Physical origins and models of energy transfer in photosynthetic light-harvesting

Exciton annihilation and diffusion length in disordered multichromophoric nanoparticles

Efficient exciton transport is the essential property of natural and synthetic light-harvesting (LH) devices. Here we investigate exciton transport properties in LH organic polymer nanoparticles (ONPs) of 40 nm diameter. The ONPs are loaded with a rhodamine B dye derivative and bulky counterion, enabling dye loadings as high as 0.3 M, while preserving fluorescence quantum yields larger than 30%. We use time-resolved fluorescence spectroscopy to monitor exciton-exciton annihilation (EEA) kinetics within the ONPs dispersed in water. We demonstrate that unlike the common practice for photoluminescence investigations of EEA, the non-uniform intensity profile of the excitation light pulse must be taken into account to analyse reliably intensity-dependent population dynamics. Alternatively, a simple confocal detection scheme is demonstrated, which enables (i) retrieving the correct value for the bimolecular EEA rate which would otherwise be underestimated by a typical factor of three, and (ii) revealing minor EEA by-products otherwise unnoticed. Considering the ONPs as homogeneous rigid solutions of weakly interacting dyes, we postulate an incoherent exciton hoping mechanism to infer a diffusion constant exceeding 0.003 cm2 s-1 and a diffusion length as large as 70 nm. This work demonstrates the success of the present ONP design strategy at engineering efficient exciton transport in disordered multichromophoric systems.

Insights into Energy Transfer in Light-Harvesting Complex II Through Machine-Learning Assisted Simulations

Light-harvesting complex II (LHCII) is the major antenna of higher plants. Energy transfer processes taking place inside its aggregate of chlorophylls have been experimentally investigated with time-resolved techniques, but a complete understanding of the most relevant energy transfer pathways and relative characteristic times remains elusive. Theoretical models to disentangle experimental data in LHCII have long been challenged by the large size and complex nature of the system. Here, we show that a fully first-principles approach combining molecular dynamics and machine learning can be successfully used to reproduce transient absorption spectra and characterize the EET pathways and the involved times.

Protein Effects on the Excitation Energies and Exciton Dynamics of the CP24 Antenna Complex

In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales.

Energy Transfer and Exciton Relaxation in B880-B800-RC Complex through Two-Dimensional Electronic Spectroscopy

The light-harvesting (LH) and reaction center (RC) core complex of purple bacterium Roseiflexus castenholzii, B880-B800-RC, are different from those of the typical photosynthetic unit, (B850-B800)x-B880-RC. To investigate the excitation flowing dynamics in this unique complex, two-dimensional electronic spectroscopy is employed. The obtained time constants for the exciton relaxation in B880, exciton relaxation in B800, B800 → B880 energy transfer (EET), and B880 → closed RC EET are 43 fs, 177 fs, 1.9 ps, and 205 ps, respectively. These time constants result in an overall EET efficiency similar to that of the typical photosynthetic unit. Analysis of the oscillatory signals reveals that while several vibronic coherences are involved in the exciton relaxation process, only one prominent vibronic coherence, with a frequency of 27 cm-1 and coupled to the B880 electronic transition, may contribute to the B800 → B880 EET process.

Interplay of decoherence and relaxation in a two-level system interacting with an infinite-temperature reservoir

We study the time evolution of a single qubit in contact with a bath, within the framework of projection operator methods. Employing the so-called modified Redfield theory, which also treats energy conserving interactions nonperturbatively, we are able to study the regime beyond the scope of the ordinary approach. Reduced equations of motion for the qubit are derived in an idealistic system where both the bath and system-bath interactions are modeled by Gaussian distributed random matrices. In the strong decoherence regime, a simple relation between the bath correlation function and the decoherence process induced by the energy conserving interaction is found. It implies that energy conserving interactions slow down the relaxation process, which leads to a Zeno freezing if they are sufficiently strong. Furthermore, our results are also confirmed in numerical simulations.

