisms for enhancing the efficiency of charge separation in macromolecular compounds are analyzed.

Synthesis and Properties of Electron-Deficient and Electron-Rich Redox-Active Ionic π-Systems

There is growing interest towards the design and synthesis of organic redox-active systems, which exist in ionic form. Multi- redox systems entail life-sustaining processes like photosynthesis and cellular respiration. The significant challenge for material scientists is to rationally design complex molecular materials that can store and transfer multiple electrons at low operational potentials and are stable under ambient conditions. Also, important are the designed ionic π-systems that combine efficient electron and ion transport. Here, we discuss the synthesis of ionic π-systems which exist in the closed-shell form. Firstly, different classes of ionic arylenediimides and viologens with different π-linkers are discussed from the synthetic, structural and redox perspective. These ionic π-systems are based on the electron deficient π-scaffolds, and are shown to accumulate upto six electrons. We then discuss electron-rich ionic arylenediimides which can exist in anionic form or zwitterionic form. The anionic electron donors have absorption extending to the near Infrared (NIR) region and can be stabilized in aqueous solution. We also discuss the effect of the electron accumulation on the aromaticity and non-aromaticity of the naphthalene and the imide rings of the naphthalenediimides. We finally discuss in brief, the applications related to the organic mixed ionic-electronic conductors.

Aromatic patterns: Tryptophan aromaticity as a catalyst for the emergence of life and rise of consciousness

Sunlight held the key to the origin of life on Earth. The earliest life forms, cyanobacteria, captured the sunlight to generate energy through photosynthesis. Life on Earth evolved in accordance with the circadian rhythms tied to sensitivity to sunlight patterns. A unique feature of cyanobacterial photosynthetic proteins and circadian rhythms' molecules, and later of nearly all photon-sensing molecules throughout evolution, is that the aromatic amino acid tryptophan (Trp) resides at the center of light-harvesting active sites. In this perspective, I review the literature and integrate evidence from different scientific fields to explore the role Trp plays in photon-sensing capabilities of living organisms through its resonance delocalization of π-electrons. The observations presented here are the product of apparently unrelated phenomena throughout evolution, but nevertheless share consistent patterns of photon-sensing by Trp-containing and Trp-derived molecules. I posit the unique capacity to transfer electrons during photosynthesis in the earliest life forms is conferred to Trp due to its aromaticity. I propose this ability evolved to assume more complex functions, serving as a host for mechanisms underlying mental aptitudes - a concept which provides a theoretical basis for defining the neural correlates of consciousness. The argument made here is that Trp aromaticity may have allowed for the inception of the mechanistic building blocks used to fabricate complexity in higher forms of life. More specifically, Trp aromatic non-locality may have acted as a catalyst for the emergence of consciousness by instigating long-range synchronization and stabilizing the large-scale coherence of neural networks, which mediate functional brain activity. The concepts proposed in this perspective provide a conceptual foundation that invites further interdisciplinary dialogue aimed at examining and defining the role of aromaticity (beyond Trp) in the emergence of life and consciousness.

A Chirality-Based Quantum Leap

There is increasing interest in the study of chiral degrees of freedom occurring in matter and in electromagnetic fields. Opportunities in quantum sciences will likely exploit two main areas that are the focus of this Review: (1) recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials and (2) rapidly evolving nanophotonic strategies designed to amplify chiral light-matter interactions. On the one hand, the CISS effect underpins the observation that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision and molecular modularity. On the other hand, chiral-optical effects that depend on both spin- and orbital-angular momentum of photons could offer key advantages in all-optical and quantum information technologies. In particular, amplification of these chiral light-matter interactions using rationally designed plasmonic and dielectric nanomaterials provide approaches to manipulate light intensity, polarization, and phase in confined nanoscale geometries. Any technology that relies on optimal charge transport, or optical control and readout, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which has not yet been fully developed. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking Review provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects and presents a vision for their possible future roles in enabling room-temperature quantum technologies.

