Understanding photosynthetic light-harvesting: a bottom up theoretical approach

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.

Structure-Based Theory of Fluctuation-Induced Energy Transfer in a Molecular Dyad

We present a microscopic theory for the description of fluctuation-induced excitation energy transfer in chromophore dimers to explain experimental data on a perylene biscarboximide dyad with orthogonal transition dipole moments. Our non-Condon extension of Förster theory takes into account the fluctuations of excitonic couplings linear and quadratic in the normal coordinates, treated microscopically by quantum chemical/electrostatic calculations. The modulation of the optical transition energies of the chromophores is inferred from optical spectra of the isolated chromophores. The application of the theory to the considered dyad reveals a two to three order of magnitude increase in the rate constant by non-Condon effects. These effects are found to be dominated by fluctuations linear in the normal coordinates and provide a structure-based qualitative interpretation of the experimental time constant for energy transfer as well as its dependence on temperature.

Wavelength-Dependent Exciton-Vibrational Coupling in the Water-Soluble Chlorophyll Binding Protein Revealed by Multilevel Theory of Difference Fluorescence Line-Narrowing

One of the most powerful line-narrowing techniques used to unravel the homogeneous lineshapes of inhomogeneously broadened systems is difference fluorescence line-narrowing spectroscopy. When this spectroscopy was applied to multichromophoric systems so far, the spectra were analyzed by an effective two-level system approach, composed of the electronic ground state and the lowest exciton state. An effective Huang-Rhys factor was assigned for the coupling of this state to the vibrations. Here, we extend this approach by including a multilevel line shape theory, which takes into account the excitonic coupling between pigments and thereby the effect of the delocalization of the excited states explicitly. In this way, it becomes possible to extract the spectral density of the local exciton-vibrational coupling. The theory is applied to the recombinant water-soluble chlorophyll binding protein reconstituted with chlorophyll a or b and reveals a significant decrease of the Huang-Rhys factor of the local exciton-vibrational coupling with decreasing transition energy of the chlorophylls. This decrease could be due to the increase in steric interactions reducing the flexibility of the environment and red-shifting the site energy of the pigments.

Simulation of Femtosecond Phase-Locked Double-Pump Signals of Individual Light-Harvesting Complexes LH2

Recent phase-locked femtosecond double-pump experiments on individual light-harvesting complexes LH2 of purple bacteria at ambient temperature revealed undamped oscillatory responses on a time scale of at least 400 fs [ Hildner et al. Science 2013 , 340 , 1448 ]. Using an excitonic Hamiltonian for LH2 available in the literature, we simulate these signals numerically by a method that treats excitonic couplings and exciton-phonon couplings in a nonperturbative manner. The simulations provide novel insights into the origin of coherent dynamics in individual LH2 complexes.

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

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

Theory of Anisotropic Circular Dichroism of Excitonically Coupled Systems: Application to the Baseplate of Green Sulfur Bacteria

A simple exciton theory for the description of anisotropic circular dichroism (ACD) spectra of multichromophoric systems is presented that is expected to be of general use for the analysis of structure-function relationships of molecular aggregates such as photosynthetic light-harvesting antennae. The theory is applied to the baseplate of green sulfur bacteria. It is demonstrated that only the combined analysis of ACD and circular dichroism (CD) spectra for the present baseplate bacteriochlorophyll (BChl) a dimer allows for an unambiguous determination of the parameters of the exciton Hamiltonian from experimental data. The analysis of experimental absorption and linear dichroism spectra suggests that either the NMR structure has to be refined or in addition to the dimers seen in the NMR structure and in the CD and ACD spectra, BChl a monomers are present in the baseplate carotenosome sample. A refined dimer structure is presented, explaining all four optical spectra.

