Coupling to Charge Transfer States is the Key to Modulate the Optical Bands for Efficient Light Harvesting in Purple Bacteria

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

PigmentHunter: A point-and-click application for automated chlorophyll-protein simulations

Chlorophyll proteins (CPs) are the workhorses of biological photosynthesis, working together to absorb solar energy, transfer it to chemically active reaction centers, and control the charge-separation process that drives its storage as chemical energy. Yet predicting CP optical and electronic properties remains a serious challenge, driven by the computational difficulty of treating large, electronically coupled molecular pigments embedded in a dynamically structured protein environment. To address this challenge, we introduce here an analysis tool called PigmentHunter, which automates the process of preparing CP structures for molecular dynamics (MD), running short MD simulations on the nanoHUB.org science gateway, and then using electrostatic and steric analysis routines to predict optical absorption, fluorescence, and circular dichroism spectra within a Frenkel exciton model. Inter-pigment couplings are evaluated using point-dipole or transition-charge coupling models, while site energies can be estimated using both electrostatic and ring-deformation approaches. The package is built in a Jupyter Notebook environment, with a point-and-click interface that can be used either to manually prepare individual structures or to batch-process many structures at once. We illustrate PigmentHunter's capabilities with example simulations on spectral line shapes in the light harvesting 2 complex, site energies in the Fenna-Matthews-Olson protein, and ring deformation in photosystems I and II.

High-Resolution Frequency-Domain Spectroscopic and Modeling Studies of Photosystem I (PSI), PSI Mutants and PSI Supercomplexes

Photosystem I (PSI) is one of the two main pigment-protein complexes where the primary steps of oxygenic photosynthesis take place. This review describes low-temperature frequency-domain experiments (absorption, emission, circular dichroism, resonant and non-resonant hole-burned spectra) and modeling efforts reported for PSI in recent years. In particular, we focus on the spectral hole-burning studies, which are not as common in photosynthesis research as the time-domain spectroscopies. Experimental and modeling data obtained for trimeric cyanobacterial Photosystem I (PSI3), PSI3 mutants, and PSI3-IsiA18 supercomplexes are analyzed to provide a more comprehensive understanding of their excitonic structure and excitation energy transfer (EET) processes. Detailed information on the excitonic structure of photosynthetic complexes is essential to determine the structure-function relationship. We will focus on the so-called "red antenna states" of cyanobacterial PSI, as these states play an important role in photochemical processes and EET pathways. The high-resolution data and modeling studies presented here provide additional information on the energetics of the lowest energy states and their chlorophyll (Chl) compositions, as well as the EET pathways and how they are altered by mutations. We present evidence that the low-energy traps observed in PSI are excitonically coupled states with significant charge-transfer (CT) character. The analysis presented for various optical spectra of PSI3 and PSI3-IsiA18 supercomplexes allowed us to make inferences about EET from the IsiA18 ring to the PSI3 core and demonstrate that the number of entry points varies between sample preparations studied by different groups. In our most recent samples, there most likely are three entry points for EET from the IsiA18 ring per the PSI core monomer, with two of these entry points likely being located next to each other. Therefore, there are nine entry points from the IsiA18 ring to the PSI3 trimer. We anticipate that the data discussed below will stimulate further research in this area, providing even more insight into the structure-based models of these important cyanobacterial photosystems.

Short-Range Effects in the Special Pair of Photosystem II Reaction Centers: The Nonconservative Nature of Circular Dichroism

Photosystem II reaction centers extract electrons from water, providing the basis of oxygenic life on earth. Among the light-sensitive pigments of the reaction center, a central chlorophyll a dimer, known as the special pair, so far has escaped a complete theoretical characterization of its excited state properties. The close proximity of the special pair pigments gives rise to short-range effects that comprise a coupling between local and charge transfer (CT) excited states as well as other intermolecular quantum effects. Using a multiscale simulation and a diabatization technique, we show that the coupling to CT states is responsible for 45% of the excitonic coupling in the special pair. The other short-range effects cause a nonconservative nature of the circular dichroism spectrum of the reaction center by effectively rotating the electric transition dipole moments of the special pair pigments inverting and strongly enhancing their intrinsic rotational strength.

