Theory of excitation energy transfer: from structure to function

Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane-anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes.

Ultrafast Energy Transfer in a Diatom Photosystem II Supercomplex

The light-harvesting complexes (LHCs) of diatoms, specifically fucoxanthin-Chl a/c binding proteins (FCPs), exhibit structural and functional diversity, as highlighted by recent structural studies of photosystem II-FCP (PSII-FCPII) supercomplexes from different diatom species. The excitation dynamics of PSII-FCPII supercomplexes isolated from the diatom Thalassiosira pseudonana was explored using time-resolved fluorescence spectroscopy and two-dimensional electronic spectroscopy at room temperature and 77 K. Energy transfer between FCPII and PSII occurred remarkably fast (<5 ps), emphasizing the efficiency of FCPII as a light-harvesting antenna. The presence of long-wavelength chlorophylls may further help concentrate excitations in the core complex and increase the efficiency of light harvesting. Structure-based calculations reveal remarkably strong excitonic couplings between chlorophylls in the FCP antenna and between FCP and the PSII core antenna that are the basis for the rapid energy transfer.

Near-atomic-resolution structure of J-aggregated helical light-harvesting nanotubes

Cryo-electron microscopy has delivered a resolution revolution for biological self-assemblies, yet only a handful of structures have been solved for synthetic supramolecular materials. Particularly for chromophore supramolecular aggregates, high-resolution structures are necessary for understanding and modulating the long-range excitonic coupling. Here, we present a 3.3 Å structure of prototypical biomimetic light-harvesting nanotubes derived from an amphiphilic cyanine dye (C8S3-Cl). Helical 3D reconstruction directly visualizes the chromophore packing that controls the excitonic properties. Our structure clearly shows a brick layer arrangement, revising the previously hypothesized herringbone arrangement. Furthermore, we identify a new non-biological supramolecular motif-interlocking sulfonates-that may be responsible for the slip-stacked packing and J-aggregate nature of the light-harvesting nanotubes. This work shows how independently obtained native-state structures complement photophysical measurements and will enable accurate understanding of (excitonic) structure-function properties, informing materials design for light-harvesting chromophore aggregates.

An Update in Computational Methods for Environmental Monitoring: Theoretical Evaluation of the Molecular and Electronic Structures of Natural Pigment-Metal Complexes

Metals are beneficial to life, but the presence of these elements in excessive amounts can harm both organisms and the environment; therefore, detecting the presence of metals is essential. Currently, metal detection methods employ powerful instrumental techniques that require a lot of time and money. Hence, the development of efficient and effective metal indicators is essential. Several synthetic metal detectors have been made, but due to their risk of harm, the use of natural pigments is considered a potential alternative. Experiments are needed for their development, but they are expensive and time-consuming. This review explores various computational methods and approaches that can be used to investigate metal-pigment interactions because choosing the right methods and approaches will affect the reliability of the results. The results show that quantum mechanical methods (ab initio, density functional theory, and semiempirical approaches) and molecular dynamics simulations have been used. Among the available methods, the density functional theory approach with the B3LYP functional and the LANL2DZ ECP and basis set is the most promising combination due to its good accuracy and cost-effectiveness. Various experimental studies were also in good agreement with the results of computational methods. However, deeper analysis still needs to be carried out to find the best combination of functions and basis sets.

Inter-subunit energy transfer processes in a minimal plant photosystem II supercomplex

Photosystem II (PSII) is an integral part of the photosynthesis machinery, in which several light-harvesting complexes rely on inter-complex excitonic energy transfer (EET) processes to channel energy to the reaction center. In this paper, we report on a direct observation of the inter-complex EET in a minimal PSII supercomplex from plants, containing the trimeric light-harvesting complex II (LHCII), the monomeric light-harvesting complex CP26, and the monomeric PSII core complex. Using two-dimensional (2D) electronic spectroscopy, we measure an inter-complex EET timescale of 50 picoseconds for excitations from the LHCII-CP26 peripheral antenna to the PSII core. The 2D electronic spectra also reveal that the transfer timescale is nearly constant over the pump spectrum of 600 to 700 nanometers. Structure-based calculations reveal the contribution of each antenna complex to the measured inter-complex EET time. These results provide a step in elucidating the full inter-complex energy transfer network of the PSII machinery.

High-resolution structure and biochemical properties of the LH1-RC photocomplex from the model purple sulfur bacterium, Allochromatium vinosum

The mesophilic purple sulfur phototrophic bacterium Allochromatium (Alc.) vinosum (bacterial family Chromatiaceae) has been a favored model for studies of bacterial photosynthesis and sulfur metabolism, and its core light-harvesting (LH1) complex has been a focus of numerous studies of photosynthetic light reactions. However, despite intense efforts, no high-resolution structure and thorough biochemical analysis of the Alc. vinosum LH1 complex have been reported. Here we present cryo-EM structures of the Alc. vinosum LH1 complex associated with reaction center (RC) at 2.24 Å resolution. The overall structure of the Alc. vinosum LH1 resembles that of its moderately thermophilic relative Alc. tepidum in that it contains multiple pigment-binding α- and β-polypeptides. Unexpectedly, however, six Ca ions were identified in the Alc. vinosum LH1 bound to certain α1/β1- or α1/β3-polypeptides through a different Ca2+-binding motif from that seen in Alc. tepidum and other Chromatiaceae that contain Ca2+-bound LH1 complexes. Two water molecules were identified as additional Ca2+-coordinating ligands. Based on these results, we reexamined biochemical and spectroscopic properties of the Alc. vinosum LH1-RC. While modest but distinct effects of Ca2+ were detected in the absorption spectrum of the Alc. vinosum LH1 complex, a marked decrease in thermostability of its LH1-RC complex was observed upon removal of Ca2+. The presence of Ca2+ in the photocomplex of Alc. vinosum suggests that Ca2+-binding to LH1 complexes may be a common adaptation in species of Chromatiaceae for conferring spectral and thermal flexibility on this key component of their photosynthetic machinery.