Robust light harvesting by a noisy antenna

Photosynthetic light harvesting can be very efficient in solar energy conversion while taking place in a highly disordered and noisy physiological environment. This efficiency is achieved by the ultrafast speed of the primary photosynthetic processes, which is enabled by a delicate interplay of quantum effects, thermodynamics and environmental noise. The primary processes take place in light-harvesting antennas built from pigments bound to a fluctuating protein scaffold. Here, we employ ultrafast single-molecule spectroscopy to follow fluctuations of the femtosecond energy transfer times in individual LH2 antenna complexes of purple bacteria. By combining single molecule results with ensemble spectroscopy through a unified theoretical description of both, we show how the protein fluctuations alter the excitation energy transfer dynamics. We find that from the thirteen orders of magnitude of possible timescales from picoseconds to minutes, the relevant fluctuations occur predominantly on a biological timescale of seconds, i.e. in the domain of slow protein motion. The measured spectra and dynamics can be explained by the protein modulating pigment excitation energies only. Moreover, we find that the small spread of pigment mean energies allows for excitation delocalization between the coupled pigments to survive. These unique features provide fast energy transport even in the presence of disorder. We conclude that this is the mechanism that enables LH2 to operate as a robust light-harvester, in spite of its intrinsically noisy biological environment.

Exciton states and optical properties of the CP26 photosynthetic protein

The photosynthetic complex CP26, one of the minor antennae of the photosystem II, plays an important role in regulation of the excitation energy transfer in the PSII. Due to instability during isolation and purification, it remained poorly studied from the viewpoint of theoretical chemistry because of the absence of X-ray crystallography data. In this work, using the recently determined three-dimensional structure of the complex we apply the quantum chemical approach to study the properties of exciton states in it. Spectral properties, structure of exciton states and roles of the pigments in the complex and photosystem II are discussed.

Fine control of chlorophyll-carotenoid interactions defines the functionality of light-harvesting proteins in plants

Photosynthetic antenna proteins can be thought of as "programmed solvents", which bind pigments at specific mutual orientations, thus tuning the overall energetic landscape and ensuring highly efficient light-harvesting. While positioning of chlorophyll cofactors is well understood and rationalized by the principle of an "energy funnel", the carotenoids still pose many open questions. Particularly, their short excited state lifetime (<25 ps) renders them potential energy sinks able to compete with the reaction centers and drastically undermine light-harvesting efficiency. Exploration of the orientational phase-space revealed that the placement of central carotenoids minimizes their interaction with the nearest chlorophylls in the plant antenna complexes LHCII, CP26, CP29 and LHCI. At the same time we show that this interaction is highly sensitive to structural perturbations, which has a profound effect on the overall lifetime of the complex. This links the protein dynamics to the light-harvesting regulation in plants by the carotenoids.

Evidence of Correlated Static Disorder in the Fenna-Matthews-Olson Complex

Observation of excitonic quantum beats in photosynthetic antennae has prompted wide debate regarding the function of excitonic coherence in pigment-protein complexes. Much of this work focuses on the interactions of excitons with the femto-to-picosecond dynamical fluctuations of their environment. However, in experiments these effects can be masked by static disorder of the excited-state energies across ensembles, whose microscopic origins are challenging to predict. Here the excited-state properties of ∼2000 atom clusters of the Fenna-Matthews-Olson complex are simulated using a unique combination of linear-scaling density functional theory and constrained geometric dynamics. While slow, large amplitude protein motion leads to large variations in the Q_y transitions of two pigments, we identify pigment-protein correlations that greatly reduce variations in the energy gap across the ensemble, which is consistent with experimental observations of suppressed inhomogeneous dephasing of quantum beats.

Surface charge dynamics in photosynthetic membranes and the structural consequences

The strict stacking of plant photosynthetic membranes into granal structures plays a vital role in energy conversion. The molecular forces that lead to grana stacking, however, are poorly understood. Here we evaluate the interplay between repulsive electrostatic (F_el) and attractive van der Waals (F_vdWaals) forces in grana stacking. In contrast to previous reports, we find that the physicochemical balance between attractive and repulsive forces fully explains grana stacking. Extending the force balance analysis to lateral interactions within the oxygen-evolving photosystem II (PSII)-light harvesting complex II (LHCII) supercomplex reveals that supercomplex stability is very sensitive to F_el changes. F_el is highly dynamic, increasing up to 1.7-fold on addition of negative charges by phosphorylation of grana-hosted proteins. We show that this leads to specific destabilization of the supercomplex, and that changes in F_el have contrasting effects on vertical stacking and lateral intramembrane organization. This enables discrete biological control of these central structural features.