Origin of Low-Lying Red States in the Lhca4 Light-Harvesting Complex of Photosystem I

The antenna complexes of Photosystem I present low-lying states visible as red-shifted and broadened absorption and fluorescence bands. Among these, Lhca4 has the most evident features of these "red" states, with a fluorescence band shifted by more than 25 nm from typical LHC emission. This signal arises from a mixing of exciton and charge-transfer (CT) states within the excitonically coupled a603-a609 chlorophyll (Chl) dimer. Here we combine molecular dynamics, multiscale quantum chemical calculations, and spectral simulations to uncover the molecular mechanism for the formation and tuning of exciton-CT interactions in Lhca4. We show that the coupling between exciton and CT states is extremely sensitive to tiny variations in the Chl dimer arrangement, explaining both the red-shifted bands and the switch between conformations with blue and red emission observed in single-molecule spectroscopy. Finally, we show that mutating the axial ligand of a603 diminishes the exciton-CT coupling, removing any red-state fingerprint.

Time-resolved circular dichroism of excitonic systems: theory and experiment on an exemplary squaraine polymer

Experimental and theoretical foundations for femtosecond time-resolved circular dichroism (TRCD) spectroscopy of excitonic systems are presented. In this method, the system is pumped with linearly polarized light and the signal is defined as the difference between the transient absorption spectrum probed with left and with right circularly polarized light. We present a new experimental setup with a polarization grating as key element to generate circularly polarized pulses. Herein the positive (negative) first order of the diffracted light is left-(right-)circularly polarized and serves as a probe pulse in a TRCD experiment. The grating is capable of transferring ultrashort broadband pulses ranging from 470 nm to 720 nm into two separate beams with opposite ellipticity. By applying a specific chopping scheme we can switch between left and right circular polarizations and detect transient absorption (TA) and TRCD spectra on a shot-to-shot basis simultaneously. We perform experiments on a squaraine polymer, investigating excitonic dynamics, and we develop a general theory for TRCD experiments of excitonically coupled systems that we then apply to describe the experimental data in this particular example. At a magic angle of 54.7° between the pump-pulse polarization and the propagation direction of the probe pulse, the TRCD and TA signals become particularly simple to analyze, since the orientational average over random orientations of complexes factorizes into that of the interaction with the pump and the probe pulse, and the intrinsic electric quadrupole contributions to the TRCD signal average to zero for isotropic samples. Application of exciton theory to linear absorption and to linear circular dichroism spectra of squaraine polymers reveals the presence of two fractions of polymer conformations, a dominant helical conformation with close interpigment distances that are suggested to lead to short-range contributions to site energy shifts and excitonic couplings of the squaraine molecules, and a fraction of unfolded random coils. Theory demonstrates that TRCD spectra of selectively excited helices can resolve state populations that are practically invisible in TA spectroscopy due to the small dipole strength of these states. A qualitative interpretation of TRCD and TA spectra in the spectral window investigated experimentally is offered. The 1 ps time component found in these spectra is related to the slow part of exciton relaxation obtained between states of the helix in the low-energy half of the exciton manifold. The dominant 140 ps time constant reflects the decay of excited states to the electronic ground state.

Understanding Primary Charge Separation in the Heliobacterial Reaction Center

The homodimeric reaction center of heliobacteria retains features of the ancestral reaction center and can thus provide insights into the evolution of photosynthesis. Primary charge separation is expected to proceed in a two-step mechanism along either of the two reaction center branches. We reveal the first charge-separation step from first-principles calculations based on time-dependent density functional theory with an optimally tuned range-separated hybrid and ab initio Born-Oppenheimer molecular dynamics: the electron is most likely localized on the electron transfer cofactor 3 (EC3, OH-chlorophyll a), and the hole on the adjacent EC2. Including substantial parts of the surrounding protein environment into the calculations shows that a distinct structural mechanism is decisive for the relative energetic positioning of the electronic excitations: specific charged amino acids in the vicinity of EC3 lower the energy of charge-transfer excitations and thus facilitate efficient charge separation. These results are discussed considering recent experimental insights.

