Two phases of trans-stilbene in a polystyrene matrix.

Variability in the spectral properties of solid conformations of stilbene under various external conditions still remains obscure. The photophysical properties of trans-stilbene solution in solid polystyrene glass have been studied by absorption and time-resolved fluorescence. Concentration-induced quenching has been observed for small concentrations of stilbene. At large concentrations, the spectroscopic characteristics become split between the two phases of the sample: single-molecule properties are responsible for absorption, while the micro-crystalline phase dominates in fluorescence. Ab initio and molecular dynamics analyses suggest permanent twisting of the stilbene molecular structure upon crystallization, which supports spectroscopic phase separation.

Electronic and Vibrational Properties of Allene Carotenoids.

Carotenoids are conjugated linear molecules built from the repetition of terpene units, which display a large structural diversity in nature. They may, in particular, contain several types of side or end groups, which tune their functional properties, such as absorption position and photochemistry. We report here a detailed experimental study of the absorption and vibrational properties of allene-containing carotenoids, together with an extensive modeling of these experimental data. Our calculations can satisfactorily explain the electronic properties of vaucheriaxanthin, where the allene group introduces the equivalent of one C═C double bond into the conjugated C═C chain. The position of the electronic absorption of fucoxanthin and butanoyloxyfucoxanthin requires long-range corrections to be found correctly on the red side of that of vaucheriaxanthin; however, these corrections tend to overestimate the effect of the conjugated and nonconjugated C═O groups in these molecules. We show that the resonance Raman spectra of these carotenoids are largely perturbed by the presence of the allene group, with the two major Raman contributions split into two components. These perturbations are satisfactorily explained by modeling, through a gain in the Raman intensity of the C═C antisymmetric stretching mode, induced by the presence of the allene group in the carotenoid C═C chain.

Structure-based model of fucoxanthin-chlorophyll protein complex: Calculations of chlorophyll electronic couplings.

Diatoms are a group of marine algae that are responsible for a significant part of global oxygen production. Adapted to life in an aqueous environment dominated by the blue-green light, their major light-harvesting antennae-fucoxanthin-chlorophyll protein complexes (FCPs)-exhibit different pigment compositions than of plants. Despite extensive experimental studies, until recently the theoretical description of excitation energy dynamics in these complexes was limited by the lack of high-resolution structural data. In this work, we use the recently resolved crystallographic information of the FCP complex from Phaeodactylum tricornutum diatom [Wang et al., Science 363, 6427 (2019)] and quantum chemistry-based calculations to evaluate the chlorophyll transition dipole moments, atomic transition charges from electrostatic potential, and the inter-chlorophyll couplings in this complex. The obtained structure-based excitonic couplings form the foundation for any modeling of stationary or time-resolved spectroscopic data. We also calculate the inter-pigment Förster energy transfer rates and identify two quickly equilibrating chlorophyll clusters.

Confronting FCP structure with ultrafast spectroscopy data: evidence for structural variations.

Diatoms are a major group of algae, responsible for a quarter of the global primary production on our planet. Their adaptation to marine environments is ensured by their light-harvesting antenna - the fucoxanthin-chlorophyll protein (FCP) complex, which absorbs strongly in the blue-green spectral region. Although these essential proteins have been the subject of many studies, for a long time their comprehensive description was not possible in the absence of structural data. Last year, the 3D structures of several FCP complexes were revealed. The structure of an FCP dimer was resolved by crystallography for the pennate diatom Phaeodactylum tricornutum [W. Wang et al., Science, 2019, 363, 6427] and the structure of the PSII supercomplex from the centric diatom Chaetoceros gracilis, containing several FCPs, was obtained by electron microscopy [X. Pi et al., Science, 2019, 365, 6452; R. Nagao et al., Nat. Plants, 2019, 5, 890]. In this Perspective article, we evaluate how precisely these structures may account for previously published ultrafast spectroscopy results, describing the excitation energy transfer in the FCP from another centric diatom Cyclotella meneghiniana. Surprisingly, we find that the published FCP structures cannot explain several observations obtained from ultrafast spectroscopy. Using the available structures, and results from electron microscopy, we construct a trimer-based FCP model for Cyclotella meneghiniana, consistent with ultrafast experimental data. As a whole, our observations suggest that the structures from the proteins belonging to the FCP family display larger variations than the equivalent LHC proteins in plants, which may reflect species-specific adaptations or original strategies for adapting to rapidly changing marine environments.