Electrostatic Asymmetry in the Reaction Center of Photosystem II

The exciton Hamiltonian of the chlorophyll (Chl) and pheophytin (Pheo) pigments in the reaction center (RC) of photosystem II is computed based on recent crystal structures by using the Poisson-Boltzmann/quantum-chemical method. Computed site energies largely confirm a previous model inferred from fits of optical spectra, in which Chl_D1 has the lowest site energy, while that of Pheo_D1 is higher than that of Pheo_D2. The latter assignment has been challenged recently under reference to mutagenesis experiments. We argue that these data are not in contradiction to our results. We conclude that Chl_D1 is the primary electron donor in both isolated RCs and intact core complexes at least at cryogenic temperatures. The main source of asymmetry in site energies is the charge distribution in the protein. Because many small contributions from various structural elements have to be taken into account, it can be assumed that this asymmetry was established in evolution by global optimization of the RC protein.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Atomistic non-adiabatic dynamics of the LH2 complex with a GPU-accelerated ab initio exciton model

We present GPU-accelerated ab initio molecular dynamics simulations of nonadiabatic dynamics in the LH2 complex in full atomistic detail.

Origin of non-conservative circular dichroism of the CP29 antenna complex of photosystem II

Structure-based explanation of the non-conservative circular dichroism spectrum of the photosynthetic antenna complex CP29 of photosystem II.

Coulomb couplings in solubilised light harvesting complex II (LHCII): challenging the ideal dipole approximation from TDDFT calculations

We investigate the coulomb coupling interactions of natural chromophores in the solubilised light harvesting complex II (LHCII) using DFT quantum chemistry calculations.

Ultrafast infrared observation of exciton equilibration from oriented single crystals of photosystem II

In oxygenic photosynthesis, two photosystems work in series. Each of them contains a reaction centre that is surrounded by light-harvesting antennae, which absorb the light and transfer the excitation energy to the reaction centre where electron transfer reactions are driven. Here we report a critical test for two contrasting models of light harvesting by photosystem II cores, known as the trap-limited and the transfer-to-the trap-limited model. Oriented single crystals of photosystem II core complexes of Synechococcus elongatus are excited by polarized visible light and the transient absorption is probed with polarized light in the infrared. The dichroic amplitudes resulting from photoselection are maintained on the 60 ps timescale that corresponds to the dominant energy transfer process providing compelling evidence for the transfer-to-the-trap limitation of the overall light-harvesting process. This finding has functional implications for the quenching of excited states allowing plants to survive under high light intensities.

Constructing an Interpolated Potential Energy Surface of a Large Molecule: A Case Study with Bacteriochlorophyll a Model in the Fenna-Matthews-Olson Complex

Constructing a reliable potential energy surface (PES) is a key step toward computationally studying the chemical dynamics of any molecular system. The interpolation scheme is a useful tool that can closely follow the accuracy of quantum chemical means at a dramatically reduced computational cost. However, applying interpolation to building a PES of a large molecule is not a straightforward black-box approach, as it frequently encounters practical difficulties associated with its large dimensionality. Here, we present detailed courses of applying interpolation toward building a PES of a large chromophore molecule. We take the example of S₀ and S₁ electronic states of bacteriochlorophyll a (BChla) molecules in the Fenna-Matthews-Olson light harvesting complex. With a reduced model molecule that bears BChla's main π-conjugated ring, various practical approaches are designed for improving the PES quality in a stable manner and for fine-tuning the final surface such that the surface can be adopted for long time molecular dynamics simulations. Combined with parallel implementation, we show that interpolated mechanics/molecular mechanics (IM/MM) simulations of the entire complex in the nanosecond time scale can be conducted readily without any practical issues. With 1500 interpolation data points for each chromophore unit, the PES error relative to the reference quantum chemical calculation is found to be ∼0.15 eV in the thermally accessible region of the conformational space, together with ∼0.01 eV error in S₀ - S₁ transition energies. The performance issue related to the use of a large interpolation database within the framework of our parallel routines is also discussed.

Applications of large-scale density functional theory in biology

Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.