Quantum chemical elucidation of a sevenfold symmetric bacterial antenna complex

The light-harvesting complex 2 (LH2) of purple bacteria is one of the most studied photosynthetic antenna complexes. Its symmetric structure and ring-like bacteriochlorophyll arrangement make it an ideal system for theoreticians and spectroscopists. LH2 complexes from most bacterial species are thought to have eightfold or ninefold symmetry, but recently a sevenfold symmetric LH2 structure from the bacterium Mch. purpuratum was solved by Cryo-Electron microscopy. This LH2 also possesses unique near-infrared absorption and circular dichroism (CD) spectral properties. Here we use an atomistic strategy to elucidate the spectral properties of Mch. purpuratum LH2 and understand the differences with the most commonly studied LH2 from Rbl. acidophilus. Our strategy exploits a combination of molecular dynamics simulations, multiscale polarizable quantum mechanics/molecular mechanics calculations, and lineshape simulations. Our calculations reveal that the spectral properties of LH2 complexes are tuned by site energies and exciton couplings, which in turn depend on the structural fluctuations of the bacteriochlorophylls. Our strategy proves effective in reproducing the absorption and CD spectra of the two LH2 complexes, and in uncovering the origin of their differences. This work proves that it is possible to obtain insight into the spectral tuning strategies of purple bacteria by quantitatively simulating the spectral properties of their antenna complexes.

Towards the description of charge transfer states in solubilised LHCII using subsystem DFT

Light harvesting complex II (LHCII) in plants and green algae have been shown to adapt their absorption properties, depending on the concentration of sunlight, switching between a light harvesting and a non-harvesting or quenched state. In a recent work, combining classical molecular dynamics (MD) simulations with quantum chemical calculations (Liguori et al. in Sci Rep 5:15661, 2015) on LHCII, it was shown that the Chl611-Chl612 cluster of the terminal emitter domain can play an important role in modifying the spectral properties of the complex. In that work the importance of charge transfer (CT) effects was highlighted, in re-shaping the absorption intensity of the chlorophyll dimer. Here in this work, we investigate the combined effect of the local excited (LE) and CT states in shaping the energy landscape of the chlorophyll dimer. Using subsystem Density Functional Theory over the classical [Formula: see text]s MD trajectory we look explicitly into the excitation energies of the LE and the CT states of the dimer and their corresponding couplings. Upon doing so, we observe a drop in the excitation energies of the CT states, accompanied by an increase in the couplings between the LE/LE and the LE/CT states facilitated by a shorter interchromophoric distance upon equilibration. Both these changes in conjunction, effectively produces a red-shift of the low-lying mixed exciton/CT states of the supramolecular chromophore pair.

Engineering excitonically coupled dimers in an artificial protein for light harvesting via computational modeling

In photosynthesis, pigment-protein complexes achieve outstanding photoinduced charge separation efficiencies through a set of strategies in which excited states delocalization over multiple pigments ("excitons") and charge-transfer states play key roles. These concepts, and their implementation in bioinspired artificial systems, are attracting increasing attention due to the vast potential that could be tapped by realizing efficient photochemical reactions. In particular, de novo designed proteins provide a diverse structural toolbox that can be used to manipulate the geometric and electronic properties of bound chromophore molecules. However, achieving excitonic and charge-transfer states requires closely spaced chromophores, a non-trivial aspect since a strong binding with the protein matrix needs to be maintained. Here, we show how a general-purpose artificial protein can be optimized via molecular dynamics simulations to improve its binding capacity of a chlorophyll derivative, achieving complexes in which chromophores form two closely spaced and strongly interacting dimers. Based on spectroscopy results and computational modeling, we demonstrate each dimer is excitonically coupled, and propose they display signatures of charge-transfer state mixing. This work could open new avenues for the rational design of chromophore-protein complexes with advanced functionalities.

Computing the electronic circular dichroism spectrum of DNA quadruple helices of different topology: A critical test for a generalized excitonic model based on a fragment diabatization

In this study, we exploit a recently developed fragment diabatization-based excitonic model, FrDEx, to simulate the electronic circular dichroism (ECD) spectra of three guanine-rich DNA sequences arranged in guanine quadruple helices with different topologies: thrombin binding aptamer (antiparallel), c-Myc promoter (parallel), and human telomeric sequence (3+1 hybrid). Starting from time-dependent density functional theory (TD-DFT) calculations with the M052X functional, we apply our protocol to parameterize the FrDEX Hamiltonian, which accounts for electron density overlap and includes both the coupling with charge transfer transitions and the effect of the surrounding bases on the local excitation of each chromophore. The TD-DFT/M052X spectral shapes are in good agreement with the experimental ones, the main source of discrepancy being related to the intrinsic error on the computed transition energies of guanine monomer. FrDEx spectra are fairly close to the reference TD-DFT ones, allowing a significant advance with respect to a more standard excitonic Hamiltonian. We also show that the ECD spectra are sensitive to the inclusion of the inner K + $$ {}^{+} $$ cation in the calculation.

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.