Strong coupling between an optical microcavity and photosystems in single living cyanobacteria

The first step in photosynthesis is an extremely efficient energy transfer mechanism that led to the debate to which extent quantum coherence may be involved in the energy transfer between the photosynthetic pigments. In search of such a coherent behavior, we have embedded living cyanobacteria between the parallel mirrors of an optical microresonator irradiated with low intensity white light. As a consequence, we observe vacuum Rabi splitting in the transmission and fluorescence spectra as a result of strong light matter coupling of the chlorophyll a molecules in the photosystems (PSs) and the cavity modes. The Rabi-splitting scales with the number of the PSs chlorophyll a pigments involved in strong coupling indicating a delocalized polaritonic state. Our data provide evidence that a delocalized polaritonic state can be established between the chlorophyll a molecule of the PSs in living cyanobacterial cells at ambient conditions in a microcavity.

Photosynthetic Nanomaterial Hybrids for Bioelectricity and Renewable Energy Systems

Harvesting solar energy in the form of electricity from the photosynthesis of plants, algal cells, and bacteria has been researched as the most environment-friendly renewable energy technology in the last decade. The primary challenge has been the engineering of electrochemical interfacing with photosynthetic apparatuses, organelles, or whole cells. However, with the aid of low-dimensional nanomaterials, there have been many advances, including enhanced photon absorption, increased generation of photosynthetic electrons (PEs), and more efficient transfer of PEs to electrodes. These advances have demonstrated the possibility for the technology to advance to a new level. In this article, the fundamentals of photosynthesis are introduced. How PE harvesting systems have improved concerning solar energy absorption, PE production, and PE collection by electrodes is discussed. The review focuses on how different kinds of nanomaterials are applied and function in interfacing with photosynthetic materials for enhanced PE harvesting. Finally, the review analyzes how the performance of PE harvesting and stand-alone systems have evolved so far and its future prospects.

Steering Triplet-Triplet Annihilation Upconversion through Enantioselective Self-Assembly in a Supramolecular Gel

Research on chiral selection and recognition not only is of fundamental importance in resolving the origin of biological homochirality, but also is instructive in the fabrication of controlled molecular organization in supramolecular systems to modulate their chirality-related functional properties. Here we report an enantioselective assembly process between a chiral energy donor and two enantiomeric energy acceptors, which further results in chirality-controlled energy transfer and enantioselective triplet-triplet annihilation upconversion (TTA-UC). It is found that the chiral energy donor Pd(II) octaethylporphyrin derivative PdOEP-LG12 (R_D) can selectively coassemble with the chiral energy acceptor LGAn (R_A) with the same chiral scaffold but tends to form segregation with the energy acceptor DGAn (S_A) with the opposite chiral scaffold in a thermodynamic equilibrium state. Thus, the coassembly of R_A/R_D shows more effective triplet-triplet energy transfer (TTET) and stronger upconverted luminescence and upconverted circularly polarized luminescence in comparison to the segregation of S_A/R_D. The establishment of such an enantioselective TTA-UC system highlights the applications of chirality-regulated triplet fusion in optoelectronic materials.

Role of Spatially Correlated Fluctuations in Photosynthetic Excitation Energy Transfer with an Equilibrium and a Nonequilibrium Initial Bath

The transfer of excitation energy in photosynthetic light-harvesting complexes has inspired growing interest for its scientific and engineering significance. Recent experimental findings have suggested that spatially correlated environmental fluctuations may account for the existence of long-lived quantum coherent energy transfer observed even at physiological temperature. In this paper, we investigate the effects of spatial correlations on the excitation energy transfer dynamics by including a nonequilibrium initial bath in a simulated donor-acceptor model. The initial bath state, which is assumed to be either equilibrium or nonequilibrium, is expanded in powers of coupling strength within the polaron formalism of a quantum master equation. The spatial correlations of bath fluctuations strongly influence the decay of coherence in the dynamics. The role of a nonequilibrium initial bath is also influenced by spatial correlations and becomes the most conspicuous for certain degrees of spatial correlations from which we propose a picture that the spatial correlations of bath fluctuations open up new energy transfer pathways, playing a role of protecting coherence. Besides, we apply the polaron master equation approach to study the dynamics in a two-site subsystem of the FMO complex and provide a practical example that shows the versatility of this approach.