Structure Prediction of Self-Assembled Dye Aggregates from Cryogenic Transmission Electron Microscopy, Molecular Mechanics, and Theory of Optical Spectra

Cryogenic transmission electron microscopy (cryo-TEM) studies suggest that TTBC molecules self-assemble in aqueous solution to form single-walled tubes with a diameter of about 35 Å. In order to reveal the arrangement and mutual orientations of the individual molecules in the tube, we combine information from crystal structure data of this dye with a calculation of linear absorbance and linear dichroism spectra and molecular dynamics simulations. We start with wrapping crystal planes in different directions to obtain tubes of suitable diameter. This set of tube models is evaluated by comparing the resulting optical spectra with experimental data. The tubes that can explain the spectra are investigated further by molecular dynamics simulations, including explicit solvent molecules. From the trajectories of the most stable tube models, the short-range ordering of the dye molecules is extracted and the optimization of the structure is iteratively completed. The final structural model is a tube of rings with 6-fold rotational symmetry, where neighboring rings are rotated by 30° and the transition dipole moments of the chromophores form an angle of 74° with respect to the symmetry axis of the tube. This model is in agreement with cryo-TEM images and can explain the optical spectra, consisting of a sharp red-shifted J-band that is polarized parallel to to the symmetry axis of the tube and a broad blue-shifted H-band polarized perpendicular to this axis. The general structure of the homogeneous spectrum of this hybrid HJ-aggregate is described by an analytical model that explains the difference in redistribution of oscillator strength inside the vibrational manifolds of the J- and H-bands and the relative intensities and excitation energies of those bands. In addition to the particular system investigated here, the present methodology can be expected to aid the structure prediction for a wide range of self-assembled dye aggregates.

Light Absorption and Energy Transfer in the Antenna Complexes of Photosynthetic Organisms

The process of photosynthesis is initiated by the capture of sunlight by a network of light-absorbing molecules (chromophores), which are also responsible for the subsequent funneling of the excitation energy to the reaction centers. Through evolution, genetic drift, and speciation, photosynthetic organisms have discovered many solutions for light harvesting. In this review, we describe the underlying photophysical principles by which this energy is absorbed, as well as the mechanisms of electronic excitation energy transfer (EET). First, optical properties of the individual pigment chromophores present in light-harvesting antenna complexes are introduced, and then we examine the collective behavior of pigment-pigment and pigment-protein interactions. The description of energy transfer, in particular multichromophoric antenna structures, is shown to vary depending on the spatial and energetic landscape, which dictates the relative coupling strength between constituent pigment molecules. In the latter half of the article, we focus on the light-harvesting complexes of purple bacteria as a model to illustrate the present understanding of the synergetic effects leading to EET optimization of light-harvesting antenna systems while exploring the structure and function of the integral chromophores. We end this review with a brief overview of the energy-transfer dynamics and pathways in the light-harvesting antennas of various photosynthetic organisms.

Challenges facing an understanding of the nature of low-energy excited states in photosynthesis

While the majority of the photochemical states and pathways related to the biological capture of solar energy are now well understood and provide paradigms for artificial device design, additional low-energy states have been discovered in many systems with obscure origins and significance. However, as low-energy states are naively expected to be critical to function, these observations pose important challenges. A review of known properties of low energy states covering eight photochemical systems, and options for their interpretation, are presented. A concerted experimental and theoretical research strategy is suggested and outlined, this being aimed at providing a fully comprehensive understanding.

The lowest-energy chlorophyll of photosystem II is adjacent to the peripheral antenna: Emitting states of CP47 assigned via circularly polarized luminescence

The identification of low-energy chlorophyll pigments in photosystem II (PSII) is critical to our understanding of the kinetics and mechanism of this important enzyme. We report parallel circular dichroism (CD) and circularly polarized luminescence (CPL) measurements at liquid helium temperatures of the proximal antenna protein CP47. This assembly hosts the lowest-energy chlorophylls in PSII, responsible for the well-known "F695" fluorescence band of thylakoids and PSII core complexes. Our new spectra enable a clear identification of the lowest-energy exciton state of CP47. This state exhibits a small but measurable excitonic delocalization, as predicated by its CD and CPL. Using structure-based simulations incorporating the new spectra, we propose a revised set of site energies for the 16 chlorophylls of CP47. The significant difference from previous analyses is that the lowest-energy pigment is assigned as Chl 612 (alternately numbered Chl 11). The new assignment is readily reconciled with the large number of experimental observations in the literature, while the most common previous assignment for the lowest energy pigment, Chl 627(29), is shown to be inconsistent with CD and CPL results. Chl 612(11) is near the peripheral light-harvesting system in higher plants, in a lumen-exposed region of the thylakoid membrane. The low-energy pigment is also near a recently proposed binding site of the PsbS protein. This result consequently has significant implications for our understanding of the kinetics and regulation of energy transfer in PSII.