Phasor Analysis Reveals Multicomponent Fluorescence Kinetics in the LH2 Complex from Marichromatium purpuratum

We investigated the fluorescence kinetics of LH2 complexes from Marichromatium purpuratum, the cryo-EM structure of which has been recently elucidated with 2.4 Å resolution. The experiments have been carried out as a function of the excitation density by varying both the excitation fluence and the repetition rate of the laser excitation. Instead of the usual multiexponential fitting procedure, we applied the less common phasor formalism for evaluating the transients because this allows for a model-free analysis of the data without a priori knowledge about the number of processes that contribute to a particular decay. For the various excitation conditions, this analysis reproduces consistently three lifetime components with decay times below 100 ps, 500 ps, and 730 ps, which were associated with the quenched state, singlet-triplet annihilation, and fluorescence decay, respectively. Moreover, it reveals that the number of decay components that contribute to the transients depends on whether the excitation wavelength is in resonance with the B800 BChl a molecules or with the carotenoids. Based on the mutual arrangement of the chromophores in their binding pockets, this leads us to conclude that the energy transfer pathways within the LH2 complex of this species differ significantly from each other for exciting either the B800 BChl molecules or the carotenoids. Finally, we speculate whether the illumination with strong laser light converts the LH2 complexes studied here into a quenched conformation that might be related to the development of the non-photochemical quenching mechanism that occurs in higher plants.

Photoinduced chlorophyll charge transfer state identified in the light-harvesting complex II from a marine green alga Bryopsis corticulans

The light-harvesting complex II of Bryopsis corticulans (B-LHCII), a green alga, differs from that of spinach (S-LHCII) in chlorophyll (Chl) and carotenoid (Car) compositions. We investigated ultrafast excitation dynamics of B-LHCII with visible-to-near infrared time-resolved absorption spectroscopy. Absolute fluorescence quantum yield (Φ _FL) of LHCII and spectroelectrochemical (SEC) spectra of Chl a and b were measured to assist the spectral analysis. Red-light excitation at Chl Q_y-band, but not Car-band, induced transient features resembling the characteristic SEC spectra of Chl a ^⋅+ and Chl b ^⋅-, indicating ultrafast photogeneration of Chl-Chl charge transfer (CT) species; Φ _FL and ³Car^∗ declined whereas CT species increased upon prolonging excitation wavelength, showing positive correlation of ¹Chl^∗ deactivation with Chl-Chl CT formation. Moreover, ultrafast Chl b-to-Chl a and Car-to-Chl singlet excitation transfer were illustrated. The red-light induction of Chl-Chl CT species, as also observed for S-LHCII, is considered a general occurrence for LHCIIs in light-harvesting form.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag20 complex), we emphasize that caution is needed to properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

Optical Signatures of the Coupling between Excitons and Charge Transfer States in Linear Molecular Aggregates

Charge Transfer (CT) has enjoyed continuous interest due to increasing experimental control over molecular structure leading to applications in, for example, photovoltaics and hydrogen production. In this paper, we investigate the effect of CT states on the absorption spectrum of linear molecular aggregates using a scattering matrix technique that allows us to deal with arbitrarily large systems. The presented theory performs well for both strong and weak mixing of exciton and CT states, bridging the gap between previously employed methods which are applicable in only one of these limits. In experimental spectra the homogeneous linewidth is often too large to resolve all optically allowed transitions individually, resulting in a characteristic two-peak absorption spectrum in both the weak- and strong-coupling regime. Using the scattering matrix technique we examine the contributions of free and bound states in detail. We conclude that the skewness of the high-frequency peak may be used as a new way to identify the exciton-CT-state coupling strength.

The atomistic modeling of light-harvesting complexes from the physical models to the computational protocol

The function of light-harvesting complexes is determined by a complex network of dynamic interactions among all the different components: the aggregate of pigments, the protein, and the surrounding environment. Complete and reliable predictions on these types of composite systems can be only achieved with an atomistic description. In the last few decades, there have been important advances in the atomistic modeling of light-harvesting complexes. These advances have involved both the completeness of the physical models and the accuracy and effectiveness of the computational protocols. In this Perspective, we present an overview of the main theoretical and computational breakthroughs attained so far in the field, with particular focus on the important role played by the protein and its dynamics. We then discuss the open problems in their accurate modeling that still need to be addressed. To illustrate an effective computational workflow for the modeling of light harvesting complexes, we take as an example the plant antenna complex CP29 and its H111N mutant.