Contribution Factors of the First Kind Calculated for the Marcus Electron-Transfer Rate and Their Applications

In this study, we applied the concept of the "contribution factor of the first kind (CFFK)" to the original electron-transfer (ET) rate theory proposed by Marcus. Mathematical derivations provided simple and convenient formulas for estimating the relative contributions of ten physical and chemical parameters involved in the Marcus ET rate formula: (1) the maximum strength of the electronic coupling energy between two molecules, (2) the exponential decay rate of the electronic coupling energy versus the distance between both molecules, (3) the distance between both molecules, (4) the equilibrium distance between both molecules, (5) the Gibbs free energy, (6) reorganization free energy in the prefactor of the Marcus ET rate equation, (7) reorganization free energy in the denominator of the exponential term, (8) reorganization free energy in the argument of the exponential term, (9) Boltzmann constant times absolute temperature in the prefactor of the rate equation, and (10) Boltzmann constant times absolute temperature in the denominator of the exponential term. We applied our theories to (i) ET reactions at bacterial photosynthesis reaction centers, PSI and PSII, and soluble ferredoxins (Fd); (ii) intraprotein ET reactions for designed azurin mutants; and (iii) ET reactions in flavodoxin (Fld). The formulas and calculations suggest that the theory behind the CFFK is useful for quantitatively identifying major and minor physical and chemical factors and corresponding trade-offs, all of which affect the magnitude of the Marcus ET rate.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.

Solar energy conversion by photosystem II: principles and structures

Photosynthetic water oxidation by Photosystem II (PSII) is a fascinating process because it sustains life on Earth and serves as a blue print for scalable synthetic catalysts required for renewable energy applications. The biophysical, computational, and structural description of this process, which started more than 50 years ago, has made tremendous progress over the past two decades, with its high-resolution crystal structures being available not only of the dark-stable state of PSII, but of all the semi-stable reaction intermediates and even some transient states. Here, we summarize the current knowledge on PSII with emphasis on the basic principles that govern the conversion of light energy to chemical energy in PSII, as well as on the illustration of the molecular structures that enable these reactions. The important remaining questions regarding the mechanism of biological water oxidation are highlighted, and one possible pathway for this fundamental reaction is described at a molecular level.

Modeling the Effect of Disorder in the Two-Dimensional Electronic Spectroscopy of Poly-3-hexyltiophene in an Organic Photovoltaic Blend: A Combined Quantum/Classical Approach

We introduce a first-principles model of the 12-mer poly-3-hexyltiophene (P3HT) polymer system in the realistic description of an organic photovoltaic blend environment. We combine Molecular Dynamics (MD) simulations of a thin-film blend of P3HT and phenyl-C61-butyric acid methyl ester (PCBM) to model the interactions with a fluctuating environment with Time-Dependent Density Functional Theory (TDDFT) calculations to parametrize the effect of the torsional flexibility in the polymer and construct an exciton-type Hamiltonian that describes the photoexcitation of the polymer. This allows us to reveal the presence of different flexibility patterns governed by the torsional angles along the polymer chain which, in the interacting fluctuating environment, control the broadening of the spectral observables. We identify the origin of the homogeneous and inhomogeneous line shape of the simulated optical signals. This is paramount to decipher the spectroscopic nature of the ultrafast electron-transfer process occurring in organic photovoltaic (OPV) materials.

Surface hopping modeling of charge and energy transfer in active environments

An active environment is any atomic or molecular system changing a chromophore's nonadiabatic dynamics compared to the isolated molecule. The action of the environment on the chromophore occurs by changing the potential energy landscape and triggering new energy and charge flows unavailable in the vacuum. Surface hopping is a mixed quantum-classical approach whose extreme flexibility has made it the primary platform for implementing novel methodologies to investigate the nonadiabatic dynamics of a chromophore in active environments. This Perspective paper surveys the latest developments in the field, focusing on charge and energy transfer processes.