Simulating energy transfer dynamics in the Fenna-Matthews-Olson complex via the modified generalized quantum master equation

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna-Matthews-Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model.

Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities

Overcoming the detrimental effect of disorder at the nanoscale is very hard since disorder induces localization and an exponential suppression of transport efficiency. Here we unveil novel and robust quantum transport regimes achievable in nanosystems by exploiting long-range hopping. We demonstrate that in a 1D disordered nanostructure in the presence of long-range hopping, transport efficiency, after decreasing exponentially with disorder at first, is then enhanced by disorder [disorder-enhanced transport (DET) regime] until, counterintuitively, it reaches a disorder-independent transport (DIT) regime, persisting over several orders of disorder magnitude in realistic systems. To enlighten the relevance of our results, we demonstrate that an ensemble of emitters in a cavity can be described by an effective long-range Hamiltonian. The specific case of a disordered molecular wire placed in an optical cavity is discussed, showing that the DIT and DET regimes can be reached with state-of-the-art experimental setups.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Energy transduction through FRET in self-assembled soft nanostructures based on surfactants/polymers: current scenario and prospects

The self-assembled systems of surfactants/polymers, which are capable of supporting energy funneling between fluorophores, have recently gained significant attraction. Surfactant and polymeric micelles form nanoscale structures spanning a radius of 2-10 nm are generally suitable for the transduction of energy among fluorophores. These systems have shown great potential in Förster resonance energy transfer (FRET) due to their unique characteristics of being aqueous based, tendency to remain self-assembled, spontaneous formation, tunable nature, and responsiveness to different external stimuli. This review presents current developments in the field of energy transfer, particularly the multi-step FRET processes in the self-assembled nanostructures of surfactants/polymers. The part one of this review presents a background and brief overview of soft systems and discusses certain aspects of the self-assemblies of surfactants/polymers and their co-solubilization property to bring fluorophores to close proximity to transduce energy. The second part of this review deals with single-step and multi-step FRET in the self-assemblies of surfactants/polymers and links FRET systems with advanced smart technologies including multicolor formation, data encryption, and artificial antenna systems. This review also discusses the diverse examples in the literature to present the emerging applications of FRET. Finally, the prospects regarding further improvement of FRET in self-assembled soft systems are outlined.

Thermal Decoherence of Superradiance in Lead Halide Perovskite Nanocrystal Superlattices

Recent experiments by Rainò et al. ( Nature 2018, 563, 671-675) have documented cooperative emission from CsPbBr₃ nanocrystal superlattices, exhibiting the hallmarks of low-temperature superradiance. In particular, the optical response is coherent and the radiative decay rate is increased by a factor of 3, relative to that of individual nanocrystals. However, the increase is 6 orders of magnitude smaller than what is theoretically expected from the superradiance of large assemblies, consisting of 10⁶-10⁸ interacting nanocrystals. Here, we develop a theoretical model of superradiance for such systems and show that thermal decoherence is largely responsible for the drastic reduction of the radiative decay rate in nanocrystal superlattices. Our theoretical approach explains the experimental results ( Nature 2018, 563, 671-675), provides insight into the design of small nanocrystal superlattices, and shows a 4 orders of magnitude enhancement in superradiant response. These quantitative predictions pave the path toward observing superradiance at higher temperatures.

