Theory of optical spectra involving charge transfer states: dynamic localization predicts a temperature dependent optical band shift

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100 fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

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.

The Structural and Spectral Features of Light-Harvesting Complex II Proteoliposomes Mimic Those of Native Thylakoid Membranes

The major photosystem II light-harvesting antenna (LHCII) is the most abundant membrane protein in nature and plays an indispensable role in light harvesting and photoprotection in the plant thylakoid. Here, we show that "pseudothylakoid characteristics" can be observed in artificial LHCII membranes. In our proteoliposomal system, at high LHCII densities, the liposomes become stacked, mimicking the in vivo thylakoid grana membranes. Furthermore, an unexpected, unstructured emission peak at ∼730 nm appears, similar in appearance to photosystem I emission, but with a clear excimeric character that has never been previously reported. These states correlate with the increasing density of LHCII in the membrane and a decrease in its average fluorescence lifetime. The appearance of these low-energy states can also occur in natural plant membrane structures, which has unique consequences for the interpretation of the spectroscopic and physiological properties of the photosynthetic membrane.

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

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

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

Fluorographene with impurities as a biomimetic light-harvesting medium

We investigate the prospect of using a two-dimensional material, fluorographene, to mimic the light-harvesting function of natural photosynthetic antennas. We show by quantum chemical calculations that isles of graphene in a fluorographene sheet can act as quasi-molecules similar to natural pigments from which the structures similar in function to photosynthetic antennas can be built. The graphene isles retain enough identity so that they can be used as building blocks to which intuitive design principles of natural photosynthetic antennas can be applied. We examine the excited state properties, stability, and interactions of these building blocks. Constraints put on the antenna structure by the two-dimensionality of the material as well as the discrete nature of fluorographene sheet are studied. We construct a hypothetical energetic funnel out of two types of quasi-molecules to show how a limited number of building blocks can be arranged to bridge the energy gap and spatial separation in excitation energy transfer. Energy transfer rates for a wide range of the system-environment interaction strengths are predicted. We conclude that conditions for the near unity quantum efficiency of energy transfer are likely to be fulfilled in fluorographene with the controlled arrangement of quasi-molecules.

Inverse molecular design from first principles: tailoring organic chromophore spectra for optoelectronic applications

The discovery of molecules with tailored optoelectronic properties such as specific frequency and intensity of absorption or emission is a major challenge in creating next-generation organic light-emitting diodes (OLEDs) and photovoltaics. This raises the question: how can we predict a potential chemical structure from these properties? Approaches that attempt to tackle this inverse design problem include virtual screening, active machine learning and genetic algorithms. However, these approaches rely on a molecular database or many electronic structure calculations, and significant computational savings could be achieved if there was prior knowledge of (i) whether the optoelectronic properties of a parent molecule could easily be improved and (ii) what morphing operations on a parent molecule could improve these properties. In this perspective we address both of these challenges from first principles. We firstly adapt the Thomas-Reiche-Kuhn sum rule to organic chromophores and show how this indicates how easily the absorption and emission of a molecule can be improved. We then show how by combining electronic structure theory and intensity borrowing perturbation theory we can predict whether or not the proposed morphing operations will achieve the desired spectral alteration, and thereby derive widely-applicable design rules. We go on to provide proof-of-concept illustrations of this approach to optimizing the visible absorption of acenes and the emission of radical OLEDs. We believe this approach can be integrated into genetic algorithms by biasing morphing operations in favour of those which are likely to be successful, leading to faster molecular discovery and greener chemistry.

Hidden vibronic and excitonic structure and vibronic coherence transfer in the bacterial reaction center

We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden vibronic and excitonic structure. Through analysis of the coherent dynamics of the BRC, we identify multiple quasi-resonances between pigment vibrations and excitonic energy gaps, and vibronic coherence transfer processes that are typically neglected in standard models of photosynthetic energy transfer and charge separation. We support our assignment with control experiments on bacteriochlorophyll and simulations of the coherent dynamics using a reduced excitonic model of the BRC. We find that specific vibronic coherence processes can readily reveal weak exciton transitions. While the functional relevance of such processes is unclear, they provide a spectroscopic tool that uses vibrations as a window for observing excited state structure and dynamics elsewhere in the BRC via vibronic coupling. Vibronic coherence transfer reveals the upper exciton of the “special pair” that was weakly visible in previous 2DES experiments.