An efficient time-domain implementation of the multichromophoric Förster resonant energy transfer method

The excitation energy transfer (EET) process for photosynthetic antenna complexes consisting of subunits, each comprised of multiple chromophores, remains challenging to describe. The multichromophoric Förster resonance energy transfer theory is a popular method to describe the EET process in such systems. This paper presents a new time-domain method for calculating energy transfer based on the combination of multichromophoric Förster resonance energy transfer theory and the Numerical Integration of the Schrödinger Equation method. After validating the method on simple model systems, we apply it to the Light-Harvesting antenna 2 (LH2) complex, a light harvesting antenna found in purple bacteria. We use a simple model combining the overdamped Brownian oscillators to describe the dynamic disorder originating from the environmental fluctuations and the transition charge from the electrostatic potential coupling model to determine the interactions between chromophores. We demonstrate that with this model, both the calculated spectra and the EET rates between the two rings within the LH2 complex agree well with experimental results. We further find that the transfer between the strongly coupled rings of neighboring LH2 complexes can also be well described with our method. We conclude that our new method accurately describes the EET rate for biologically relevant multichromophoric systems, which are similar to the LH2 complex. Computationally, the new method is very tractable, especially for slow processes. We foresee that the method can be applied to efficiently calculate transfer in artificial systems as well and may pave the way for calculating multidimensional spectra of extensive multichromophoric systems in the future.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Conformation of Light-Harvesting Complex II Trimer Depends upon Its Binding Site

The light-harvesting complex II (LHCII) trimer in plants functions as a major antenna complex and a quencher to protect it from photooxidative damage. Theoretical studies on the structure of an LHCII trimer have demonstrated that excitation energy transfer between chlorophylls (Chls) in LHCII can be modulated by its exquisite conformational fluctuation. However, conformational changes depending on its binding location have not yet been investigated, even though reorganization of protein complexes occurs by physiological regulations. In this study, we investigated conformational differences in LHCII by comparing published structures of an identical LHCII trimer in the three different photosystem supercomplexes from the green alga Chlamydomonas reinhardtii. Our results revealed distinct differences in Chl configurations as well as polypeptide conformations of the LHCII trimers depending on its binding location. We propose that these configurational differences readily modulate the function of LHCII and possibly lead to a change in excitation-energy flow over the photosynthetic supercomplex.

Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations

The recently introduced multisite tensor network path integral (MS-TNPI) allows simulation of extended quantum systems coupled to dissipative media. We use MS-TNPI to simulate the exciton transport and the absorption spectrum of a B850 bacteriochlorophyll (BChl) ring. The MS-TNPI network is extended to account for the ring topology of the B850 system. Accurate molecular-dynamics-based description of the molecular vibrations and the protein scaffold is incorporated through the framework of Feynman-Vernon influence functional. To relate the present work with the excitonic picture, an exploration of the absorption spectrum is done by simulating it using approximate and topologically consistent transition dipole moment vectors. Comparison of these numerically exact MS-TNPI absorption spectra are shown with second-order cumulant approximations. The effect of temperature on both the exact and the approximate spectra is also explored.

Molecular mechanisms of light harvesting in the minor antenna CP29 in near-native membrane lipidic environment

CP29, a chlorophyll a/ b-xanthophyll binding protein, bridges energy transfer between the major LHCII antenna complexes and photosystem II reaction centers. It hosts one of the two identified quenching sites, making it crucial for regulated photoprotection mechanisms. Until now, the photophysics of CP29 has been studied on the purified protein in detergent solutions since spectrally overlapping signals affect in vivo measurements. However, the protein in detergent assumes non-native conformations compared to its physiological state in the thylakoid membrane. Here, we report a detailed photophysical study on CP29 inserted in discoidal lipid bilayers, known as nanodiscs, which mimic the native membrane environment. Using picosecond time-resolved fluorescence and femtosecond transient absorption (TA), we observed shortening of the Chl fluorescence lifetime with a decrease of the carotenoid triplet formation yield for CP29 in nanodiscs as compared to the protein in detergent. Global analysis of TA data suggests a 1Chl* quenching mechanism dependent on excitation energy transfer to a carotenoid dark state, likely the proposed S*, which is believed to be formed due to a carotenoid conformational change affecting the S1 state. We suggest that the accessibility of the S* state in different local environments plays a key role in determining the quenching of Chl excited states. In vivo, non-photochemical quenching is activated by de-epoxidation of violaxanthin into zeaxanthin. CP29-zeaxanthin in nanodiscs further shortens the Chl lifetime, which underlines the critical role of zeaxanthin in modulating photoprotection activity.

Exact simulation of pigment-protein complexes unveils vibronic renormalization of electronic parameters in ultrafast spectroscopy

The primary steps of photosynthesis rely on the generation, transport, and trapping of excitons in pigment-protein complexes (PPCs). Generically, PPCs possess highly structured vibrational spectra, combining many discrete intra-pigment modes and a quasi-continuous of protein modes, with vibrational and electronic couplings of comparable strength. The intricacy of the resulting vibronic dynamics poses significant challenges in establishing a quantitative connection between spectroscopic data and underlying microscopic models. Here we show how to address this challenge using numerically exact simulation methods by considering two model systems, namely the water-soluble chlorophyll-binding protein of cauliflower and the special pair of bacterial reaction centers. We demonstrate that the inclusion of the full multi-mode vibronic dynamics in numerical calculations of linear spectra leads to systematic and quantitatively significant corrections to electronic parameter estimation. These multi-mode vibronic effects are shown to be relevant in the longstanding discussion regarding the origin of long-lived oscillations in multidimensional nonlinear spectra.

Multimode vibronic mixing in model photosynthetic systems revealed by numerically exact simulations is shown to strongly modify linear and non-linear optical responses and facilitate the persistence of coherent dynamics.