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.

Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes

Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.

Bridging Carotenoid-to-Bacteriochlorophyll Energy Transfer of Purple Bacteria LH2 With Temperature Variations: Insights From Conformational Changes

Photosynthesis is a key process for converting light energy into chemical energy and providing food for lives on Earth. Understanding the mechanism for the energy transfers could provide insights into regulating energy transfers in photosynthesis and designing artificial photosynthesis systems. Many efforts have been devoted to exploring the mechanism of temperature variations affecting the excitonic properties of LH2. In this study, we performed all-atom molecular dynamics (MD) simulations and quantum mechanics calculations for LH2 complex from purple bacteria along with its membrane environment under three typical temperatures: 270, 300, and 330 K. The structural analysis from validated MD simulations showed that the higher temperature impaired interactions at N-terminus of both α and β polypeptide helices and led to the dissociation of this hetero polypeptide dimer. Rhodopin-β-D-glucosides (RG1) moved centripetally with α polypeptide helices when temperature increased and enlarged their distances with bacteriochlorophylls molecules that have the absorption peak at 850 nm (B850), which resulted in reducing the coupling strengths between RG1 and B850 molecules. The present study reported a cascading mechanism for temperature regulating the energy transfers in LH2 of purple bacteria.

Spectral Tuning Mechanism of Photosynthetic Light-Harvesting Complex II Revealed by Ab Initio Dimer Exciton Model

Excited states of two kinds of bacteriochlorophyll (BChl) aggregates, B850 and B800, in photosynthetic light-harvesting complex II (LH2) are theoretically investigated by developing and using an extended exciton model considering efficiently evaluated excitonic coupling. Our exciton model based on dimer fragmentation is shown to reproduce the experimental absorption spectrum of LH2 with good accuracy, entailing their different redshifts originating from aggregations of B850 and B800. The systematic analysis has been performed on the spectra by quantitatively decomposing their spectral shift energies into the contributions of various effects: structural distortion, electrostatic, excitonic coupling, and charge-transfer (CT) effects. Our results show that the spectral redshift of B800 is mainly attributed to its electrostatic interaction with the protein environment, while that of B850 arises from the marked effect of the excitonic coupling between BChl units. The interchromophore CT excitation also plays a key role in the spectral redshift of B850. This CT effect can be effectively described using our dimer model. This suited characterization reveals that the pronounced CT effect originates from the characteristics of B850 that has closely spaced BChls as dimers. We highlight the importance of the refinement of the crystal structure with the use of quantum chemical methods for prediction of the spectrum.

Electronic Circular Dichroism Spectra of DNA Quadruple Helices Studied by Molecular Dynamics Simulations and Excitonic Calculations including Charge Transfer States

We here investigate the Electronic Circular Dichroism (ECD) Spectra of two representative Guanine-rich sequences folded in a Quadruple helix (GQ), by using a recently developed fragment diabatisation based excitonic model (FrDEx). FrDEx can include charge transfer (CT) excited states and consider the effect of the surrounding monomers on the local excitations (LEs). When applied to different structures generated by molecular dynamics simulations on a fragment of the human telomeric sequence (Tel21/22), FrDEx provides spectra fully consistent with the experimental one and in good agreement with that provided by quantum mechanical (QM) method used for its parametrization, i.e., TD-M05-2X. We show that the ECD spectrum is moderately sensitive to the conformation adopted by the bases of the loops and more significantly to the thermal fluctuations of the Guanine tetrads. In particular, we show how changes in the overlap of the tetrads modulate the intensity of the ECD signal. We illustrate how this correlates with changes in the character of the excitonic states at the bottom of the La and Lb bands, with larger LE and CT involvement of bases that are more closely stacked. As an additional test, we utilised FrDEx to compute the ECD spectrum of the monomeric and dimeric forms of a GQ forming sequence T30695 (5′TGGGTGGGTGGGTGGG3′), i.e., a system containing up to 24 Guanine bases, and demonstrated the satisfactory reproduction of the experimental and QM reference results. This study provides new insights on the effects modulating the ECD spectra of GQs and, more generally, further validates FrDEx as an effective tool to predict and assign the spectra of closely stacked multichromophore systems.