Self-interaction correction, electrostatic, and structural influences on time-dependent density functional theory excitations of bacteriochlorophylls from the light-harvesting complex 2

First-principles calculations offer the chance to obtain a microscopic understanding of light-harvesting processes. Time-dependent density functional theory can have the computational efficiency to allow for such calculations. However, the (semi-)local exchange-correlation approximations that are computationally most efficient fail to describe charge-transfer excitations reliably. We here investigate whether the inexpensive average density self-interaction correction (ADSIC) remedies the problem. For the systems that we study, ADSIC is even more prone to the charge-transfer problem than the local density approximation. We further explore the recently reported finding that the electrostatic potential associated with the chromophores' protein environment in the light-harvesting complex 2 beneficially shifts spurious excitations. We find a great sensitivity on the chromophores' atomistic structure in this problem. Geometries obtained from classical molecular dynamics are more strongly affected by the spurious charge-transfer problem than the ones obtained from crystallography or density functional theory. For crystal structure geometries and density-functional theory optimized ones, our calculations confirm that the electrostatic potential shifts the spurious excitations out of the energetic range that is most relevant for electronic coupling.

Energy transfer under natural incoherent light: Effects of asymmetry on efficiency

The non-equilibrium stationary coherences that form in donor-acceptor systems are investigated to determine their relationship to the efficiency of energy transfer to a neighboring reaction center. It is found that the effects of asymmetry in the dimer are generally detrimental to the transfer of energy. Four types of systems are examined, arising from combinations of localized trapping, delocalized (Forster) trapping, eigenstate dephasing, and site basis dephasing. In the cases of site basis dephasing, the interplay between the energy gap of the excited dimer states and the environment is shown to give rise to a turnover effect in the efficiency under weak dimer coupling conditions. Furthermore, the nature of the coherences and associated flux is interpreted in terms of pathway interference effects. In addition, regardless of the cases considered, the ratio of the real part and the imaginary part of the coherences in the energy-eigenbasis tends to a constant value in the steady state limit.

Delocalized Two-Exciton States in DNA Scaffolded Cyanine Dimers

The engineering and manipulation of delocalized molecular exciton states is a key component for artificial biomimetic light harvesting complexes as well as alternative circuitry platforms based on exciton propagation. Here we examine the consequences of strong electronic coupling in cyanine homodimers on DNA duplex scaffolds. The most closely spaced dyes, attached to positions directly across the double-helix from one another, exhibit pronounced Davydov splitting due to strong electronic coupling. We demonstrate that the DNA scaffold is sufficiently robust to support observation of the transition from the lowest energy (J-like) one-exciton state to the nonlocal two-exciton state, where each cyanine dye is in the excited state. This transition proceeds via sequential photon absorption and persists for the lifetime of the exciton, establishing this as a controlled method for creating two-exciton states. Our observations suggest that DNA-organized dye networks have potential as platforms for molecular logic gates and entangled photon emission based on delocalized two-exciton states.

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.

Molecular and Supramolecular Multiredox Systems

The design and synthesis of molecular and supramolecular multiredox systems have been summarized. These systems are of great importance as they can be employed in the next generation of materials for energy storage, energy transport, and solar fuel production. Nature provides guiding pathways and insights to judiciously incorporate and tune the various molecular and supramolecular design aspects that result in the formation of complex and efficient systems. In this review, we have classified molecular multiredox systems into organic and organic-inorganic hybrid systems. The organic multiredox systems are further classified into multielectron acceptors, multielectron donors and ambipolar molecules. Synthetic chemists have integrated different electron donating and electron withdrawing groups to realize these complex molecular systems. Further, we have reviewed supramolecular multiredox systems, redox-active host-guest recognition, including mechanically interlocked systems. Finally, the review provides a discussion on the diverse applications, e. g. in artificial photosynthesis, water splitting, dynamic random access memory, etc. that can be realized from these artificial molecular or supramolecular multiredox systems.