First-principles simulation of excitation energy transfer and transient absorption spectroscopy in the CP29 light-harvesting complex

The dynamics of delocalized excitons in light-harvesting complexes (LHCs) can be investigated using different experimental techniques, and transient absorption (TA) spectroscopy is one of the most valuable methods for this purpose. A careful interpretation of TA spectra is essential for the clarification of excitation energy transfer (EET) processes occurring during light-harvesting. However, even in the simplest LHCs, a physical model is needed to interpret transient spectra as the number of EET processes occurring at the same time is very large to be disentangled from measurements alone. Physical EET models are commonly built by fittings of the microscopic exciton Hamiltonians and exciton-vibrational parameters, an approach that can lead to biases. Here, we present a first-principles strategy to simulate EET and transient absorption spectra in LHCs, combining molecular dynamics and accurate multiscale quantum chemical calculations to obtain an independent estimate of the excitonic structure of the complex. The microscopic parameters thus obtained are then used in EET simulations to obtain the population dynamics and the related spectroscopic signature. We apply this approach to the CP29 minor antenna complex of plants for which we follow the EET dynamics and transient spectra after excitation in the chlorophyll b region. Our calculations reproduce all the main features observed in the transient absorption spectra and provide independent insight on the excited-state dynamics of CP29. The approach presented here lays the groundwork for the accurate simulation of EET and unbiased interpretation of transient spectra in multichromophoric systems.

Excitation energy equilibration in a trimeric LHCII complex involves unusual pathways

We explore the energy equilibration within the LHCII trimer using various approaches, including the Redfield-Förster method (with different compartmentalization schemes) and the exact hierarchical equation of motion (HEOM). We demonstrate that the inter-monomeric migration in the trimeric LHCII complex is not limited to direct transfers between quasi-equilibrated chlorophylls (Chls) a, but also involves additional pathways with uphill transfers from Chls a to the stromal-side Chls b (connecting the Chls a clusters from different monomeric subunits). Although these uphill transfers are slow they still can increase the total rate of inter-monomeric transfers by a factor of 1.5. The same stromal-side Chls b also promote a depopulation of the Chl a604 long-lived state (blue-shifted and mixed with the lumenal-side Chls b). Due to the connection between the stromal- and lumenal-side Chls b clusters the intra- and inter-monomeric transfers from a604 to the main Chls a become faster by a factor of 1.6 and 1.75, respectively.

Impact of Structure, Coupling Scheme, and State of Interest on the Energy Transfer in CP29

The Qy and Bx excitation energy transfer (EET) in the minor light-harvesting complex CP29 (LHCII B4.1) antenna complex of Pisum sativum was characterized using a computational approach. We applied Förster resonance energy transfer (FRET) and the transition density cube (TDC) method to estimate the Coulombic coupling, based on a combination of classical molecular dynamics and quantum mechanics/molecular mechanics calculations. Employing TDC instead of FRET mostly affects the EET between chlorophylls (Chls) and carotenoids (Crts), as expected due to the Crts being spatially more challenging for FRET. Only between Chls, effects are found to be small (about only 0.1 EET efficiency change when introducing TDC instead of FRET). Effects of structural sampling were found to be small, illustrated by a small average standard deviation for the Qy state coupling elements (FRET/TDC: 0.97/0.94 cm-1). Due to the higher flexibility of the Bx state, the corresponding deviations are larger (FRET/TDC between Chl-Chl pairs: 17.58/22.67 cm-1, between Crt-Chl pairs: 62.58/31.63 cm-1). In summary, it was found for the Q band that the coupling between Chls varies only slightly depending on FRET or TDC, resulting in a minute effect on EET acceptor preference. In contrast, the coupling in the B band spectral region is found to be more affected. Here, the S2 (1Bu) states of the spatially challenging Crts may act as acceptors in addition to the B states of the Chls. Depending on FRET or TDC, several Chls show different Chl-to-Crt couplings. Interestingly, the EET between Chls or Crts in the B band is found to often outcompete the corresponding decay processes. The individual efficiencies for B band EET to Crts vary however strongly with the chosen coupling scheme (e.g., up to 0.29/0.99 FRET/TDC efficiency for the Chl a604/neoxanthin pair). Thus, the choice of the coupling scheme must involve a consideration of the state of interest.