Fine Tuning of Chlorophyll Spectra by Protein-Induced Ring Deformation

The ability to tune the light-absorption properties of chlorophylls by their protein environment is the key to the robustness and high efficiency of photosynthetic light-harvesting proteins. Unfortunately, the intricacy of the natural complexes makes it very difficult to identify and isolate specific protein-pigment interactions that underlie the spectral-tuning mechanisms. Herein we identify and demonstrate the tuning mechanism of chlorophyll spectra in type II water-soluble chlorophyll binding proteins from Brassicaceae (WSCPs). By comparing the molecular structures of two natural WSCPs we correlate a shift in the chlorophyll red absorption band with deformation of its tetrapyrrole macrocycle that is induced by changing the position of a nearby tryptophan residue. We show by a set of reciprocal point mutations that this change accounts for up to 2/3 of the observed spectral shift between the two natural variants.

Distinguishing the roles of energy funnelling and delocalization in photosynthetic light harvesting

Photosynthetic complexes improve the transfer of excitation energy from peripheral antennas to reaction centers in several ways. In particular, a downward energy funnel can direct excitons in the right direction, while coherent excitonic delocalization can enhance transfer rates through the cooperative phenomenon of supertransfer. However, isolating the role of purely coherent effects is difficult because any change to the delocalization also changes the energy landscape. Here, we show that the relative importance of the two processes can be determined by comparing the natural light-harvesting apparatus with counterfactual models in which the delocalization and the energy landscape are altered. Applied to the example of purple bacteria, our approach shows that although supertransfer does enhance the rates somewhat, the energetic funnelling plays the decisive role. Because delocalization has a minor role (and is sometimes detrimental), it is most likely not adaptive, being a side-effect of the dense chlorophyll packing that evolved to increase light absorption per reaction center.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Hole-Burning Spectroscopy on Excitonically Coupled Pigments in Proteins: Theory Meets Experiment

A theory for the calculation of resonant and nonresonant hole-burning (HB) spectra of pigment–protein complexes is presented and applied to the water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The theory is based on a non-Markovian line shape theory (Renger and MarcusJ. Chem. Phys.2002, 116, 9997) and includes exciton delocalization, vibrational sidebands, and lifetime broadening. An earlier approach by Reppert (J. Phys. Chem. Lett.2011, 2, 2716) is found to describe nonresonant HB spectra only. Here we present a theory that can be used for a quantitative description of HB data for both nonresonant and resonant burning conditions. We find that it is important to take into account the excess energy of the excitation in the HB process. Whereas excitation of the zero-phonon transition of the lowest exciton state, that is, resonant burning allows the protein to access only its conformational substates in the neighborhood of the preburn state, any higher excitation gives the protein full access to all conformations present in the original inhomogeneous ensemble. Application of the theory to recombinant WSCP from cauliflower, reconstituted with chlorophyll a or chlorophyll b, gives excellent agreement with experimental data by Pieper et al. (J. Phys. Chem. B2011, 115, 405321417356) and allows us to obtain an upper bound of the lifetime of the upper exciton state directly from the HB experiments in agreement with lifetimes measured recently in time domain 2D experiments by Alster et al. (J. Phys. Chem. B2014, 118, 352424627983).