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.

Temperature Dependence of Tryptophan Fluorescence Lifetime as an Indicator of Its Microenvironment Dynamics

The spectral-kinetic characteristics of the fluorescence of the tryptophan molecule in an aqueous solution and in the composition of a protein (albumin) were studied in the temperature range from -170 to 25°C. To explain the observed changes in the spectra and the tryptophan fluorescence lifetime with temperature, a model of transitions between the excited and ground states involving a charge-transfer state was used, which takes into account the nonlinear nature of the dynamics of these transitions. In these processes, an important role is played by the interaction of tryptophan molecules with its microenvironment, as well as rearrangements in the system of hydrogen bonds of the water-protein matrix surrounding the tryptophan molecule.

Semiclassical Modified Redfield and Generalized Förster Theories of Exciton Relaxation/Transfer in Light-Harvesting Complexes: The Quest for the Principle of Detailed Balance

A conceptual problem of transfer theories that use a semiclassical description of the electron-vibrational coupling is the neglect of the correlation between momenta and coordinates of nuclei. In the Redfield theory of exciton relaxation, this neglect leads to a violation of the principle of detailed balance; equal “uphill” and “downhill” transfer rate constants are obtained. Here, we investigate how this result depends on nuclear reorganization effects, neglected in Redfield but taken into account in the modified Redfield theory. These reorganization effects, resulting from a partial localization of excited states, are found to promote a preferential “downhill” relaxation of excitation energy. However, for realistic spectral densities of light-harvesting antennae in photosynthesis, the reorganization effects are too small to compensate for the missing coordinate–momentum uncertainty. For weaker excitonic couplings as they occur between domains of strongly coupled pigments, we find the principle of detailed balance to be fulfilled in a semiclassical variant of the generalized Förster theory. A qualitatively correct description of the transfer is obtained with this theory at a significantly lower computational cost as with the quantum generalized Förster theory. Larger deviations between the two theories are expected for large energy gaps as they occur in complexes with chemically different pigments.

Complete mapping of energy transfer pathways in the plant light-harvesting complex Lhca4

The Lhca4 antenna complex of plant Photosystem I (PSI) is characterized by extremely red-shifted and broadened absorption and emission bands from its low-energy chlorophylls (Chls). The mixing of a charge-transfer (CT) state with the excited state manifold causing these so-called red forms results in highly complicated multi-component excited energy transfer (EET) kinetics within the complex. The two-dimensional electronic spectroscopy experiments presented here reveal that EET towards the CT state occurs on three timescales: fast from the red Chls (within 1 ps), slower (5-7 ps) from the stromal side Chls, and very slow (100-200 ps) from a newly discovered 690 nm luminal trap. The excellent agreement between the experimental data with the previously presented Redfield-Förster exciton model of Lhca4 strongly supports the equilibration scheme of the bulk excitations with the dynamically localized CT on the stromal side. Thus, a complete picture of the energy transfer pathways leading to the population of the CT final trap within the whole Lhca4 complex is presented. In view of the environmental sensitivity of the CT contribution to the Lhca4 energy landscape, we speculate that one role of the CT states is to regulate the EET from the peripheral antenna to the PSI core.

Charge transfer states in phycobilisomes

Phycobilisomes (PBs) absorb light and supply downstream photosynthetic processes with excitation energy in many cyanobacteria and algae. In response to a sudden increase in light intensity, excess excitation energy is photoprotectively dissipated in PBs by means of the orange carotenoid protein (OCP)-related mechanism or via a light-activated intrinsic decay channel. Recently, we have identified that both mechanisms are associated with far-red emission states. Here, we investigate the far-red states involved with the light-induced intrinsic mechanism by exploring the energy landscape and electro-optical properties of the pigments in PBs. While Stark spectroscopy showed that the far-red states in PBs exhibit a strong charge-transfer (CT) character at cryogenic temperatures, single molecule spectroscopy revealed that CT states should also be present at room temperature. Owing to the strong environmental sensitivity of CT states, the knowledge gained from this study may contribute to the design of a new generation of fluorescence markers.