The location of the low-energy states in Lhca1 favors excitation energy transfer to the core in the plant PSI-LHCI supercomplex

Lhca1 is one of the four pigment-protein complexes composing the outer antenna of plant Photosystem I-light-havesting I supercomplex (PSI-LHCI). It forms a functional dimer with Lhca4 but, differently from this complex, it does not contain 'red-forms,' i.e., pigments absorbing above 700 nm. Interestingly, the recent PSI-LHCI structures suggest that Lhca1 is the main point of delivering the energy harvested by the antenna to the core. To identify the excitation energy pathways in Lhca1, we developed a structure-based exciton model based on the simultaneous fit of the low-temperature absorption, linear dichroism, and fluorescence spectra of wild-type Lhca1 and two mutants, lacking chlorophylls contributing to the long-wavelength region of the absorption. The model enables us to define the locations of the lowest energy pigments in Lhca1 and estimate pathways and timescales of energy transfer within the complex and to the PSI core. We found that Lhca1 has a particular energy landscape with an unusual (compared to Lhca4, LHCII, and CP29) configuration of the low-energy states. Remarkably, these states are located near the core, facilitating direct energy transfer to it. Moreover, the low-energy states of Lhca1 are also coupled to the red-most state (red forms) of the neighboring Lhca4 antenna, providing a pathway for effective excitation energy transfer from Lhca4 to the core.

Recent progress in atomistic modeling of light-harvesting complexes: a mini review

In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as site energies, excitonic couplings, and spectral densities are key quantities which usually need to be extracted to be able to determine the exciton dynamics and spectroscopic properties. The recently developed multiscale approach based on the numerically efficient density functional tight-binding framework followed by excited state calculations has been shown to be superior to the scheme based on pure classical molecular dynamics simulations. The enhanced approach, which improves the description of the internal vibrational dynamics of the pigment molecules, yields spectral densities in good agreement with the experimental counterparts for various bacterial and plant LH systems. Here, we provide a brief overview of those results and described the theoretical foundation of the multiscale protocol.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

Bethe-Salpeter equation insights into the photo-absorption function and exciton structure of chlorophyll a and b in light-harvesting complex II

The photo-absorption process and the excitation of chlorophyll (Chl) is the primary and essential step of photosynthesis in green plants. By solving the Bethe-Salpeter equation (BSE) on top of the GW approximation within ab initio many-body perturbation theory, we calculate the photo-absorption function and the excitons structure of Chl a and b in their in vivo conformations as measured by X-ray diffraction in the light-harvesting complex (LHC) II. BSE optical absorption spectra are in good agreement with the experiment and we discuss residual discrepancies. The experimental evidence of multiple Chla forms in vivo is explained by BSE. The Chla and Chlb BSE exciton wavefunctions present important charge-transfer differences on the Soret band. Q excitons are almost identical, apart from charge (both electron and hole) localization on the Chlb C7 aldheide formyl group, absent on the Chla methyl C7, that is exactly the group where the two chlorophylls differ.

Leveraging Dynamical Symmetries in Two-Dimensional Electronic Spectra to Extract Population Transfer Pathways

We present a method to deterministically isolate population transfer kinetics from two-dimensional electronic spectroscopic signals. Central to this analysis is the characterization of how all possible subensembles of excited state systems evolve through the population time. When these dynamics are diagrammatically mapped by using double-sided Feynman pathways where population time dynamics are included, a useful symmetry emerges between excited state absorption and ground state bleach recovery dynamics of diagonal and below diagonal cross-peak signals. This symmetry allows removal of pathways from the spectra to isolate signals that evolve according to energy transfer kinetics. We describe a regression procedure to fit to energy transfer time constants and characterize the accuracy of the method in a variety of complex excited state systems using simulated two-dimensional spectra. Our results show that the method is robust for extracting ultrafast energy transfer in multistate excitonic systems, systems containing dark states that affect the signal kinetics, and systems with interfering vibrational relaxation pathways. This procedure can be used to accurately extract energy transfer kinetics from a wide variety of condensed phase systems.

Spectral densities and absorption spectra of the core antenna complex CP43 from photosystem II

Besides absorbing light, the core antenna complex CP43 of photosystem II is of great importance in transferring excitation energy from the antenna complexes to the reaction center. Excitation energies, spectral densities, and linear absorption spectra of the complex have been evaluated by a multiscale approach. In this scheme, quantum mechanics/molecular mechanics molecular dynamics simulations are performed employing the parameterized density functional tight binding (DFTB) while the time-dependent long-range-corrected DFTB scheme is applied for the excited state calculations. The obtained average spectral density of the CP43 complex shows a very good agreement with experimental results. Moreover, the excitonic Hamiltonian of the system along with the computed site-dependent spectral densities was used to determine the linear absorption. While a Redfield-like approximation has severe shortcomings in dealing with the CP43 complex due to quasi-degenerate states, the non-Markovian full second-order cumulant expansion formalism is able to overcome the drawbacks. Linear absorption spectra were obtained, which show a good agreement with the experimental counterparts at different temperatures. This study once more emphasizes that by combining diverse techniques from the areas of molecular dynamics simulations, quantum chemistry, and open quantum systems, it is possible to obtain first-principle results for photosynthetic complexes, which are in accord with experimental findings.