Towards an ab initio description of the optical spectra of light-harvesting antennae: application to the CP29 complex of photosystem II

Light-harvesting pigment-protein complexes (PPC) represent the fundamental units through which the photosynthetic organisms absorb sunlight and funnel the energy to the reaction centre for carrying out the primary energy conversion reactions of photosynthesis. Here we apply a multiscale computational strategy to a specific PPC present in the photosystem II of plants and algae (CP29) to investigate in what detail should the environment effects due to protein and membrane/solvent be included for an accurate description of optical spectra. We find that a refinement of the crystal structure is needed before any meaningful quantum chemical calculations of pigment transition energies can be performed. For this purpose we apply classical molecular dynamics simulations of the PPC within its natural environment and we perform ab initio computations of the exciton Hamiltonian of the complex, including the environment either implicitly by the polarizable continuum model (PCM) or explicitly using the polarizable QM/MM methodology (MMPol). However, PCM essentially leads to an unspecific redshift of all transition energies, and MMPol is able to reveal site-specific changes in the optical properties of the pigments. Based on the latter and the excitonic couplings obtained within a polarizable QM/MM methodology, optical spectra are calculated, which are in good qualitative agreement with experimental data. A weakness of the approach is however found in the overestimation of the fluctuations of the excitonic parameters of the pigments along the MD trajectory. An explanation for such a finding in terms of the limits of the force fields commonly used for protein cofactors is presented and discussed.

Virtual eyes for technology and cultural heritage: toward computational strategy for new and old indigo-based dyes

A cost-effective, robust, and reliable computational strategy is applied to simulate peak positions and band-shapes of UV-vis spectra together with the dye colours perceived by human eyes. The features of our virtual multifrequency spectrometer (VMS) relevant to this topic are sketched with special focus on the selection of density functional, vibronic model, and solvent description. Furthermore, the new VMS-Draw graphical user interface (GUI) is employed for user-friendly pre- and post-processing of the computed data. The family of indigo dyes is used as case study in view of their continued use in the field of cultural heritage, together with new promising applications for photonics and sustainable energy. After assessment of different simplified models employed in previous studies, the role of several substituents and of dimerization in tuning the colour and spectral features are analyzed in detail by means of both accurate computations and interpretative models. The results are in remarkable agreement with experiment and allow to rationalize the behaviour of this class of dyes.

A simple model for exploring the role of quantum coherence and the environment in excitonic energy transfer

We investigate the role of quantum coherence in modulating the energy transfer rate between two independent energy donors and a single acceptor participating in an excitonic energy transfer process. The energy transfer rate depends explicitly on the nature of the initial coherent superposition state of the two donors and we connect it to the observed absorption profile of the acceptor and the stimulated emission profile of the energy donors. We consider simple models with mesoscopic environments interacting with the donors and the acceptor and compare the expression we obtained for the energy transfer rate with the results of numerical integration.

Variation of exciton-vibrational coupling in photosystem II core complexes from Thermosynechococcus elongatus as revealed by single-molecule spectroscopy

The spectral properties and dynamics of the fluorescence emission of photosystem II core complexes are investigated by single-molecule spectroscopy at 1.6 K. The emission spectra are dominated by sharp zero-phonon lines (ZPLs). The sharp ZPLs are the result of weak to intermediate exciton-vibrational coupling and slow spectral diffusion. For several data sets, it is possible to surpass the effect of spectral diffusion by applying a shifting algorithm. The increased signal-to-noise ratio enables us to determine the exciton-vibrational coupling strength (Huang-Rhys factor) with high precision. The Huang-Rhys factors vary between 0.03 and 0.8. The values of the Huang-Rhys factors show no obvious correlation between coupling strength and wavelength position. From this result, we conclude that electrostatic rather than exchange or dispersive interactions are the main contributors to the exciton-vibrational coupling in this system.

Site-dependence of van der Waals interaction explains exciton spectra of double-walled tubular J-aggregates

The simulation of the optical properties of supramolecular aggregates requires the development of methods, which are able to treat a large number of coupled chromophores interacting with the environment. Since it is currently not possible to treat large systems by quantum chemistry, the Frenkel exciton model is a valuable alternative. In this work we show how the Frenkel exciton model can be extended in order to explain the excitonic spectra of a specific double-walled tubular dye aggregate explicitly taking into account dispersive energy shifts of ground and excited states due to van der Waals interaction with all surrounding molecules. The experimentally observed splitting is well explained by the site-dependent energy shift of molecules placed at the inner or outer side of the double-walled tube, respectively. Therefore we can conclude that inclusion of the site-dependent dispersive effect in the theoretical description of optical properties of nanoscaled dye aggregates is mandatory.