Unusual temperature dependence of the fluorescence decay in heterostructured stilbene.

Fluorescence spectra as well as the fluorescence decay kinetics of hot-pressed and sublimated films of stilbene have been studied in a wide temperature range, from 15 K up to room temperature. The fluorescence decay kinetics demonstrate unusual elongation of the excitation lifetime with a temperature increase. This is in contrast to the corresponding data of stilbene solutions in chloroform and in a polystyrene (PS) matrix. It is well known that the excitation dynamics of stilbene in solution and in a PS matrix is controlled by the molecular isomerization/twisting process of separate molecules. The data analysis and quantum chemistry calculations of stilbene aggregates suggest that the temperature dependence of the fluorescence kinetics of bulk stilbene solids can be explained by fast exciton diffusion, which yields a thermalized exciton distribution in a relatively small number of fluorescence centres. The temperature dependence of the distribution can thus explain the observed fluorescence decay lifetimes.

Stark absorption and Stark fluorescence spectroscopies: Theory and simulations.

Stark spectroscopy experiments are widely used to study the properties of molecular systems, particularly those containing charge-transfer (CT) states. However, due to the small transition dipole moments and large static dipole moments of the CT states, the standard interpretation of the Stark absorption and Stark fluorescence spectra in terms of the Liptay model may be inadequate. In this work, we provide a theoretical framework for calculations of Stark absorption and Stark fluorescence spectra and propose new methods of simulations that are based on the quantum-classical theory. In particular, we use the forward-backward trajectory solution and a variant of the Poisson bracket mapping equation, which have been recently adapted for the calculation of conventional (field-free) absorption and fluorescence spectra. For comparison, we also apply the recently proposed complex time-dependent Redfield theory, while exact results are obtained using the hierarchical equations of motion approach. We show that the quantum-classical methods produce accurate results for a wide range of systems, including those containing CT states. The CT states contribute significantly to the Stark spectra, and the standard Liptay formalism is shown to be inapplicable for the analysis of spectroscopic data in those cases. We demonstrate that states with large static dipole moments may cause a pronounced change in the total fluorescence yield of the system in the presence of an external electric field. This effect is correctly captured by the quantum-classical methods, which should therefore prove useful for further studies of Stark spectra of real molecular systems. As an example, we calculate the Stark spectra for the Fenna-Matthews-Olson complex of green sulfur bacteria.

Modeling Dynamic Conformations of Organic Molecules: Alkyne Carotenoids in Solution.

Calculating the spectroscopic properties of complex conjugated organic molecules in their relaxed state is far from simple. An additional complexity arises for flexible molecules in solution, where the rotational energy barriers are low enough so that nonminimum conformations may become dynamically populated. These metastable conformations quickly relax during the minimization procedures preliminary to density functional theory calculations, and so accounting for their contribution to the experimentally observed properties is problematic. We describe a strategy for stabilizing these nonminimum conformations in silico, allowing their properties to be calculated. Diadinoxanthin and alloxanthin present atypical vibrational properties in solution, indicating the presence of several conformations. Performing energy calculations in vacuo and polarizable continuum model calculations in different solvents, we found three different conformations with values for the δ dihedral angle of the end ring ca. 0, 180, and 90° with respect to the plane of the conjugated chain. The latter conformation, a nonglobal minimum, is not stable during the minimization necessary for modeling its spectroscopic properties. To circumvent this classical problem, we used a Car-Parinello MD supermolecular approach, in which diadinoxanthin was solvated by water molecules so that metastable conformations were stabilized by hydrogen-bonding interactions. We progressively removed the number of solvating waters to find the minimum required for this stabilization. This strategy represents the first modeling of a carotenoid in a distorted conformation and provides an accurate interpretation of the experimental data.

Analytical derivation of equilibrium state for open quantum system.

Calculation of the equilibrium state of an open quantum system interacting with a bath remains a challenge to this day, mostly due to a huge number of bath degrees of freedom. Here, we present an analytical expression for the reduced density operator in terms of an effective Hamiltonian for a high temperature case. Comparing with numerically exact results, we show that our theory is accurate for slow baths and up to intermediate system-bath coupling strengths. Our results demonstrate that the equilibrium state does not depend on the shape of spectral density in the slow bath regime. The key quantity in our theory is the effective coupling between the states, which depends exponentially on the ratio of the reorganization energy to temperature and, thus, has opposite temperature dependence than could be expected from the small polaron transformation.