Understanding the Relation between Structural and Spectral Properties of Light-Harvesting Complex II

Light-harvesting complex II (LHCII) is a pigment-protein complex present in higher plants and green algae. LHCII represents the main site of light absorption, and its role is to transfer the excitation energy toward the photosynthetic reaction centers, where primary energy conversion reactions take place. The optical properties of LHCII are known to depend on protein conformation. However, the relation between the structural and spectroscopic properties of the pigments is not fully understood yet. In this respect, previous classical molecular dynamics simulations of LHCII in a model membrane [Sci. Rep. 2015, 5, 1-10] have shown that the configuration and excitonic coupling of a chlorophyll (Chl) dimer functioning as the main terminal emitter of the complex are particularly sensitive to conformational changes. Here, we use quantum chemistry calculations to investigate in greater detail the effect of pigment-pigment interactions on the excited-state landscape. While most previous studies have used a local picture in which electrons are localized on single pigments, here we achieve a more accurate description of the Chl dimer by adopting a supramolecular picture where time-dependent density functional theory is applied to the whole system at once. Our results show that specific dimer configurations characterized by shorter inter-pigment distances can result in a sizable intensity decrease (up to 36%) of the Chl absorption bands in the visible spectral region. Such a decrease can be predicted only when accounting for Chl-Chl charge-transfer excitations, which is possible using the above-mentioned supramolecular approach. The charge-transfer character of the excitations is quantified by two types of analyses: one focusing on the composition of the excitations and the other directly on the observable total absorption intensities.

The origin of unidirectional charge separation in photosynthetic reaction centers: nonadiabatic quantum dynamics of exciton and charge in pigment-protein complexes

Exciton charge separation in photosynthetic reaction centers from purple bacteria (PbRC) and photosystem II (PSII) occurs exclusively along one of the two pseudo-symmetric branches (active branch) of pigment-protein complexes. The microscopic origin of unidirectional charge separation in photosynthesis remains controversial. Here we elucidate the essential factors leading to unidirectional charge separation in PbRC and PSII, using nonadiabatic quantum dynamics calculations in conjunction with time-dependent density functional theory (TDDFT) with the quantum mechanics/molecular mechanics/polarizable continuum model (QM/MM/PCM) method. This approach accounts for energetics, electronic coupling, and vibronic coupling of the pigment excited states under electrostatic interactions and polarization of whole protein environments. The calculated time constants of charge separation along the active branches of PbRC and PSII are similar to those observed in time-resolved spectroscopic experiments. In PbRC, Tyr-M210 near the accessary bacteriochlorophyll reduces the energy of the intermediate state and drastically accelerates charge separation overcoming the electron-hole interaction. Remarkably, even though both the active and inactive branches in PSII can accept excitons from light-harvesting complexes, charge separation in the inactive branch is prevented by a weak electronic coupling due to symmetry-breaking of the chlorophyll configurations. The exciton in the inactive branch in PSII can be transferred to the active branch via direct and indirect pathways. Subsequently, the ultrafast electron transfer to pheophytin in the active branch prevents exciton back transfer to the inactive branch, thereby achieving unidirectional charge separation.

Spectral tuning of chlorophylls in proteins - electrostatics vs. ring deformation

In photosynthetic complexes, tuning of chlorophyll light-absorption spectra by the protein environment is crucial to their efficiency and robustness. Recombinant type II water soluble chlorophyll-binding proteins from Brassicaceae (WSCPs) are useful for studying spectral tuning mechanisms due to their symmetric homotetramer structure, and the ability to rigorously modify the chlorophyll's protein surroundings. Our previous comparison of the crystal structures of two WSCP homologues suggested that protein-induced chlorophyll ring deformation is the predominant spectral tuning mechanism. Here, we implement a more rigorous analysis based on hybrid quantum mechanics and molecular mechanics calculations to quantify the relative contributions of geometrical and electrostatic factors to the absorption spectra of WSCP-chlorophyll complexes. We show that when considering conformational dynamics, geometry distortions such as chlorophyll ring deformation accounts for about one-third of the spectral shift, whereas the direct polarization of the electron density accounts for the remaining two-thirds. From a practical perspective, protein electrostatics is easier to manipulate than chlorophyll conformations, thus, it may be more readily implemented in designing artificial protein-chlorophyll complexes.