Excitonic Nature of Carotenoid–Phthalocyanine Dyads and Its Role in Transient Absorption Spectra

Artificial carotenoid–tetrapyrrole dyads have been extensively used as model systems to understand the quenching mechanisms that occur in light-harvesting complexes during nonphotochemical quenching. In particular, dyads containing a carotenoid covalently linked to a zinc phthalocyanine have been studied by transient absorption spectroscopy, and the observed signals have been interpreted in terms of an excitonically coupled state involving the lowest excited states of the two fragments. If present, such excitonic delocalization would have significant implications on the mechanism of nonphotochemical quenching. Here, we use quantum chemical calculations to show that this delocalization is not needed to reproduce the transient absorption spectra. On the contrary, the observed signals can be explained through excitonic couplings in the higher-energy manifold of states. We also argue that the covalent linkage between the two fragments allows for electronic communications, which complicates the analysis of the spectra based on two independent but coupled moieties. These findings call for a more thorough reassessment of the photophysics in these dyads and its implications in the context of natural nonphotochemical quenching.

Mechanism of Ir(ppy)3 Guest Exciton Formation with the Exciplex-Forming TCTA:TPBI Cohost within a Phosphorescent Organic Light-Emitting Diode Environment

Cohosts based on hole transporting and electron transporting materials often act as exciplexes in the form of intermolecular charge transfer complexes. Indeed, exciplex-forming cohosts have been widely developed as the host materials for efficient phosphorescent organic light-emitting diodes (OLEDs). In host–guest systems of OLEDs, the guest can be excited by two competing mechanisms, namely, excitation energy transfer (EET) and charge transfer (CT). Experimentally, it has been reported that the EET mechanism is dominant and the excitons are primarily formed in the host first and then transferred to the guest in phosphorescent OLEDs based on exciplex-forming cohosts. With this, exciplex-forming cohosts are widely employed for avoiding the formation of trapped charge carriers in the phosphorescent guest. However, theoretical studies are still lacking toward elucidating the relative importance between EET and CT processes in exciting the guest molecules in such systems. Here, we obtain the kinetics of guest excitation processes in a few trimer model systems consisting of an exciplex-forming cohost pair and a phosphorescent guest. We adopt the Förster resonance energy transfer (FRET) rate constants for the electronic transitions between excited states toward solving kinetic master equations. The input parameters for calculating the FRET rate constants are obtained from density functional theory (DFT) and time-dependent DFT. The results show that while the EET mechanism is important, the CT mechanism may still play a significant role in guest excitations. In fact, the relative importance of CT over EET depends strongly on the location of the guest molecule relative to the cohost pair. This is understandable as both the coupling for EET and the interaction energy for CT are strongly influenced by the geometric constraints. Understanding the energy transfer pathways from the exciplex state of cohost to the emissive state of guest may provide insights for improving exciplex-forming materials adopted in OLEDs.

PyFREC 2.0: Software for excitation energy transfer modeling

Excitation energy transfer is a ubiquitous process of fundamental importance for understanding natural phenomena, such as photosynthesis, as well as advancing technologies ranging from photovoltaics to development of photosensitizers and fluorescent probes used to explore molecular interactions inside living cells. The current version of PyFREC 2.0 is an advancement of the previously reported software (D. Kosenkov, J. Comput. Chem. 2016, 37, 1847-1854). The current update is primarily focused on providing a computational tool based on Förster theory for bridging a gap between theoretically calculated molecular properties (e.g., electronic couplings, orientation factors, etc.) and experimentally measured emission and absorption spectra of molecules. The software is aimed to facilitate deeper understanding of photochemical mechanisms of fluorescence resonance energy transfer (FRET) in donor-acceptor pairs. Specific updates of the software include implementations of overlap integrals between donor emission and acceptor absorption spectra of FRET pairs, estimation of Strickler-Berg fluorescence lifetimes, calculation of Förster radii, energy transfer efficiency, and radiation zones that, in particular, determine applicability of the Förster theory.

A Ca2+-binding motif underlies the unusual properties of certain photosynthetic bacterial core light-harvesting complexes

The mildly thermophilic purple phototrophic bacterium Allochromatium tepidum provides a unique model for investigating various intermediate phenotypes observed between those of thermophilic and mesophilic counterparts. The core light-harvesting (LH1) complex from A. tepidum exhibits an absorption maximum at 890 nm and mildly enhanced thermostability, both of which are Ca²⁺-dependent. However, it is unknown what structural determinants might contribute to these properties. Here, we present a cryo-EM structure of the reaction center–associated LH1 complex at 2.81 Å resolution, in which we identify multiple pigment-binding α- and β-polypeptides within an LH1 ring. Of the 16 α-polypeptides, we show that six (α1) bind Ca²⁺ along with β1- or β3-polypeptides to form the Ca²⁺-binding sites. This structure differs from that of fully Ca²⁺-bound LH1 from Thermochromatium tepidum, enabling determination of the minimum structural requirements for Ca²⁺-binding. We also identified three amino acids (Trp44, Asp47, and Ile49) in the C-terminal region of the A. tepidum α1-polypeptide that ligate each Ca ion, forming a Ca²⁺-binding WxxDxI motif that is conserved in all Ca²⁺-bound LH1 α-polypeptides from other species with reported structures. The partial Ca²⁺-bound structure further explains the unusual phenotypic properties observed for this bacterium in terms of its Ca²⁺-requirements for thermostability, spectroscopy, and phototrophic growth, and supports the hypothesis that A. tepidum may represent a “transitional” species between mesophilic and thermophilic purple sulfur bacteria. The characteristic arrangement of multiple αβ-polypeptides also suggests a mechanism of molecular recognition in the expression and/or assembly of the LH1 complex that could be regulated through interactions with reaction center subunits.