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.

Ultrafast Excitation Energy Transfer Dynamics in the LHCII-CP29-CP24 Subdomain of Plant Photosystem II

We measure the two-dimensional electronic spectra of the LHCII(M)-CP29-CP24 complex in photosystem II (PSII) and provide the first study of the ultrafast excitation energy transfer (EET) processes of an asymmetric and native light-harvesting assembly of the antenna of PSII. With comparisons to LHCII, we observe faster energy equilibrations in the intermediate levels of the LHCII(M)-CP29-CP24 complex at 662 and 670 nm. Notably, the putative "bottleneck" states in LHCII exhibit faster effective dynamics in the LHCII(M)-CP24-CP29 complex, with the average lifetime shortening from 2.5 ps in LHCII to 1.2 ps in the bigger assembly. The observations are supported by high-level structure-based calculations, and the accelerated dynamics can be attributed to the structural change of LHCII(M) in the bigger complex. This study shows that the biological functioning structures of the complexes are important to understand the overall EET dynamics of the PSII supercomplex.

Vibrational and vibronic coherences in the energy transfer process of light-harvesting complex II revealed by two-dimensional electronic spectroscopy

The presence of quantum coherence in light-harvesting complex II (LHCII) as a mechanism to understand the efficiency of the light-harvesting function in natural photosynthetic systems is still debated due to its structural complexity and weak-amplitude coherent oscillations. Here, we revisit the coherent dynamics and clarify different types of coherences in the energy transfer processes of LHCII using a joint method of the high-S/N transient grating and two-dimensional electronic spectroscopy. We find that the electronic coherence decays completely within 50 fs at room temperature. The vibrational coherences of chlorophyll a dominate over oscillations within 1 ps, whereas a low-frequency mode of 340 cm−1 with a vibronic mixing character may participate in vibrationally assisted energy transfer between chlorophylls a. Our results may suggest that vibronic mixing is relevant for rapid energy transfer processes among chlorophylls in LHCII.

Observation of robust energy transfer in the photosynthetic protein allophycocyanin using single-molecule pump-probe spectroscopy

Photosynthetic organisms convert sunlight to electricity with near unity quantum efficiency. Absorbed photoenergy transfers through a network of chromophores positioned within protein scaffolds, which fluctuate due to thermal motion. The resultant variation in the individual energy transfer steps has not yet been measured, and so how the efficiency is robust to this variation has not been determined. Here, we describe single-molecule pump-probe spectroscopy with facile spectral tuning and its application to the ultrafast dynamics of single allophycocyanin, a light-harvesting protein from cyanobacteria. We disentangled the energy transfer and energetic relaxation from nuclear motion using the spectral dependence of the dynamics. We observed an asymmetric distribution of timescales for energy transfer and a slower and more heterogeneous distribution of timescales for energetic relaxation, which was due to the impact of the protein environment. Collectively, these results suggest that energy transfer is robust to protein fluctuations, a prerequisite for efficient light harvesting.

Probing twisted intramolecular charge transfer of pyrene derivatives as organic emitters in OLEDs

Intramolecular charge transfer (ICT) plays a critical role in determining the photophysical properties of organic molecules, including their luminescence efficiencies. Twisted intramolecular charge transfer (TICT) is a process in which...

Time-dependent atomistic simulations of the CP29 light-harvesting complex

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Artificial Photosynthesis: Is Computation Ready for the Challenge Ahead?