Dynamics of the Excited State in Photosynthetic Bacterial Reaction Centers

In the initial charge-separation reaction of photosynthetic bacterial reaction centers, a dimer of strongly interacting bacteriochlorophylls (P) transfers an electron to a third bacteriochlorophyll (B_L). It has been suggested that light first generates an exciton state of the dimer and that an electron then moves from one bacteriochlorophyll to the other within P to form a charge-transfer state (P_L⁺P_M^-), which passes an electron to B_L. This scheme, however, is at odds with the most economical analysis of the spectroscopic properties of the reaction center and particularly with the unusual temperature dependence of the long-wavelength absorption band. The present paper explores this conflict with the aid of a simple model in which exciton and charge-transfer states are coupled to three vibrational modes. It then uses a similar model to show that the main experimental evidence suggesting the formation of P_L⁺P_M^- as an intermediate could reflect pure dephasing of vibrational modes that modulate stimulated emission.

High-Pressure Modulation of Primary Photosynthetic Reactions

Photochemical charge separation is key to biological solar energy conversion. Although many features of this highly quantum-efficient process have been described, others remain poorly understood. Herein, ultrafast fluorescence barospectroscopy is used for the first time to obtain insights into the mechanism of primary charge separation in a YM210W mutant bacterial reaction center under novel surrounding modulating conditions. Over a range of applied hydrostatic pressures reaching 10 kbar, the rate of primary charge separation monotonously increased and that of the electron transfer to secondary acceptor decreased. While the inferred free energy gap for charge separation generally narrowed with increasing pressure, a pressure-induced break of a protein-cofactor hydrogen bond observed at ∼2 kbar significantly (by 219 cm^-1 or 27 meV) increased this gap, resulting in a drop in fluorescence. The findings strongly favor a model for primary charge separation that incorporates charge recombination and restoration of the excited primary pair state, over a purely sequential model. We show that the main reason for the almost threefold acceleration of the primary electron transfer rate is the pressure-induced increase of the electronic coupling energy, rather than a change of activation energy. We also conclude that across all applied pressures, the primary electron transfer in the mutant reaction center studied can be considered nonadiabatic, normal region, and thermally activated.

Coherent intradimer dynamics in reaction centers of photosynthetic green bacterium Chloroflexus aurantiacus

Early-time dynamics of absorbance changes (light minus dark) in the long-wavelength Q_y absorption band of bacteriochlorophyll dimer P of isolated reaction centers (RCs) from thermophilic green bacterium Chloroflexus (Cfx.) aurantiacus was studied by difference pump-probe spectroscopy with 18-fs resolution at cryogenic temperature. It was found that the stimulated emission spectrum gradually moves to the red on the ~100-fs time scale and subsequently oscillates with a major frequency of ~140 cm⁻¹. By applying the non-secular Redfield theory and linear susceptibility theory, the coherent dynamics of the stimulated emission from the excited state of the primary electron donor, bacteriochlorophyll dimer P*, was modeled. The model showed the possibility of an extremely fast transition from the locally excited state P₁* to the spectrally different excited state P₂*. This transition is clearly seen in the kinetics of the stimulated emission at 880 and 945 nm, where mostly P₁* and P₂* states emit, respectively. These findings are similar to those obtained previously in RCs of the purple bacterium Rhodobacter (Rba.) sphaeroides. The assumption about the existence of the second excited state P₂* helps to explain the complicated temporal behavior of the ΔA spectrum measured by pump-probe spectroscopy. It is interesting that, in spite of the strong coupling between the P₁* and P₂* states assumed in our model, the form of the coherent oscillations is mainly defined by pure vibrational coherence in the excited states. A possible nature of the P₂* state is discussed.

New Perspectives on Photosystem II Reaction Centres

We apply the differential optical spectroscopy techniques of circular polarisation of luminescence (CPL) and magnetic CPL (MCPL) to the study of isolated reaction centres (RCs) of photosystem II (PS II). The data and subsequent analysis provide insights into aspects of the RC chromophore site energies, exciton couplings, and heterogeneities. CPL measurements are able to identify weak luminescence associated with the unbound chlorophyll-a (Chl-a) present in the sample. The overall sign and magnitude of the CPL observed relates well to the circular dichroism (CD) of the sample. Both CD and CPL are reasonably consistent with modelling of the RC exciton structure. The MCPL observed for the free Chl-a luminescence component in the RC samples is also easily understandable, but the MCPL seen near 680nm at 1.8K is anomalous, appearing to have a narrow, strongly negative component. A negative sign is inconsistent with MCPL of (exciton coupled) Qy states of either Chl-a or pheophytin-a (Pheo-a). We propose that this anomaly may arise as a result of the luminescence from a transient excited state species created following photo-induced charge separation within the RC. A comparison of CD spectra and modelling of RC preparations having a different number of pigments suggests that the non-conservative nature of the CD spectra observed is associated with the ‘special pair’ pigments PD1 and PD2.