Benchmarking the forward-backward trajectory solution of the quantum-classical Liouville equation.

Various quantum-classical approaches to the simulation of processes taking place in real molecular systems have been shown to provide quantitatively correct results in a number of scenarios. However, it is not immediately clear how strongly the approximations related to the classical treatment of the system's environment compromise the accuracy of these methods. In this work, we present the analysis of the accuracy of the forward-backward trajectory solution (FBTS) of the quantum-classical Liouville equation. To this end, we simulate the excitation dynamics in a molecular dimer using the FBTS and the exact hierarchical equations of motion approach. To facilitate the understanding of the possible benefits of the FBTS, the simulations are also performed using a closely related quantum-classical Poisson Bracket Mapping Equation (PBME) method, as well as the well-known Förster and Redfield theories. We conclude that the FBTS is considerably more accurate than the PBME and the perturbative approaches for most realistic parameter sets and is, therefore, more versatile. We investigate the impact each parameter has on the accuracy of the FBTS. Our results can be used to predict whether the FBTS may be expected to yield satisfactory results when calculating system dynamics for the given system parameters.

Can red-emitting state be responsible for fluorescence quenching in LHCII aggregates?

Non-photochemical quenching (NPQ) is responsible for protecting the light-harvesting apparatus of plants from damage at high light conditions. Although it is agreed that the major part of NPQ, an energy-dependent quenching (qE), originates in the light-harvesting antenna, its exact mechanism is still debated. In our earlier work (Chmeliov et al. in Nat Plants 2:16045, 2016), we have analyzed the time-resolved fluorescence (TRF) from the trimers and aggregates of the major light-harvesting complexes of plants (LHCII) over a broad temperature range and came to a conclusion that three distinct states are required to describe the experimental data: two of them correspond to the emission bands centered at ~680 and ~700 nm, and the third state is responsible for the excitation quenching. This was opposite to earlier suggestions of a two-state model, where the red-shifted fluorescence and excitation quenching were assumed to be related. To examine such possibility, in the current work we repeat our analysis of the TRF data in terms of the two-state model. We find that even though it can reasonably describe the aggregate fluorescence, it fails to do so for the LHCII trimers. We conclude that the red-emitting state cannot be responsible for fluorescence quenching in the LHCII aggregates and reaffirm that the three-state model is the simplest possible description of the experimental data.

Fluorescence Microscopy of Single Liposomes with Incorporated Pigment-Proteins.

Reconstitution of transmembrane proteins into liposomes is a widely used method to study their behavior under conditions closely resembling the natural ones. However, this approach does not allow precise control of the liposome size, reconstitution efficiency, and the actual protein-to-lipid ratio in the formed proteoliposomes, which might be critical for some applications and/or interpretation of data acquired during the spectroscopic measurements. Here, we present a novel strategy employing methods of proteoliposome preparation, fluorescent labeling, purification, and surface immobilization that allow us to quantify these properties using fluorescence microscopy at the single-liposome level and for the first time apply it to study photosynthetic pigment-protein complexes LHCII. We show that LHCII proteoliposome samples, even after purification with a density gradient, always contain a fraction of nonreconstituted protein and are extremely heterogeneous in both protein density and liposome sizes. This strategy enables quantitative analysis of the reconstitution efficiency of different protocols and precise fluorescence spectroscopic study of various transmembrane proteins in a controlled nativelike environment.

Tracing feed-back driven exciton dynamics in molecular aggregates.

Perturbative treatment of excitation dynamics in molecular systems with respect to external interactions with a dissipative environment is extensively used for the description of excitation energy transfer and relaxation. However the simulated dynamics becomes sensitive to a specific representation basis set, which makes the conclusions obscure and questionable. We revisit questions of excitation creation patterns, coherent dynamics, relaxation and detection from a theoretical viewpoint, and demonstrate that a mixture of specific requirements should be met to observe coherent phenomena and incoherent decay processes. We discuss how intermixing of coherent components in relaxation phenomena is related to a non-perturbative regime of dynamics leading to nonlinear feed-back effects where bath relaxation also affects excitation wavepackets. We also discuss how bath equilibration causes local heating effects which is often neglected in numerical simulations. The parameters reflecting the complexity of the processes are related to excitation delocalization patterns in various basis representations. While these seem to be auxiliary nonobservable features, their evaluation allows better investigation of the physical behavior of quantum relaxation processes in molecular aggregate systems.