A tremendous effort is currently devoted to the generation of novel hybrid materials with enhanced electronic properties for the creation of artificial photosynthetic systems. This compelling and challenging problem is well-defined from an experimental point of view, as the design of such materials relies on combining organic materials or metals with biological systems like light harvesting and redox-active proteins. Such hybrid systems can be used, e.g., as bio-sensors, bio-fuel cells, biohybrid photoelectrochemical cells, and nanostructured photoelectronic devices. Despite these efforts, the main bottleneck is the formation of efficient interfaces between the biological and the organic/metal counterparts for efficient electron transfer (ET). It is within this aspect that computation can make the difference and improve the current understanding of the mechanisms underneath the interface formation and the charge transfer efficiency. Yet, the systems considered (i.e., light harvesting protein, self-assembly monolayer and surface assembly) are more and more complex, reaching (and often passing) the limit of current computation power. In this review, recent developments in computational methods for studying complex interfaces for artificial photosynthesis will be provided and selected cases discussed, to assess the inherent ability of computation to leave a mark in this field of research.

DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum-classical description. To this end, Born-Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna-Matthews-Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

Absorption and Circular Dichroism Spectra of Molecular Aggregates With the Full Cumulant Expansion

The exciton Hamiltonian of multichromophoric aggregates can be probed by spectroscopic techniques such as linear absorption and circular dichroism. To compare calculated Hamiltonians to experiments, a lineshape theory is needed, which takes into account the coupling of the excitons with inter- and intramolecular vibrations. This coupling is normally introduced in a perturbative way through the cumulant expansion formalism and further approximated by assuming a Markovian exciton dynamics, for example with the modified Redfield theory. Here, we present the implementation of the full cumulant expansion (FCE) formalism (J. Chem. Phys.142, 2015, 09410625747060) to efficiently compute absorption and circular dichroism spectra of molecular aggregates beyond the Markov approximation, without restrictions on the form of exciton–phonon coupling. By employing the LH2 system of purple bacteria as a challenging test case, we compare the FCE lineshapes with the Markovian lineshapes obtained with the modified Redfield theory, showing that the latter presents a less satisfying agreement with experiments. The FCE approach instead accurately describes the lineshapes, especially in the vibronic sideband of the B800 peak. We envision that the FCE approach will become a valuable tool for accurately comparing model exciton Hamiltonians with optical spectroscopy experiments.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Consciousness as an Emergent Phenomenon: A Tale of Different Levels of Description

One of the biggest queries in cognitive sciences is the emergence of consciousness from matter. Modern neurobiological theories of consciousness propose that conscious experience is the result of interactions between large-scale neuronal networks in the brain, traditionally described within the realm of classical physics. Here, we propose a generalized connectionist framework in which the emergence of "conscious networks" is not exclusive of large brain areas, but can be identified in subcellular networks exhibiting nontrivial quantum phenomena. The essential feature of such networks is the existence of strong correlations in the system (classical or quantum coherence) and the presence of an optimal point at which the system's complexity and energy dissipation are maximized, whereas free-energy is minimized. This is expressed either by maximization of the information content in large scale functional networks or by achieving optimal efficiency through the quantum Goldilock effect.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

Bilirubin analogues as model compounds for exciton coupling

A series of phycobilin analogues have been investigated in terms of coupled excitonic systems. These compounds consist of a monomer, a tetrapyrrole structurally similar to bilirubin (bR), and two conjugated bR analogues. Spectroscopic and computational methods have been used to investigate the degree of interchromophore coupling. We find the synthesised bR analogue shows stronger excitonic coupling than bR, owing to a different molecular geometry. The excitonic coupling in the conjugated molecules can be controlled by modifying the bridge side-group. New computed energy levels for bR using the DFT/MRCI method are also presented, which improve on published values and re-assign the character of excited singlet states.

Coherent and incoherent theories for photosynthetic energy transfer

There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Förster theory and modified Redfield theory (MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion (HEOM), quantum path integral, coherent modified Redfield theory (CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer (EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.

On the arrangement of chromophores in light harvesting complexes: chance versus design

We used a homogeneous computational approach to derive the excitonic Hamiltonian for five light harvesting complexes containing only one type of chromophore and compare them in terms of statistical descriptors. We then studied the approximate exciton dynamics for the five complexes introducing a measure, the (averaged and time-dependent) inverse participation ratio, that enables the comparison between very diverse complexes on the same ground. We find that the global dynamics are very similar across the set of systems despite the variety of geometric structures of the complexes. In particular, the dynamics of four out of five light harvesting complexes are barely distinguishable with a small variation from the norm seen only for the Fenna-Matthews-Olson complex. We use the information from the realistic Hamiltonians to build a reduced model system that shows how the global dynamics are ultimately dominated by a single parameter, the degree of localization of the excitonic Hamiltonian eigenstates. Considering the physically plausible range of system parameters, the reduced model explains why the dynamics are so similar across most light harvesting complexes containing a single type of chromophore regardless of the detailed pattern of the inter-chromophore excitonic coupling.

Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

Successes & challenges in the atomistic modeling of light-harvesting and its photoregulation

Light-harvesting is a crucial step of photosynthesis. Its mechanisms and related energetics have been revealed by a combination of experimental investigations and theoretical modeling. The success of theoretical modeling is largely due to the application of atomistic descriptions combining quantum chemistry, classical models and molecular dynamics techniques. Besides the important achievements obtained so far, a complete and quantitative understanding of how the many different light-harvesting complexes exploit their structural specificity is still missing. Moreover, many questions remain unanswered regarding the mechanisms through which light-harvesting is regulated in response to variable light conditions. Here we show that, in both fields, a major role will be played once more by atomistic descriptions, possibly generalized to tackle the numerous time and space scales on which the regulation takes place: going from the ultrafast electronic excitation of the multichromophoric aggregate, through the subsequent conformational changes in the embedding protein, up to the interaction between proteins.

Cavity-Modified Exciton Dynamics in Photosynthetic Units

Recently, exciton-photon strong coupling has been proposed as a means to control and enhance energy transfer in ensembles of organic molecules. Here, we demonstrate that the exciton dynamics in an archetypal purple bacterial photosynthetic unit, composed of six LH2 antennas surrounding a single LH1 complex, is greatly modified by its interaction with an optical cavity. We develop a Bloch-Redfield master equation approach that accounts for the interplay between the B800 and B850 bacteriochlorophyll molecules within each LH2 antenna, as well as their interactions with the central LH1 complex. Using a realistic parametrization of both the photosynthetic unit and optical cavity, we investigate the formation of polaritons in the system, revealing that these can be tuned to accelerate its exciton dynamics by 3 orders of magnitude. This yields a significant occupation of the LH1 complex, the stage immediately prior to the reaction center, with only a few-femtosecond delay after the initial excitation of the LH2 B800 pigments. Our theoretical findings unveil polaritonic phenomena as a promising route for the characterization, tailoring, and optimization of light-harvesting mechanisms in natural and artificial photosynthetic processes.

A theoretical study on the dynamics of light harvesting in the dimeric photosystem II core complex: regulation and robustness of energy transfer pathways

Here we present our theoretical investigations into the light reaction in the dimeric photosystem II (PSII) core complex. An effective model for excitation energy transfer (EET) and primary charge separation (CS) in the PSII core complex was developed, with model parameters constructed based on molecular dynamics (MD) simulation data. Compared to experimental results, we demonstrated that this model faithfully reproduces the absorption spectra of the RC and core light-harvesting complexes (CP43 and CP47) as well as the full EET dynamics among the chromophores in the PSII core complex. We then applied master equation simulations and network analysis to investigate detailed EET plus CS dynamics in the system, allowing us to identify key EET pathways and produce a coarse-grained cluster model for the light reaction in the dimeric PSII core complex. We show that non-equilibrium energy transfer channels play important roles in the efficient light harvesting process and that multiple EET pathways exist between subunits of PSII to ensure the robustness of light harvesting in the system. Furthermore, we revealed that inter-monomer energy transfer dominated by the coupling between the two CLA625 molecules enables efficient energy exchange between two CP47s in the dimeric PSII core complex, which leads to significant energy pooling in the CP47 domain during the light reaction. Our study provides a blueprint for the design of light harvesting in the PSII core and show that a structure-based approach using molecular dynamics simulations and quantum chemistry calculations can be effectively utilized to elucidate the dynamics of light harvesting in complex photosynthetic systems.

The future of quantum biology

Biological systems are dynamical, constantly exchanging energy and matter with the environment in order to maintain the non-equilibrium state synonymous with living. Developments in observational techniques have allowed us to study biological dynamics on increasingly small scales. Such studies have revealed evidence of quantum mechanical effects, which cannot be accounted for by classical physics, in a range of biological processes. Quantum biology is the study of such processes, and here we provide an outline of the current state of the field, as well as insights into future directions.