Rational Design of Photo-Electrochemical Hybrid Devices Based on Graphene and Chlamydomonas reinhardtii Light-Harvesting Proteins

Dye-sensitized solar cells (DSSCs) have been highlighted as the promising alternative to generate clean energy based on low pay-back time materials. These devices have been designed to mimic solar energy conversion processes from photosynthetic organisms (the most efficient energy transduction phenomenon observed in nature) with the aid of low-cost materials. Recently, light-harvesting complexes (LHC) have been proposed as potential dyes in DSSCs based on their higher light-absorption efficiencies as compared to synthetic dyes. In this work, photo-electrochemical hybrid devices were rationally designed by adding for the first time Leu and Lys tags to heterologously expressed light-harvesting proteins from Chlamydomonas reinhardtii, thus allowing their proper orientation and immobilization on graphene electrodes. The light-harvesting complex 4 from C. reinhardtii (LHC4) was initially expressed in Escherichia coli, purified via affinity chromatography and subsequently immobilized on plasma-treated thin-film graphene electrodes. A photocurrent density of 40.30 ± 9.26 μA/cm2 was measured on devices using liquid electrolytes supplemented with a phosphonated viologen to facilitate charge transfer. Our results suggest that a new family of graphene-based thin-film photovoltaic devices can be manufactured from rationally tagged LHC proteins and opens the possibility to further explore fundamental processes of energy transfer for biological components interfaced with synthetic materials.

Photochemical dynamics under incoherent illumination: Light harvesting in self-assembled molecular J-aggregates

Transport phenomena in organic, self-assembled molecular J-aggregates have long attracted a great deal of attention due to their potential role in designing novel organic photovoltaic devices. A large number of theoretical and experimental studies have been carried out describing excitonic energy transfer in J-aggregates under the assumption that excitons are induced by a coherent laser-light source or initialized by a localized excitation on a particular chromophore. However, these assumptions may not provide an accurate description to assess the efficiency of J-aggregates, particularly as building blocks of organic solar cells. Under natural conditions, J-aggregates would be subjected to an incoherent source of light (as is sunlight), which would illuminate the whole photosynthetic complex rather than a single molecule. In this work, we present the first study of the efficiency of photosynthetic energy transport in self-assembled molecular aggregates under incoherent sunlight illumination. By making use of a minimalistic model of a cyanine dye J-aggregate, we demonstrate that long-range transport efficiency is enhanced when exciting the aggregate with incoherent light. Our results thus support the conclusion that J-aggregates are, indeed, excellent candidates for devices where efficient long-range incoherently induced exciton transport is desired, such as in highly efficient organic solar cells.

Thermoresponsive Micellar Assembly Constructed from a Hexameric Hemoprotein Modified with Poly(N-isopropylacrylamide) toward an Artificial Light-Harvesting System

Artificial protein assemblies inspired by nature have significant potential in development of emergent functional materials. In order to construct an artificial protein assembly, we employed a mutant of a thermostable hemoprotein, hexameric tyrosine-coordinated heme protein (HTHP), as a building block. The HTHP mutant which has cysteine residues introduced on the bottom surface of its columnar structure was reacted with maleimide-tethering thermoresponsive poly(N-isopropylacrylamide), PNIPAAm, to generate the protein assembly upon heating. The site-specific modification of the cysteine residues with PNIPAAm on the protein surface was confirmed by SDS-PAGE and analytical size exclusion chromatography (SEC). The PNIPAAm-modified HTHP (PNIPAAm-HTHP) is found to provide a 43 nm spherical structure at 60 °C, and the structural changes observed between the assembled and the disassembled forms were duplicated at least five times. High-speed atomic force microscopic measurements of the micellar assembly supported by cross-linkage with glutaraldehyde indicate that the protein matrices are located on the surface of the sphere and cover the inner PNIPAAm core. Furthermore, substitution of heme with a photosensitizer, Zn protoporphyrin IX (ZnPP), in the micellar assembly provides an artificial light-harvesting system. Photochemical measurements of the ZnPP-substituted micellar assembly demonstrate that energy migration among the arrayed ZnPP molecules occurs within the range of several tens of picoseconds. Our present work represents the first example of an artificial light-harvesting system based on an assembled hemoprotein oligomer structure to replicate natural light-harvesting systems.