The carotenoid pathway: what is important for excitation quenching in plant antenna complexes?

Plant light-harvesting is regulated by the Non-Photochemical Quenching (NPQ) mechanism involving the reversible formation of excitation quenching sites in the Photosystem II (PSII) antenna in response to high light. While the major antenna complex, LHCII, is known to be a site of NPQ, the precise mechanism of excitation quenching is not clearly understood. A preliminary model of the quenched crystal structure of LHCII implied that quenching arises from slow energy capture by Car pigments. It predicted a thoroughly quenched system but offered little insight into the defining aspects of this quenching. In this work, we present a thorough theoretical investigation of this quenching, addressing the factors defining the quenching pathway and possible mechanism for its (de)activation. We show that quenching in LHCII crystals is the result of slow energy transfer from chlorophyll to the centrally-bound lutein Cars, predominantly the Lut620 associated with the chlorophyll 'terminal emitter', one of the proposed in vivo pathways. We show that this quenching is rather independent of the particular species of Car and excitation 'site' energy. The defining parameter is the resonant coupling between the pigment co-factors. Lastly, we show that these interactions must be severely suppressed for a light-harvesting state to be recovered.

Ultrafast energy transfer within the photosystem II core complex.

We report 2D electronic spectroscopy on the photosystem II core complex (PSII CC) at 77 K under different polarization conditions. A global analysis of the high time-resolution 2D data shows rapid, sub-100 fs energy transfer within the PSII CC. It also reveals the 2D spectral signatures of slower energy equilibration processes occurring on several to hundreds of picosecond time scales that are consistent with previous work. Using a recent structure-based model of the PSII CC [Y. Shibata, S. Nishi, K. Kawakami, J. R. Shen and T. Renger, J. Am. Chem. Soc., 2013, 135, 6903], we simulate the energy transfer in the PSII CC by calculating auxiliary time-resolved fluorescence spectra. We obtain the observed sub-100 fs evolution, even though the calculated electronic energy shows almost no dynamics at early times. On the other hand, the electronic-vibrational interaction energy increases considerably over the same time period. We conclude that interactions with vibrational degrees of freedom not only induce population transfer between the excitonic states in the PSII CC, but also reshape the energy landscape of the system. We suggest that the experimentally observed ultrafast energy transfer is a signature of excitonic-polaron formation.

Applicability of transfer tensor method for open quantum system dynamics.

Accurate simulations of open quantum system dynamics is a long standing issue in the field of chemical physics. Exact methods exist, but are costly, while perturbative methods are limited in their applicability. Recently a new black-box type method, called transfer tensor method (TTM), was proposed [J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)]. It allows one to accurately simulate long time dynamics with a numerical cost of solving a time-convolution master equation, provided many initial system evolution trajectories are obtained from some exact method beforehand. The possible time-savings thus strongly depend on the ratio of total versus initial evolution lengths. In this work, we investigate the parameter regimes where an application of TTM would be most beneficial in terms of computational time. We identify several promising parameter regimes. Although some of them correspond to cases when perturbative theories could be expected to perform well, we find that the accuracy of such approaches depends on system parameters in a more complex way than it is commonly thought. We propose that the TTM should be applied whenever system evolution is expected to be long and accuracy of perturbative methods cannot be ensured or in cases when the system under consideration does not correspond to any single perturbative regime.

Spectroscopic properties of photosystem II reaction center revisited.

Photosystem II (PSII) is the only biological system capable of splitting water to molecular oxygen. Its reaction center (RC) is responsible for the primary charge separation that drives the water oxidation reaction. In this work, we revisit the spectroscopic properties of the PSII RC using the complex time-dependent Redfield (ctR) theory for optical lineshapes [A. Gelzinis et al., J. Chem. Phys. 142, 154107 (2015)]. We obtain the PSII RC model parameters (site energies, disorder, and reorganization energies) from the fits of several spectra and then further validate the model by calculating additional independent spectra. We obtain good to excellent agreement between theory and calculations. We find that overall our model is similar to some of the previous asymmetric exciton models of the PSII RC. On the other hand, our model displays differences from previous work based on the modified Redfield theory. We extend the ctR theory to describe the Stark spectrum and use its fit to obtain the parameters of a single charge transfer state included in our model. Our results suggest that ChlD1+PheoD1- is most likely the primary charge transfer state, but that the Stark spectrum of the PSII RC is probably also influenced by other states.