Transient synchronisation and quantum coherence in a bio-inspired vibronic dimer

Synchronisation is a collective phenomenon widely investigated in classical oscillators and, more recently, in quantum systems. However it remains unclear what features distinguish synchronous behaviour in these two scenarios. Recent works have shown that investigating synchronisation dynamics in open quantum systems can give insight into this issue. Here we study transient synchronisation in a bio-inspired vibronic dimer, where electronic excitation dynamics is mediated by coherent interactions with intramolecular vibrational modes. We show that the synchronisation dynamics of local mode displacements exhibit a rich behaviour which arises directly from the distinct time-evolutions of different vibronic quantum coherences. Furthermore, our study shows that coherent energy transport in this bio-inspired system is concomitant with the emergence of positive synchronisation between mode displacements. Our work provides further understanding of the relations between quantum coherence and synchronisation in open quantum systems and suggests an interesting role for coherence in biomolecules, that of promoting synchronisation of vibrational motions driven out of thermal equilibrium.

pH dependence of water anomaly temperature investigated by Eu(III) cryptate luminescence

Although water has been extensively studied, not all of its unique properties have been fully understood. There is still controversy about the temperature at which hydrogen bonds are broken or weakened, producing the anomalous temperature dependence of many water properties. Different temperatures between 23 and 48 °C have been reported, but no study has scrutinized the reasons for this discrepancy. We suggest the determining role of pH in the alteration of the water anomaly temperature. We employed a luminescent europium trisbipyridine cryptate, which is highly sensitive to changes in the arrangement of water molecules and whose luminescence intensity and lifetime are not significantly influenced by variations over a broad pH range. Our results revealed an increase of the crossover temperature from circa 35 °C at pH 3.5 to circa 45 °C at pH 7 to 9, which explains the discrepancies of previous studies. The pH dependence of water anomaly temperature is an important property for a better understanding of water and water-based systems and applications.

Mixed Upper Exciton State of the Special Pair in Bacterial Reaction Centers

Excitonic interactions between two closely separated bacteriochlorophyll a molecules (BChls) in the special pair of the reaction center (RC) of purple bacteria determine the positions and relative oscillator strengths of its two excitonic components. While the absorption of the lower excitonic band is well-defined, the position and the intensity of the upper excitonic band ( P_Y+) are still under debate. Recent 77 K two-dimensional electronic spectroscopy data on Rba. capsulatus suggested that the P_Y+ component absorbs at ∼840 nm, i.e., at a significantly lower energy than previously suggested. In the present work, we argue that the P_Y+ state is mixed with the excited states of the accessory BChls ( B*/ P _Y+) leading to excitons contributing to the 785-825 nm spectral region which is consistent with previously published data. This conclusion is based on hole-burning/linear dichroism data and modeling studies of the excitonic structure of the RC using a non-Markovian reduced density matrix approach.

Intramolecular Vibrations Complement the Robustness of Primary Charge Separation in a Dimer Model of the Photosystem II Reaction Center

The energy conversion of oxygenic photosynthesis is triggered by primary charge separation in proteins at the photosystem II reaction center. Here, we investigate the impacts of the protein environment and intramolecular vibrations on primary charge separation at the photosystem II reaction center. This is accomplished by combining the quantum dynamic theories of condensed phase electron transfer with quantum chemical calculations to evaluate the vibrational Huang-Rhys factors of chlorophyll and pheophytin molecules. We report that individual vibrational modes play a minor role in promoting charge separation, contrary to the discussion in recent publications. Nevertheless, these small contributions accumulate to considerably influence the charge separation rate, resulting in subpicosecond charge separation almost independent of the driving force and temperature. We suggest that the intramolecular vibrations complement the robustness of the charge separation in the photosystem II reaction center against the inherently large static disorder of the involved electronic energies.