Plant and Algal PSII-LHCII Supercomplexes: Structure, Evolution and Energy Transfer

Photosynthesis is the process conducted by plants and algae to capture photons and store their energy in chemical forms. The light-harvesting, excitation transfer, charge separation and electron transfer in photosystem II (PSII) are the critical initial reactions of photosynthesis and thereby largely determine its overall efficiency. In this review, we outline the rapidly accumulating knowledge about the architectures and assemblies of plant and green algal PSII-light harvesting complex II (LHCII) supercomplexes, with a particular focus on new insights provided by the recent high-resolution cryo-electron microscopy map of the supercomplexes from a green alga Chlamydomonas reinhardtii. We make pair-wise comparative analyses between the supercomplexes from plants and green algae to gain insights about the evolution of the PSII-LHCII supercomplexes involving the peripheral small PSII subunits that might have been acquired during the evolution and about the energy transfer pathways that define their light-harvesting and photoprotective properties.

Robust Strategy for Photoprotection in the Light-Harvesting Antenna of Diatoms: A Molecular Dynamics Study

Diatoms generate a large portion of the oxygen produced on earth due to their exceptional light-harvesting properties involving fucoxanthin and chlorophyll-binding proteins (FCP). At the same time, an efficient adaptation of these complexes to fluctuating light conditions is necessary to protect the diatoms against photodamage. So far, structural and dynamic data for the interaction between FCP and the photoprotective LHCX family of proteins in diatoms are lacking. In this computational study, we provide a structural basis for a remarkable pH-dependent adaptation at the molecular level. Upon binding of the LHCX1 protein to the FCP complex together with a change in pH, conformational changes within the FCP protein result in a variation of the electronic coupling in a specific chlorophyll-fucoxanthin pair, leading to a change in the exciton transfer rate by almost an order of magnitude. A common strategy for photoprotection between diatoms and higher plants is identified and discussed.

Electrostatic charge controls the lowest LH1 Qy transition energy in the triply extremophilic purple phototrophic bacterium, Halorhodospira halochloris

Halorhodospira (Hlr.) halochloris is a unique phototrophic purple bacterium because it is a triple extremophile-the organism is thermophilic, alkalophilic, and halophilic. The most striking photosynthetic feature of Hlr. halochloris is that the bacteriochlorophyll (BChl) b-containing core light-harvesting (LH1) complex surrounding its reaction center (RC) exhibits its LH1 Q_y absorption maximum at 1016 nm, which is the lowest transition energy among phototrophic organisms. Here we report that this extraordinarily red-shifted LH1 Q_y band of Hlr. halochloris exhibits interconvertible spectral shifts depending on the electrostatic charge distribution around the BChl b molecules. The 1016 nm band of the Hlr. halochloris LH1-RC complex was blue-shifted to 958 nm upon desalting or pH decrease but returned to its original position when supplemented with salts or pH increase. Resonance Raman analysis demonstrated that these interconvertible spectral shifts are not associated with the strength of hydrogen-bonding interactions between BChl b and LH1 polypeptides. Furthermore, circular dichroism signals for the LH1 Q_y transition of Hlr. halochloris appeared with a positive sign (as in BChl b-containing Blastochloris species) and opposite those of BChl a-containing purple bacteria, possibly due to a combined effect of slight differences in the transition dipole moments between BChl a and BChl b and in the interactions between adjacent BChls in their assembled state. Based on these findings and LH1 amino acid sequences, it is proposed that Hlr. halochloris evolved its unique and tunable light-harvesting system with electrostatic charges in order to carry out photosynthesis and thrive in its punishing hypersaline and alkaline habitat.

Fully Quantum Modeling of Exciton Diffusion in Mesoscale Light Harvesting Systems

It has long been a challenge to accurately and efficiently simulate exciton-phonon dynamics in mesoscale photosynthetic systems with a fully quantum mechanical treatment due to extensive computational resources required. In this work, we tackle this seemingly intractable problem by combining the Dirac-Frenkel time-dependent variational method with Davydov trial states and implementing the algorithm in graphic processing units. The phonons are treated on the same footing as the exciton. Tested with toy models, which are nanoarrays of the B850 pigments from the light harvesting 2 complexes of purple bacteria, the methodology is adopted to describe exciton diffusion in huge systems containing more than 1600 molecules. The superradiance enhancement factor extracted from the simulations indicates an exciton delocalization over two to three pigments, in agreement with measurements of fluorescence quantum yield and lifetime in B850 systems. With fractal analysis of the exciton dynamics, it is found that exciton transfer in B850 nanoarrays exhibits a superdiffusion component for about 500 fs. Treating the B850 ring as an aggregate and modeling the inter-ring exciton transfer as incoherent hopping, we also apply the method of classical master equations to estimate exciton diffusion properties in one-dimensional (1D) and two-dimensional (2D) B850 nanoarrays using derived analytical expressions of time-dependent excitation probabilities. For both coherent and incoherent propagation, faster energy transfer is uncovered in 2D nanoarrays than 1D chains, owing to availability of more numerous propagating channels in the 2D arrangement.