Exploring the Spatial Features of Electronic Transitions in Molecular and Biomolecular Systems by Swift Electrons

We devise a new kind of experiment that extends the technology of electron energy loss spectroscopy to probe (supra-)molecular systems: by using an electron beam in a configuration that avoids molecular damage and a very recently introduced electron optics setup for the analysis of the outcoming electrons, one can obtain information on the spatial features of the investigated excitations. Physical insight into the proposed experiment is provided by means of a simple but rigorous model to obtain the transition rate and selection rule. Numerical simulations of DNA G-quadruplexes and other biomolecular systems, based on time dependent density functional theory calculations, point out that the conceived new technique can probe the multipolar components and even the chirality of molecular transitions, superseding the usual optical spectroscopies for those cases that are problematic, such as dipole-forbidden transitions, at a very high spatial resolution.

Excitonic Model for Strongly Coupled Multichromophoric Systems: The Electronic Circular Dichroism Spectra of Guanine Quadruplexes as Test Cases

We here propose a general and flexible approach, based on fragment diabatization, which incorporates charge transfer states and significantly increases the reliability of excitonic Hamiltonians for systems where the chromophores are very close. This model (FrDEx) is used to compute the electronic circular dichroism and absorption spectra of two prototype guanine-rich DNA sequences folded in quadruple helices (GQs), i.e., a fragment of the human telomeric sequence (Tel21, antiparallel), and (TGGGGT)₄ (TG4T, parallel). Calculations on different subsets of Tel21 and TG4T, from dimers to tetramers, show that FrDEx provides spectra close to the reference full quantum mechanical (QM) ones (obtained with time-dependent density functional theory), with significant improvements with respect to "standard" excitonic Hamiltonians. Furthermore, these tests enable the most cost-effective procedure for the whole GQ to be determined. FrDEx spectra of Tel21 and TG4T are also in good agreement with the QM and experimental ones and give access to interesting insights into the chemical-physical effects modulating the spectral signals. FrDEx could be profitably used to investigate many other biological and nanotechnological materials, from DNA to (opto)electronic polymers.

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.

Hybrid theoretical models for molecular nanoplasmonics

The multidisciplinary nature of the research in molecular nanoplasmonics, i.e., the use of plasmonic nanostructures to enhance, control, or suppress properties of molecules interacting with light, led to contributions from different theory communities over the years, with the aim of understanding, interpreting, and predicting the physical and chemical phenomena occurring at molecular- and nano-scale in the presence of light. Multiscale hybrid techniques, using a different level of description for the molecule and the plasmonic nanosystems, permit a reliable representation of the atomistic details and of collective features, such as plasmons, in such complex systems. Here, we focus on a selected set of topics of current interest in molecular plasmonics (control of electronic excitations in light-harvesting systems, polaritonic chemistry, hot-carrier generation, and plasmon-enhanced catalysis). We discuss how their description may benefit from a hybrid modeling approach and what are the main challenges for the application of such models. In doing so, we also provide an introduction to such models and to the selected topics, as well as general discussions on their theoretical descriptions.

Electronic couplings for photo-induced processes from subsystem time-dependent density-functional theory: The role of the diabatization

Subsystem time-dependent density-functional theory (sTDDFT) making use of approximate non-additive kinetic energy (NAKE) functionals is known to be capable of describing excitation energy transfer processes in a variety of applications. Here, we show that sTDDFT, especially when combined with projection-based embedding (PbE), can be employed for the entire range of photo-induced electronic couplings essential for modeling photophysical properties of complex chemical and biological systems and therefore represents a complete toolbox for this class of problems. This means that it is capable of capturing the interaction/coupling associated with local- and charge-transfer (CT) excitons. However, this requires the choice of a reasonable diabatic basis. We therefore propose different diabatization strategies of the virtual orbital space in PbE-sTDDFT and show how CT excitations can be included in sTDDFT using NAKE functionals via a phenomenological approach. Finally, these electronic couplings are compared to couplings from a multistate fragment excitation difference (FED)-fragment charge difference (FCD) diabatization procedure. We show that both procedures, multistate FED-FCD and sTDDFT (with the right diabatization procedure chosen), lead to an overall good agreement for the electronic couplings, despite differences in their general diabatization strategy. We conclude that the entire range of photo-induced electronic couplings can be obtained using sTDDFT (with the right diabatization procedure chosen) in a black-box manner.