Surface Hopping within an Exciton Picture. An Electrostatic Embedding Scheme

We report the development and the implementation of an exciton approach that allows ab initio nonadiabatic dynamics simulations of electronic excitation energy transfer in multichromophoric systems. For the dynamics, a trajectory-based strategy is used within the surface hopping formulation. The approach features a consistent hybrid formulation that allows the construction of potential energy surfaces and gradients by combining quantum mechanics and molecular mechanics within an electrostatic embedding scheme. As an application, the study of a molecular dyad consisting of a covalently bound BODIPY moiety and a tetrathiophene group is presented using time-dependent density functional theory (TDDFT). The results obtained with the exciton model are compared to previously performed full TDDFT dynamics of the same system. Our results show excellent agreement with the full TDDFT results, indicating that the couplings that lead to excitation energy transfer (EET) are dominated by Coulomb interaction terms and that charge-transfer states are not necessary to properly describe the nonadiabatic dynamics of the system. The exciton model also reveals ultrafast coherent oscillations of the excitation between the two units in the dyad, which occur during the first 50 fs.

Correlated fluorescence quenching and topographic mapping of Light-Harvesting Complex II within surface-assembled aggregates and lipid bilayers

Light-Harvesting Complex II (LHCII) is a chlorophyll-protein antenna complex that efficiently absorbs solar energy and transfers electronic excited states to photosystems I and II. Under excess light intensity LHCII can adopt a photoprotective state in which excitation energy is safely dissipated as heat, a process known as Non-Photochemical Quenching (NPQ). In vivo NPQ is triggered by combinatorial factors including transmembrane ΔpH, PsbS protein and LHCII-bound zeaxanthin, leading to dramatically shortened LHCII fluorescence lifetimes. In vitro, LHCII in detergent solution or in proteoliposomes can reversibly adopt an NPQ-like state, via manipulation of detergent/protein ratio, lipid/protein ratio, pH or pressure. Previous spectroscopic investigations revealed changes in exciton dynamics and protein conformation that accompany quenching, however, LHCII-LHCII interactions have not been extensively studied. Here, we correlated fluorescence lifetime imaging microscopy (FLIM) and atomic force microscopy (AFM) of trimeric LHCII adsorbed to mica substrates and manipulated the environment to cause varying degrees of quenching. AFM showed that LHCII self-assembled onto mica forming 2D-aggregates (25-150 nm width). FLIM determined that LHCII in these aggregates were in a quenched state, with much lower fluorescence lifetimes (~0.25 ns) compared to free LHCII in solution (2.2-3.9 ns). LHCII-LHCII interactions were disrupted by thylakoid lipids or phospholipids, leading to intermediate fluorescent lifetimes (0.6-0.9 ns). To our knowledge, this is the first in vitro correlation of nanoscale membrane imaging with LHCII quenching. Our findings suggest that lipids could play a key role in modulating the extent of LHCII-LHCII interactions within the thylakoid membrane and so the propensity for NPQ activation.

An efficient approach to the quantum dynamics and rates of processes induced by natural incoherent light

In many important cases, the rate of excitation of a system embedded in an environment is significantly smaller than the internal system relaxation rates. An important example is that of light-induced processes under natural conditions, in which the system is excited by weak, incoherent (e.g., solar) radiation. Simulating the dynamics on the time scale of the excitation source can thus be computationally intractable. Here we describe a method for obtaining the dynamics of quantum systems without directly solving the master equation. We present an algorithm for the numerical implementation of this method and, as an example, use it to reconstruct the internal conversion dynamics of pyrazine excited by sunlight. Significantly, this approach also allows us to assess the role of quantum coherence on biological time scales, which is a topic of ongoing interest.

Dynamics of the mixed exciton and charge-transfer states in light-harvesting complex Lhca4: Hierarchical equation approach

We model the energy transfer dynamics in the Lhca4 peripheral antenna of photosystem I from higher plants. Equilibration between the bulk exciton levels of the antenna and the red-shifted charge-transfer (CT) states is described using the numerically inexpensive Redfield-Förster approach and exact hierarchical equation (HEOM) method. We propose a compartmentalization scheme allowing a quantitatively correct description of the dynamics with the Redfield-Förster theory, including the exciton-type relaxation within strongly coupled compartments and hopping-type migration between them. The Redfield-Förster method gives the kinetics close to the HEOM solution when treating the CT state as dynamically localized. We also demonstrate that the excited states strongly coupled with the CT should be considered as localized as well.

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.