Consistency landscape of network communities

The concept of community detection has long been used as a key device for handling the mesoscale structures in networks. Suitably conducted community detection reveals various embedded informative substructures of network topology. However, regarding the practical usage of community detection, it has always been a tricky problem to assign a reasonable community resolution for networks of interest. Because of the absence of the unanimously accepted criterion, most of the previous studies utilized rather ad hoc heuristics to decide the community resolution. In this work, we harness the concept of consistency in community structures of networks to provide the overall community resolution landscape of networks, which we eventually take to quantify the reliability of detected communities for a given resolution parameter. More precisely, we exploit the ambiguity in the results of stochastic detection algorithms and suggest a method that denotes the relative validity of community structures in regard to their stability of global and local inconsistency measures using multiple detection processes. Applying our framework to synthetic and real networks, we confirm that it effectively displays insightful fundamental aspects of community structures.

An Exciton Dynamics Model of Bryopsis corticulans Light-Harvesting Complex II

Bryopsis corticulans is a marine green macroalga adapted to the intertidal environment. It possesses siphonaxanthin-binding light-harvesting complexes of photosystem II (LHCII) with spectroscopic properties markedly different from the LHCII in plants. By applying a phenomenological fitting procedure to the two-dimensional electronic spectra of the LHCII from B. corticulans measured at 77 K, we can extract information about the excitonic states and energy-transfer processes. The fitting method results in well-converged parameters, including excitonic energy levels with their respective transition dipole moments, spectral widths, energy-transfer rates, and coupling properties. The 2D spectra simulated from the fitted parameters concur very well with the experimental data, showing the robustness of the fitting method. An excitonic energy-transfer scheme can be constructed from the fitting parameters. It shows the rapid energy transfer from chlorophylls (Chls) b to a at subpicosecond time scales and a long-lived state in the Chl b region at around 659 nm. Three weakly connected terminal states are resolved at 671, 675, and 677 nm. The lowest state is higher in energy than that in plant LHCII, which is probably because of the fewer number of Chls a in a B. corticulans LHCII monomer. Modeling based on existing Hamiltonians for the plant LHCII structure with two Chls a switched to Chls b suggests several possible Chl a-b replacements in comparison with those of plant LHCII. The adaptive changes result in a slower energy equilibration in the complex, revealed by the longer relaxation times of several exciton states compared to those of plant LHCII. The strength of our phenomenological fitting method for obtaining excitonic energy levels and energy-transfer network is put to the test in systems such as B. corticulans LHCII, where prior knowledge on exact assignment and spatial locations of pigments are lacking.

An effective potential for Frenkel excitons

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is introduced that is valid in a wide range of intermolecular distances. The proposed approach is based on the effective elimination of electron repulsion integrals from the excitonic Hamiltonian matrix elements via the density-fitting approach and distributed multipole approximation. The excitonic Hamiltonian represented in a basis including charge transfer (CT) states is re-cast in terms of the effective one-electron potential functions (EOPs) and adapted into the effective fragment parameter (EFP) framework. Calculations for model systems indicate that the speedup of at least three orders of magnitude, as compared to the state-of-the-art methods, can be achieved while maintaining the accuracy of the EET couplings even at short intermolecular distances.

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

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

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

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

Two Distinct Photoprocesses in Cyanobacterial Bilin Pigments: Energy Migration in Light‐Harvesting Phycobiliproteins versus Photoisomerization in Phytochromes

The evolution of oxygenic photosynthesis, respiration and photoperception are connected with the appearance of cyanobacteria. The key compounds, which are involved in these processes, are tetrapyrroles: open chain — bilins and cyclic — chlorophylls and heme. The latter are characterized by their covalent bond with the apoprotein resulting in the formation of biliproteins. This type of photoreceptors is unique in that it can perform important and opposite functions—light‐harvesting in photosynthesis with the participation of phycobiliproteins and photoperception mediated by phycochromes and phytochromes. In this review, cyanobacterial phycobiliproteins and phytochrome Cph1 are considered from a comparative point of view. Structural features of these pigments, which provide their contrasting photophysical and photochemical characteristics, are analyzed. The determining factor in the case of energy migration with the participation of phycobiliproteins is blocking the torsional relaxations of the chromophore, its D‐ring, in the excited state and their freedom, in the case of phytochrome photoisomerization. From the energetics point of view, this distinction is preconditioned by the height of the activation barrier for the photoreaction and relaxation in the excited state, which depends on the degree of the chromophore fixation by its protein surroundings.