Mapping energy transfer channels in fucoxanthin-chlorophyll protein complex.

Fucoxanthin-chlorophyll protein (FCP) is the key molecular complex performing the light-harvesting function in diatoms, which, being a major group of algae, are responsible for up to one quarter of the total primary production on Earth. These photosynthetic organisms contain an unusually large amount of the carotenoid fucoxanthin, which absorbs the light in the blue-green spectral region and transfers the captured excitation energy to the FCP-bound chlorophylls. Due to the large number of fucoxanthins, the excitation energy transfer cascades in these complexes are particularly tangled. In this work we present the two-color two-dimensional electronic spectroscopy experiments on FCP. Analysis of the data using the modified decay associated spectra permits a detailed mapping of the excitation frequency dependent energy transfer flow with a femtosecond time resolution.

Role of coherent vibrations in energy transfer and conversion in photosynthetic pigment-protein complexes.

Oscillatory features of two-dimensional spectra of photosynthetic pigment-protein complexes during few picoseconds after electronic excitations of chlorophylls in various pigment-proteins were recently related to the coherent nuclear vibrations. It has been also speculated that the vibrations may assist the excitonic energy transfer and charge separation, hence contributing to energy transport and energy conversion efficiency. Here, we consider three theoretical approaches usually used for characterization of the excitation dynamics and charge separation, namely Redfield, Förster, and Marcus model descriptions, regarding this question. We show that two out of the three mechanisms require explicit resonances of excitonic splittings and the nuclear vibration frequencies. However, the third one related to the electron transfer is in principle off resonant.

Excitation migration in fluctuating light-harvesting antenna systems.

Complex multi-exponential fluorescence decay kinetics observed in various photosynthetic systems like photosystem II (PSII) have often been explained by the reversible quenching mechanism of the charge separation taking place in the reaction center (RC) of PSII. However, this description does not account for the intrinsic dynamic disorder of the light-harvesting proteins as well as their fluctuating dislocations within the antenna, which also facilitate the repair of RCs, state transitions, and the process of non-photochemical quenching. Since dynamic fluctuations result in varying connectivity between pigment-protein complexes, they can also lead to non-exponential excitation decay kinetics. Based on this presumption, we have recently proposed a simple conceptual model describing excitation diffusion in a continuous medium and accounting for possible variations of the excitation transfer pathways. In the current work, this model is further developed and then applied to describe fluorescence kinetics originating from very diverse antenna systems, ranging from PSII of various sizes to LHCII aggregates and even the entire thylakoid membrane. In all cases, complex multi-exponential fluorescence kinetics are perfectly reproduced on the entire relevant time scale without assuming any radical pair equilibration at the side of the excitation quencher, but using just a few parameters reflecting the mean excitation energy transfer rate as well as the overall average organization of the photosynthetic antenna.

Dynamic quenching in single photosystem II supercomplexes.

Photosystem II (PSII) is a huge pigment-protein supercomplex responsible for the primary steps of photosynthesis in green plants. Its light-harvesting antenna exhibits efficient transfer of the absorbed excitation energy to the reaction center and also contains a well-regulated protection mechanism against over-excitation in strong light conditions. The latter is based on conformational changes in antenna complexes that open up excitation decay channels resulting in considerable fluorescence quenching. Meanwhile, fluorescence blinking, observed in single antennas, is likely caused by a similar mechanism. Thus the question arises whether this effect is also present in and relevant to the native supramolecular organization of a fully assembled PSII. To further investigate energy transfer and quenching in single PSII, we performed single-molecule experiments on PSII supercomplexes at 5 °C. Analysis of the fluorescence intensity and mean lifetime allowed us to distinguish detached antennas and specifically analyze PSII supercomplexes. The average fluorescence lifetime in PSII of about 100-150 ps, measured under our extreme excitation conditions, is surprisingly similar to published ensemble lifetime data of photochemical quenching in PSII of a similar size. In our case, this lifetime is nevertheless caused by either one or multiple quenched antennas or by a quencher in the reaction center. The observed reversible light-induced changes in fluorescence intensity on a millisecond timescale are reminiscent of blinking subunits. Our results therefore directly illustrate how environmental control over a fluctuating antenna can regulate light-harvesting in plant photosynthesis.