Evidence for coherent mixing of excited and charge-transfer states in the major plant light-harvesting antenna, LHCII

LHCII, the major light harvesting antenna from plants, plays a dual role in photosynthesis. In low light it is a light-harvester, while in high light it is a quencher that protects the organism from photodamage. The switching mechanism between these two orthogonal conditions is mediated by protein dynamic disorder and photoprotective energy dissipation. The latter in particular is thought to occur in part via spectroscopically 'dark' states. We searched for such states in LHCII trimers from spinach, at both room temperature and at 77 K. Using 2D electronic spectroscopy, we explored coherent interactions between chlorophylls absorbing on the low-energy side of LHCII, which is the region that is responsible for both light-harvesting and photoprotection. 2D beating frequency maps allow us to identify four frequencies with strong excitonic character. In particular, our results show the presence of a low-lying state that is coupled to a low-energy excitonic state. We assign this to a mixed excitonic-charge transfer state involving the state with charge separation within the Chl a603-b609 heterodimer, borrowing some dipole strength from the Chl a602-a603 excited states. Such a state may play a role in photoprotection, in conjunction with specific and environmentally controlled realizations of protein dynamic disorder. Our identification and assignment of the coherences observed in the 2D frequency maps suggests that the structure of exciton states as well as a mixing of the excited and charge-transfer states is affected by coupling of these states to resonant vibrations in LHCII.

Carbon dot–Au(i)Ag(0) assembly for the construction of an artificial light harvesting system

Significant transfer of energy from a carbon dot, GCD, to a fluorescent assembly, AuAgFA, paves the way to construct an artificial light harvesting system out of a GCD–AuAgFA pair.

How reduced excitonic coupling enhances light harvesting in the main photosynthetic antennae of diatoms

Strong excitonic interactions are a key design strategy in photosynthetic light harvesting, expanding the spectral cross-section for light absorption and creating considerably faster and more robust excitation energy transfer. These molecular excitons are a direct result of exceptionally densely packed pigments in photosynthetic proteins. The main light-harvesting complexes of diatoms, known as fucoxanthin-chlorophyll proteins (FCPs), are an exception, displaying surprisingly weak excitonic coupling between their chlorophyll (Chl) a's, despite a high pigment density. Here, we show, using single-molecule spectroscopy, that the FCP complexes of Cyclotella meneghiniana switch frequently into stable, strongly emissive states shifted 4-10 nm toward the red. A few percent of isolated FCPa complexes and ∼20% of isolated FCPb complexes, on average, were observed to populate these previously unobserved states, percentages that agree with the steady-state fluorescence spectra of FCP ensembles. Thus, the complexes use their enhanced sensitivity to static disorder to increase their light-harvesting capability in a number of ways. A disordered exciton model based on the structure of the main plant light-harvesting complex explains the red-shifted emission by strong localization of the excitation energy on a single Chl a pigment in the terminal emitter domain due to very specific pigment orientations. We suggest that the specific construction of FCP gives the complex a unique strategy to ensure that its light-harvesting function remains robust in the fluctuating protein environment despite limited excitonic interactions.

Apoprotein heterogeneity increases spectral disorder and a step-wise modification of the B850 fluorescence peak position

It has already been established that the quaternary structure of the main light-harvesting complex (LH2) from the photosynthetic bacterium Rhodopseudomonas palustris is a nonameric 'ring' of PucAB heterodimers and under low-light culturing conditions an increased diversity of PucB synthesis occurs. In this work, single molecule fluorescence emission studies show that different classes of LH2 'rings' are present in "low-light" adapted cells and that an unknown chaperon process creates multiple sub-types of 'rings' with more conformational sub-states and configurations. This increase in spectral disorder significantly augments the cross-section for photon absorption and subsequent energy flow to the reaction centre trap when photon availability is a limiting factor. This work highlights yet another variant used by phototrophs to gather energy for cellular development.

Quantum design of photosynthesis for bio-inspired solar-energy conversion

Photosynthesis is the natural process that converts solar photons into energy-rich products that are needed to drive the biochemistry of life. Two ultrafast processes form the basis of photosynthesis: excitation energy transfer and charge separation. Under optimal conditions, every photon that is absorbed is used by the photosynthetic organism. Fundamental quantum mechanics phenomena, including delocalization, underlie the speed, efficiency and directionality of the charge-separation process. At least four design principles are active in natural photosynthesis, and these can be applied practically to stimulate the development of bio-inspired, human-made energy conversion systems.