Structure and Efficiency in Bacterial Photosynthetic Light Harvesting

Photosynthetic organisms use networks of chromophores to absorb and deliver solar energy to reaction centers. We present a detailed model of the light-harvesting complexes in purple bacteria, including explicit interaction with sunlight, radiative and nonradiative energy loss, and dephasing and thermalizing effects of coupling to a vibrational bath. We capture the effect of slow vibrations by introducing time-dependent disorder. Our model describes the experimentally observed high efficiency of light harvesting, despite the absence of long-range quantum coherence. The one-exciton part of the quantum state fluctuates continuously but remains highly mixed at all times. These results suggest a relatively minor role for structure in determining efficiency. We build hypothetical models with randomly arranged chromophores but still observe high efficiency when nearest-neighbor distances are comparable to those in nature. This helps explain the high transport efficiency in organisms with widely differing antenna structures and suggests new design criteria for artificial light-harvesting devices.

Turning the challenge of quantum biology on its head: biological control of quantum optical systems

When light-harvesting complex II (LHCII), isolated from spinach, is adsorbed onto arrays of gold nanostructures formed by interferometric lithography, a pronounced splitting of the plasmon band is observed that is attributable to strong coupling of the localised surface plasmon resonance to excitons in the pigment-protein complex. The system is modelled as coupled harmonic oscillators, yielding an exciton energy of 2.24 ± 0.02 eV. Analysis of dispersion curves yields a Rabi energy of 0.25 eV. Extinction spectra of the strongly coupled system yield a resonance at 1.43 eV that varies as a function of the density of nanostructures in the array. The enhanced intensity of this feature is attributed to strong plasmon-exciton coupling. Comparison of data for a large number of light-harvesting complexes indicates that by control of the protein structure and/or pigment compliment it is possible to manipulate the strength of plasmon-exciton coupling. In strongly coupled systems, ultra-fast exchange of energy occurs between pigment molecules: coherent coupling between non-local excitons can be manipulated via selection of the protein structure enabling the observation of transitions that are not seen in the weak coupling regime. Synthetic biology thus provides a means to control quantum-optical interactions in the strong coupling regime.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I2Kr18 cluster using the G-MCTDH method

The molecular dynamics following the electronic BΠu30⁺⟵XΣg+1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I₂Kr₁₈ cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I₂ energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < R_I-I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I₂-krypton system addressed in Paper II.

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.

Signatures of Exciton Delocalization and Exciton-Exciton Annihilation in Fluorescence-Detected Two-Dimensional Coherent Spectroscopy

Incoherently detected coherent multidimensional spectroscopy is rapidly gaining popularity, promising a different application range and sensitivity than its traditional counterpart. While measuring the same response, the two methods are not equivalent. We present calculations of the fluorescence-detected coherent two-dimensional (F-2DES) spectra of a molecular heterodimer. We compare how the F-2DES technique differs from standard coherently detected two-dimensional (2DES) spectroscopy in measuring exciton delocalization. We analyze which processes contribute to cross-peaks in the zero-waiting-time spectra obtained by the two methods. Strictly on the basis of time-dependent perturbation theory, we study how in both methods the varying degree of cancellation between perturbative contributions gives rise to cross-peaks and we identify exciton annihilation and exciton relaxation contributions to the cross-peak in the zero-waiting-time F-2DES. We propose that time-gated fluorescence detection can be used to isolate the annihilation contribution to F-2DES both to retrieve information equivalent to 2DES spectroscopy and to study the annihilation contribution itself.

Coherent phenomena in photosynthetic light harvesting: part two-observations in biological systems

Considerable debate surrounds the question of whether or not quantum mechanics plays a significant, non-trivial role in photosynthetic light harvesting. Many have proposed that quantum superpositions and/or quantum transport phenomena may be responsible for the efficiency and robustness of energy transport present in biological systems. The critical experimental observations comprise the observation of coherent oscillations or "quantum beats" via femtosecond laser spectroscopy, which have been observed in many different light harvesting systems. Part Two of this review aims to provide an overview of experimental observations of energy transfer in the most studied light harvesting systems. Length scales, derived from crystallographic studies, are combined with energy and time scales of the beats observed via spectroscopy. A consensus is emerging that most long-lived (hundreds of femtoseconds) coherent phenomena are of vibrational or vibronic origin, where the latter may result in coherent excitation transport within a protein complex. In contrast, energy transport between proteins is likely to be incoherent in nature. The question of whether evolution has selected for these non-trivial quantum phenomena may be an unanswerable question, as dense packings of chromophores will lead to strong coupling and hence non-trivial quantum phenomena. As such, one cannot discern whether evolution has optimised light harvesting systems for high chromophore density or for the ensuing quantum effects as these are inextricably linked and cannot be switched off.