Dynamic Disorder Drives Exciton Transfer in Tubular Chlorosomal Assemblies

Chlorosomes stand out for their highly efficient excitation energy transfer (EET) in extreme low light conditions. Yet, little is known about the EET when a chlorosome is excited to a pure state that is an eigenstate of the exciton Hamiltonian. In this work, we consider the dynamic disorder in the intermolecular electronic coupling explicitly by calculating the electronic coupling terms in the Hamiltonian using nuclear coordinates that are taken from molecular dynamics simulation trajectories. We show that this dynamic disorder is capable of driving the evolution of the exciton, being a stationary state of the initial Hamiltonian. In particular, long-distance excitation energy transfer between domains of high exciton population and oscillatory behavior of the population in the site basis are observed, in line with two-dimensional electronic spectroscopy studies. We also found that in the high exciton population domains, their population variation is correlated with their overall coupling strength. Analysis in a reference state basis shows that such dynamic disorder, originating from thermal energy, creates a fluctuating landscape for the exciton and promotes the EET process. We propose such dynamic disorder as an important microscopic origin for the high efficient EET widely observed in different types of chlorosomes, bioinspired tubular aggregates, or other light-harvesting complexes.

Two Distinct Photoprocesses in Cyanobacterial Bilin Pigments: Energy Migration in Light-Harvesting Phycobiliproteins versus Photoisomerization in Phytochromes

The evolution of oxygenic photosynthesis, respiration and photoperception are connected with the appearance of cyanobacteria. The key compounds, which are involved in these processes, are tetrapyrroles: open chain - bilins and cyclic - chlorophylls and heme. The latter are characterized by their covalent bond with the apoprotein resulting in the formation of biliproteins. This type of photoreceptors is unique in that it can perform important and opposite functions-light-harvesting in photosynthesis with the participation of phycobiliproteins and photoperception mediated by phycochromes and phytochromes. In this review, cyanobacterial phycobiliproteins and phytochrome Cph1 are considered from a comparative point of view. Structural features of these pigments, which provide their contrasting photophysical and photochemical characteristics, are analyzed. The determining factor in the case of energy migration with the participation of phycobiliproteins is blocking the torsional relaxations of the chromophore, its D-ring, in the excited state and their freedom, in the case of phytochrome photoisomerization. From the energetics point of view, this distinction is preconditioned by the height of the activation barrier for the photoreaction and relaxation in the excited state, which depends on the degree of the chromophore fixation by its protein surroundings.

Light harvesting and energy transfer in a porphyrin-based metal organic framework

We present the synthesis and photophysical characterization of a water stable PCN-223(freebase) metal organic framework (MOF) constructed from meso-tetrakis(4-carboxyphenyl)porphyrin (TCPP). The photophysical properties of the synthesized crystalline material were studied using a wide range of steady-state and time-resolved spectroscopic techniques. Quenching experiments performed on TCPP and PCN-223 demonstrated that the extent and the rate of quenching in the MOF is significantly higher than the monomeric ligand. Based on these results, we propose that upon photo-excitation, the singlet excitation energy migrates across neutral TCPP linkers until it is quenched by a N-protonated TCPP linker. The N-protonated linkers act as trap states that deactivate the excited state to the ground state. Variable temperature measurements aided in understanding the mechanism of singlet-singlet energy transfer in the PCN-223 MOF. The rate of energy transfer and the total exciton hopping distance in PCN-223 were calculated in order to quantify the energy transfer characteristics of PCN-223. Nanosecond transient absorption spectroscopy was used to study the triplet excited state photophysics in both the free ligand and PCN-223 MOF. Furthermore, femtosecond transient absorption spectroscopy was employed to get a better understanding of the photophysical processes taking place in the ligand and MOF on ultrafast timescales. Efficient energy transfer (Förster radius = 54.5 Å) accompanied with long distance exciton hopping (173 Å) was obtained for the PCN-223 MOF.

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.

Intermolecular Energy Transfer in Real Time

Resonance energy transfer (RET) is a complex phenomenon where energy is transferred between two nonequivalent molecules. In the Förster picture, that applies to the weak coupling regime, RET occurs from the energy donor molecule in the relaxed excited state toward the acceptor, in an energy-conserving process. However, energy dissipation is crucial for a more general picture of RET that also applies to the strong coupling regime. Here we present a dynamical, nonadiabatic model for RET also accounting for energy relaxation. We exploit the essential state formalism to set up a model for the RET pair that yields an accurate picture of the relevant physics, accounting for just a few electronic states and a single coupled vibrational coordinate per molecule. Molecular vibrations are treated in a nonadiabatic approach, and energy dissipation is dealt within the Redfield formalism. The approach is first validated on an isolated dye, demonstrating that a very simple relaxation model, defined in terms of a single relaxation parameter, properly describes the different regimes of energy dissipation expected for a molecule, with a fast (fs time window) internal conversion to the lowest excited state and a slow relaxation toward the ground state (ns time window). The same approach is then applied to follow the real time dynamics of a RET pair. In line with the Förster model, in the weak coupling regime the internal conversion of the donor molecule is completed before energy transfer takes place. Our approach also applies to the strong coupling regime, where we observe ultrafast energy transfer occurring well before the internal relaxation of the energy donor is completed.