Origin of the Two Bands in the B800 Ring and Their Involvement in the Energy Transfer Network of Allochromatium vinosum

Bacterial photosynthesis features robust and adaptable energy-harvesting processes in which light-harvesting proteins play a crucial role. The peripheral light-harvesting complex of the purple bacterium Allochromatium vinosum is particularly distinct, featuring a double peak structure in its B800 absorption band. Two hypotheses-not necessarily mutually exclusive-concerning the origin of this splitting have been proposed; either two distinct B800 bacteriochlorophyll site energies are involved, or an excitonic dimerization of bacteriochlorophylls within the B800 ring takes place. Through the use of two-dimensional electronic spectroscopy, we present unambiguous evidence that excitonic interaction shapes the split band. We further identify and characterize all of the energy transfer pathways within this complex by using a global kinetic fitting procedure. Our approach demonstrates how the combination of two-dimensional spectral resolution and self-consistent fitting allows for extraction of information on light-harvesting processes, which would otherwise be inaccessible due to signal congestion.

Exciton-vibrational resonance and dynamics of charge separation in the photosystem II reaction center

The dynamics of charge separation in the photosystem II reaction center (PSII-RC) in the presence of intramolecular vibrations with their frequency matching the energy gap between the exciton state acting as the primary electron donor and the first charge-transfer (CT) state are investigated. A reduced PSII-RC 4-state model explicitly including a CT state is analyzed within Redfield relaxation theory in the multidimensional exciton-vibrational (vibronic) basis. This model is used to study coherent energy/electron transfers and their spectral signatures obtained by two-dimensional electronic spectroscopy (2DES). Modeling of the time-resolved 2D frequency maps obtained by wavelet analysis reveals the origins of the coherences which produce the observed oscillating features in 2DES and allows comparing the lifetimes of the coherences. The results suggest faster excitonic decoherence as compared with longer-lived vibronic oscillations. The emerging picture of the dynamics unravels the role of resonant vibrations in sustaining the effective energy conversion in the PSII-RC. We demonstrate that the mixing of the exciton and CT states promoted by a resonant vibrational quantum allows faster penetration of excitation energy into the CT with subsequent dynamic localization at the bottom of the CT potential induced by the remaining non-resonant nuclear modes. The degree of vibration-assisted mixing and, correspondingly, the rate of primary charge separation, increases significantly in the case of electron-vibrational resonance. The observed features illustrate the principles of quantum design of the photosynthetic unit. These principles are connected with the phenomenon of coherent mixing within vibronic eigenstates, increasing the effectiveness of charge separation not only upon coherent and impulsive laser excitation utilized in the 2DES experiment, but also under natural conditions under non-coherent non-impulsive solar light illumination.

Two-dimensional electronic spectroscopy of anharmonic molecular potentials

Two-dimensional electronic spectroscopy (2DES) is a powerful tool in the study of coupled electron-phonon dynamics, yet very little is known about how nonlinearities in the electron-phonon coupling, arising from anharmonicities in the nuclear potentials, affect the spectra. These become especially relevant when the coupling is strong. From the linear spectroscopies, anharmonicities are known to give structure to the zero-phonon line and to break mirror-symmetry between absorption and emission, but the 2D analogues of these effects have not been identified. Using a simple two-level model where the electronic states are described by (displaced) harmonic oscillators with differing curvatures or displaced Morse oscillators, we find that the zero-phonon line shape is essentially transferred to the diagonal in 2DES spectra, and that anharmonicities break a horizontal mirror-symmetry in the infinite waiting time limit. We also identify anharmonic effects that are only present in 2DES spectra: twisting of cross-peaks stemming from stimulated emission signals; and oscillation period mismatch between ground state bleach and stimulated emission (for harmonic oscillators with differing curvatures), or inherently chaotic oscillations (for Morse oscillators). Our findings will facilitate an improved understanding of 2DES spectra and aid the interpretation of signals that are more realistic than those arising from simple models.

Femtosecond Relaxation Processes in Rhodobacter sphaeroides Reaction Centers

Energy relaxation was studied with difference femtosecond spectroscopy in reaction centers of the YM210L mutant of the purple photosynthetic bacterium Rhodobacter sphaeroides at low temperature (90 K). A dynamical long-wavelength shift of stimulated emission of the excited state of the bacteriochlorophyll dimer P was found, which starts simultaneously with P* formation and is accompanied by a change in the spectral shape of this emission. The characteristic value of this shift was about 30 nm, and the characteristic time about 200 fs. Difference kinetics ΔA measured at fixed wavelengths demonstrate the femtosecond shift of the P* stimulated emission appearing as a dependence of these kinetics on wavelength. We found that the reported long-wavelength shift can be explained in terms of electron-vibrational relaxation of the P* excited state with time constants of vibrational and electronic relaxation of 100 and 50 fs, respectively. Alternative mechanisms of the dynamical shift of the P* stimulated emission spectrum are also discussed in terms of energy redistribution between vibrational modes or coherent excitation of the modes.