The Role of Quantum Decoherence in FRET

Resonance energy transfer has become an indispensable experimental tool for single-molecule and single-cell biophysics. Its physical underpinnings, however, are subtle: it involves a discrete jump of excitation from one molecule to another, and so we regard it as a strongly quantum-mechanical process. And yet its kinetics differ from what many of us were taught about two-state quantum systems, quantum superpositions of the states do not seem to arise, and so on. Although J. R. Oppenheimer and T. Förster navigated these subtleties successfully, it remains hard to find an elementary derivation in modern language. The key step involves acknowledging quantum decoherence. Appreciating that aspect can be helpful when we attempt to extend our understanding to situations in which Förster's original analysis is not applicable.

A synthetic biological quantum optical system

In strong plasmon-exciton coupling, a surface plasmon mode is coupled to an array of localized emitters to yield new hybrid light-matter states (plexcitons), whose properties may in principle be controlled via modification of the arrangement of emitters. We show that plasmon modes are strongly coupled to synthetic light-harvesting maquette proteins, and that the coupling can be controlled via alteration of the protein structure. For maquettes with a single chlorin binding site, the exciton energy (2.06 ± 0.07 eV) is close to the expected energy of the Qy transition. However, for maquettes containing two chlorin binding sites that are collinear in the field direction, an exciton energy of 2.20 ± 0.01 eV is obtained, intermediate between the energies of the Qx and Qy transitions of the chlorin. This observation is attributed to strong coupling of the LSPR to an H-dimer state not observed under weak coupling.

Shedding (Incoherent) Light on Quantum Effects in Light-Induced Biological Processes

Light-induced processes that occur in nature, such as photosynthesis and photoisomerization in the first steps in vision, are often studied in the laboratory using coherent pulsed laser sources, which induce time-dependent coherent wavepacket molecule dynamics. Nature, however, uses stationary incoherent thermal radiation, such as sunlight, leading to a totally different molecular response, the time-independent steady state. It is vital to appreciate this difference in order to assess the role of quantum coherence effects in biological systems. Developments in this area are discussed in detail.

DNA as UV light-harvesting antenna

The ordered structure of UV chromophores in DNA resembles photosynthetic light-harvesting complexes in which quantum coherence effects play a major role in highly efficient directional energy transfer. The possible role of coherent excitons in energy transport in DNA remains debated. Meanwhile, energy transport properties are greatly important for understanding the mechanisms of photochemical reactions in cellular DNA and for DNA-based artificial nanostructures. Here, we studied energy transfer in DNA complexes formed with silver nanoclusters and with intercalating dye (acridine orange). Steady-state fluorescence measurements with two DNA templates (15-mer DNA duplex and calf thymus DNA) showed that excitation energy can be transferred to the clusters from 21 and 28 nucleobases, respectively. This differed from the DNA-acridine orange complex for which energy transfer took place from four neighboring bases only. Fluorescence up-conversion measurements showed that the energy transfer took place within 100 fs. The efficient energy transport in the Ag-DNA complexes suggests an excitonic mechanism for the transfer, such that the excitation is delocalized over at least four and seven stacked bases, respectively, in one strand of the duplexes stabilizing the clusters. This result demonstrates that the exciton delocalization length in some DNA structures may not be limited to just two bases.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

Dynamics of coherence, localization and excitation transfer in disordered nanorings