Computational Modeling of Exciton-Bath Hamiltonians for Light Harvesting 2 and Light Harvesting 3 Complexes of Purple Photosynthetic Bacteria at Room Temperature

Light harvesting 2 (LH2) complex is the primary component of the photosynthetic unit of purple bacteria that is responsible for harvesting and relaying excitons. The electronic absorption line shape of LH2 contains two major bands at 800 and 850 nm wavelength regions. Under low light conditions, some species of purple bacteria replace LH2 with light harvesting 3 (LH3), a variant form with almost the same structure as the former but with distinctively different spectral features. The major difference between the absorption line shapes of LH2 and LH3 is the shift of the 850 nm band of the former to a new 820 nm region. The microscopic origin of this difference has been the subject of some theoretical/computational investigations. However, the genuine molecular level source of such a difference is not clearly understood yet. This work reports a comprehensive computational study of LH2 and LH3 complexes so as to clarify different molecular level features of LH2 and LH3 complexes and to construct simple exciton-bath models with a common form. All-atomistic molecular dynamics simulations of both LH2 and LH3 complexes provide detailed molecular level structural differences of bacteriochlorophylls (BChls) in the two complexes, in particular, in their patterns of hydrogen bonding (HB) and torsional angles of the acetyl group. Time-dependent density functional theory calculation of the excitation energies of BChls for structures sampled from the MD simulations suggests that the observed differences in the HB and torsional angles cannot fully account for the experimentally observed spectral shift of LH3. Potential sources that can explain the actual spectral shift of LH3 are discussed, and their magnitudes are assessed through fitting of experimental line shapes. These results demonstrate the feasibility of developing simple exciton-bath models for both LH2 and LH3, which can be employed for large-scale exciton quantum dynamics in their aggregates.

Control of Excitation Energy Transfer in Condensed Phase Molecular Systems by Floquet Engineering

Excitation energy transfer (EET) is one of the most important processes in both natural and artificial chemical systems including, for example, photosynthetic complexes and organic solar cells. The EET rate, however, is strongly suppressed when there is a large difference in the excitation energy between the donor and acceptor molecules. Here, we demonstrate both analytically and numerically that the EET rate can be greatly enhanced by periodically modulating the excitation energy difference. The enhancement of EET by using this Floquet engineering, in which the system's Hamiltonian is made periodically time-dependent, turns out to be efficient even in the presence of strong fluctuations and dissipations induced by the coupling with a huge number of dynamic degrees of freedom in the surrounding molecular environments. As an effect of the environment on the Floquet engineering of EET, the optimal driving frequency is found to depend on the relative magnitudes of the system and environment's characteristic time scales with an observed frequency shift when moving from the limit of slow environmental fluctuations (inhomogeneous broadening limit) to that of fast fluctuations (homogeneous broadening limit).

Aggregates of quadrupolar dyes for two-photon absorption: the role of intermolecular interactions

We present a theoretical investigation of small aggregates of quadrupolar (A-π-D-π-A or D-π-A-π-D) charge-transfer dyes, with attention focused on the role of intermolecular interactions in determining their optical properties. We tackle the theoretical issue by adopting essential-state models (ESMs), which describe an isolated molecule in terms of a minimal number of electronic states, corresponding to the resonance structures. ESMs quite naturally describe intermolecular interactions relaxing the dipolar approximation and accounting for molecular polarizabilities. The approach is applied to curcuminoid and squaraine dyes, two families of chromophores with weak and strong quadrupolar character, respectively. The method is validated against experiment and for curcuminoids also against time-dependent density functional theory. ESMs rationalize the strong ultra-excitonic effects recurrently observed in the experimental optical spectra of aggregates of highly polarizable quadrupolar dyes, offering a valuable tool to exploit the supramolecular design of material properties.

Ultrafast Electronic Energy Transfer in an Orthogonal Molecular Dyad

Understanding electronic energy transfer (EET) is an important ingredient in the development of artificial photosynthetic systems and photovoltaic technologies. Although EET is at the heart of these applications and crucially influences their light-harvesting efficiency, the nature of EET over short distances for covalently bound donor and acceptor units is often not well understood. Here we investigate EET in an orthogonal molecular dyad (BODT4), in which simple models fail to explain the very origin of EET. On the basis of nonadiabatic ab initio molecular dynamics calculations and ultrafast fluorescence experiments, we gain detailed microscopic insights into the ultrafast electrovibrational dynamics following photoexcitation. Our analysis offers molecular-level insights into these processes and reveals that it takes place on time scales ≲100 fs and occurs through an intermediate charge-transfer state.

Biomimetic Light-Harvesting Antenna Based on the Self-Assembly of Conjugated Polyelectrolytes Embedded within Lipid Membranes

Here we report a biomimetic light-harvesting antenna based on negatively charged poly(phenylene ethynylene) conjugated polyelectrolytes assembled within a positively charged lipid membrane scaffold constructed by the lipid 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP). Light harvested by the polymers was transferred via through-space mechanisms to a lipophilic energy acceptor (the cyanine dye DiI) whose effective molar absorption was enhanced by up to 18-fold due to the antenna effect. Absorption amplification of DiI was found to be due primarily to direct energy transfer from polymers. The efficiency of homoenergy transfer among polymers was next probed by the membrane embedding fullerene derivative phenyl-C₆₁-butryic acid methyl ester (PCBM) acting as an electron acceptor. PCBM was able to quench the emission of up to five polymers, consistent with a modest amount of homotransfer. The ability of the membrane to accommodate a high density of polymer donors without self-quenching was crucial to the success of electronic energy harvesting achieved. This work highlights the potential of lipid membranes as a platform to organize light-harvesting molecules on the nanoscale toward achieving efficient energy transfer to a target chromophore/trap.