Two-dimensional electronic Stark spectroscopy of a photosynthetic dimer

Stark spectroscopy, which measures changes in the linear absorption of a sample in the presence of an external DC electric field, is a powerful experimental tool for probing the existence of charge-transfer (CT) states in photosynthetic systems. CT states often have small transition dipole moments, making them insensitive to other spectroscopic methods, but are particularly sensitive to Stark spectroscopy due to their large permanent dipole moment. In a previous study, we demonstrated a new experimental method, two-dimensional electronic Stark spectroscopy (2DESS), which combines two-dimensional electronic spectroscopy (2DES) and Stark spectroscopy. In order to understand how the presence of CT states manifest in 2DESS, here, we perform computational modeling and calculations of 2DESS as well as 2DES and Stark spectra, studying a photosynthetic dimer inspired by the photosystem II reaction center. We identify specific cases where qualitatively different sets of system parameters produce similar Stark and 2DES spectra but significantly different 2DESS spectra, showing the potential for 2DESS to aid in identifying CT states and their coupling to excitonic states.

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

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

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.

Comparison of the Energy-Transfer Rates in Structural and Spectral Variants of the B800-850 Complex from Purple Bacteria

Photosynthetic light harvesting can occur with a remarkable near-unity quantum efficiency. The B800-850 complex, also known as light-harvesting complex 2 (LH2), is the primary light-harvesting complex in purple bacteria and has been extensively studied as a model system. The bacteriochlorophylls of the B800-850 complex are organized into two concentric rings, known as the B800 and B850 rings. However, depending on the species and growth conditions, the number of constituent subunits, the pigment geometry, and the absorption energies vary. While the dynamics of some B800-850 variants have been exhaustively characterized, others have not been measured. Furthermore, a direct and simultaneous comparison of how both structural and spectral differences between variants affect these dynamics has not been performed. In this work, we utilize ultrafast transient absorption measurements to compare the B800 to B850 energy-transfer rates in the B800-850 complex as a function of the number of subunits, geometry, and absorption energies. The nonameric B800-850 complex from Rhodobacter (Rb.) sphaeroides is 40% faster than the octameric B800-850 complex from Rhodospirillum (Rs.) molischianum, consistent with structure-based predictions. In contrast, the blue-shifted B800-820 complex from Rs. molischianum is only 20% faster than the B800-850 complex from Rs. molischianum despite an increase in the spectral overlap between the rings that would be expected to produce a larger increase in the energy-transfer rate. These measurements support current models that contain dark, higher-lying excitonic states to bridge the energy gap between rings, thereby maintaining similar energy-transfer dynamics. Overall, these results demonstrate that energy-transfer dynamics in the B800-850 complex are robust to the spectral and structural variations between species used to optimize energy capture and flow in purple bacteria.

Charge transfer from the carotenoid can quench chlorophyll excitation in antenna complexes of plants

The photosynthetic apparatus of higher plants can dissipate excess excitation energy during high light exposure, by deactivating excited chlorophylls through a mechanism called nonphotochemical quenching (NPQ). However, the precise molecular details of quenching and the mechanism regulating the quenching level are still not completely understood. Focusing on the major light-harvesting complex LHCII of Photosystem II, we show that a charge transfer state involving Lutein can efficiently quench chlorophyll excitation, and reduce the excitation lifetime of LHCII to the levels measured in the deeply quenched LHCII aggregates. Through a combination of molecular dynamics simulations, multiscale quantum chemical calculations, and kinetic modeling, we demonstrate that the quenching level can be finely tuned by the protein, by regulating the energy of the charge transfer state. Our results suggest that a limited conformational rearrangement of the protein scaffold could act as a molecular switch to activate or deactivate the quenching mechanism.

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.

The molecular mechanisms of light adaption in light-harvesting complexes of purple bacteria revealed by a multiscale modeling

The light-harvesting in photosynthetic purple bacteria can be tuned in response to the light conditions during cell growth. One of the used strategies is to change the energy of the excitons in the major fight-harvesting complex, commonly known as LH2. In the present study we report the first systematic investigation of the microscopic origin of the exciton tuning using three complexes, namely the common (high-light) and the low-light forms of LH2 from Rps. acidophila plus a third complex analogous to the PucD complex from Rps. palustris. The study is based on the combination of classical molecular dynamics of each complex in a lipid membrane and excitonic calculations based on a multiscale quantum mechanics/molecular mechanics approach including a polarizable embedding. From the comparative analysis, it comes out that the mechanisms that govern the adaptation of the complex to different light conditions use the different H-bonding environment around the bacteriochlorophyll pigments to dynamically control both internal and inter-pigment degrees of freedom. While the former have a large effect on the site energies, the latter significantly change the electronic couplings, but only the combination of the two effects can fully reproduce the tuning of the final excitons and explain the observed spectroscopic differences.

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.