Self-assembled supramolecular aggregates are excellent candidates for the design of efficient excitation transport devices. Both artificially prepared and natural photosynthetic aggregates in plants and bacteria present an important degree of disorder that is supposed to hinder excitation transport. Besides, molecular excitations couple to nuclear motion affecting excitation transport in a variety of ways. We present an exhaustive study of exciton dynamics in disordered nanorings with long-range interactions under the influence of a phonon bath taking the LH2 system of purple bacteria as a model. Nuclear motion is explicitly taken into account by employing the Davydov ansatz description of the polaron and quantum dynamics are obtained using a time-dependent variational method. We reveal an optimal exciton-phonon coupling that suppresses disorder-induced localization and facilitate excitation de-trapping. This excitation transfer enhancement, mediated by environmental phonons, is attributed to energy relaxation toward extended, low-energy excitons provided by the precise LH2 geometry with anti-parallel dipoles and long-range interactions. An analysis of localization and spectral statistics is followed by dynamic measures of coherence and localization, transfer efficiency and superradiance. Linear absorption, 2D photon-echo spectra and diffusion measures of the exciton are examined to monitor the diffusive behavior as a function of the strengths of disorder and exciton-phonon coupling.

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 Redirection of Antenna Absorption to Photosynthetic Reaction Centers

The early steps of photosynthesis involve the photoexcitation of reaction centers (RCs) and light-harvesting (LH) units. Here, we show that the historically overlooked excitonic delocalization across RC and LH pigments results in a redistribution of absorption amplitudes that benefits the absorption cross section of the optical bands associated with the RC of several species. While we prove that this redistribution is robust to the microscopic details of the dephasing between these units in the purple bacterium Rhodospirillum rubrum, we are able to show that the redistribution witnesses a more fragile, but persistent, coherent population dynamics which directs excitations from the LH toward the RC units under incoherent illumination and physiological conditions. Even though the redirection does not seem to affect importantly the overall efficiency in photosynthesis, stochastic optimization allows us to delineate clear guidelines and develop simple analytic expressions in order to amplify the coherent redirection in artificial nanostructures.

Giant light-harvesting nanoantenna for single-molecule detection in ambient light

Here, we explore the enhancement of single molecule emission by polymeric nano-antenna that can harvest energy from thousands of donor dyes to a single acceptor. In this nano-antenna, the cationic dyes are brought together in very close proximity using bulky counterions, thus enabling ultrafast diffusion of excitation energy (≤30 fs) with minimal losses. Our 60-nm nanoparticles containing >10,000 rhodamine-based donor dyes can efficiently transfer energy to 1-2 acceptors resulting in an antenna effect of ~1,000. Therefore, single Cy5-based acceptors become 25-fold brighter than quantum dots QD655. This unprecedented amplification of the acceptor dye emission enables observation of single molecules at illumination powers (1-10 mW cm^-2) that are >10,000-fold lower than typically required in single-molecule measurements. Finally, using a basic setup, which includes a 20X air objective and a sCMOS camera, we could detect single Cy5 molecules by simply shining divergent light on the sample at powers equivalent to sunlight.

Ab Initio Nonadiabatic Dynamics with Coupled Trajectories: A Rigorous Approach to Quantum (De)Coherence

We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron-nuclear wave function. Our approach (a coupled-trajectory mixed quantum-classical, CT-MQC, scheme) is based on the quantum-classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.

Chirality and energy transfer amplified circularly polarized luminescence in composite nanohelix

Transfer of both chirality and energy information plays an important role in biological systems. Here we show a chiral donor π-gelator and assembled it with an achiral π-acceptor to see how chirality and energy can be transferred in a composite donor-acceptor system. It is found that the individual chiral gelator can self-assemble into nanohelix. In the presence of the achiral acceptor, the self-assembly can also proceed and lead to the formation of the composite nanohelix. In the composite nanohelix, an energy transfer is realized. Interestingly, in the composite nanohelix, the achiral acceptor can both capture the supramolecular chirality and collect the circularly polarized energy from the chiral donor, showing both supramolecular chirality and energy transfer amplified circularly polarized luminescence (ETACPL).