Tracking the coherent generation of polaron pairs in conjugated polymers

The optical excitation of organic semiconductors not only generates charge-neutral electron-hole pairs (excitons), but also charge-separated polaron pairs with high yield. The microscopic mechanisms underlying this charge separation have been debated for many years. Here we use ultrafast two-dimensional electronic spectroscopy to study the dynamics of polaron pair formation in a prototypical polymer thin film on a sub-20-fs time scale. We observe multi-period peak oscillations persisting for up to about 1 ps as distinct signatures of vibronic quantum coherence at room temperature. The measured two-dimensional spectra show pronounced peak splittings revealing that the elementary optical excitations of this polymer are hybridized exciton-polaron-pairs, strongly coupled to a dominant underdamped vibrational mode. Coherent vibronic coupling induces ultrafast polaron pair formation, accelerates the charge separation dynamics and makes it insensitive to disorder. These findings open up new perspectives for tailoring light-to-current conversion in organic materials.

Understanding of charge transfer dynamics is essential to the design of high-performance organic semiconductors for optoelectronic applications. Here, the authors show that excitons, polaron pairs and a long-lived vibrational mode are strongly coupled to each other up to 1 picosecond in polythiophene.

Spectral and kinetic effects accompanying the assembly of core complexes of Rhodobacter sphaeroides

In the present work, spectral and kinetic changes accompanying the assembly of the light-harvesting 1 (LH1) complex with the reaction center (RC) complex into monomeric RC-LH1 and dimeric RC-LH1-PufX core complexes of the photosynthetic purple bacterium Rhodobacter sphaeroides are systematically studied over the temperature range of 4.5-300K. The samples were interrogated with a combination of optical absorption, hole burning, fluorescence excitation, steady state and picosecond time resolved fluorescence spectroscopy. Fair additivity of the LH1 and RC absorption spectra suggests rather weak electronic coupling between them. A low-energy tail revealed at cryogenic temperatures in the absorption spectra of both monomeric and dimeric core complexes is proved to be due to the special pair of the RC. At selected excitation intensity and temperature, the fluorescence decay time of core complexes is shown to be a function of multiple factors, most importantly of the presence/absence of RCs, the supramolecular architecture (monomeric or dimeric) of the complexes, and whether the complexes were studied in a native membrane environment or in a detergent - purified state.

Mixing of exciton and charge-transfer states in light-harvesting complex Lhca4

Structure-based modeling of spectra of the wild-type Lhca4 and NH mutant enables us to build the exciton model of the complex that includes a charge-transfer state mixed with the excited-state manifold.

Spectral exhibition of electron-vibrational relaxation in P* state of Rhodobacter sphaeroides reaction centers

Electron-vibrational relaxation in the excited state of the primary electron donor, bacteriochlorophyll dimer P, in the reaction centers (RCs) of purple photosynthetic bacteria Rhodobacter sphaeroides is modeled. A multimode model of three states (i.e., the ground state Pg, initially excited P1*, and relaxed excited P2*) is used to calculate the incoherent dynamics of the difference (ΔA) spectra on a femtosecond timescale for the YM210 W mutant RCs. The relaxation processes are described by the step-ladder model. The model shows that the electron-vibrational relaxation in the excited state of P is visualized by the transient red shift of the stimulated emission from P*. The dynamics of this shift is observed as a change in the ΔA spectrum shape in its red-most part, within a few hundreds of femtoseconds after excitation. As a result, an initial rise in the red-side ΔA kinetics is delayed with respect to the blue-side kinetics. The time constant of the P1* → P2* electronic relaxation (54 fs) and the Pg, P1*, and P2* vibrational relaxations (120 fs), used in the model, provided the best fit of the experimental time-resolved ΔA spectra and kinetics at 90 and 293 K. The possible nature of the P1* → P2* electronic relaxation is discussed.

Dynamics of exciton-polaron transition in molecular assemblies: the variational approach

Dynamics of excitonic polaron formation in molecular systems coupled to an overdamped bath are investigated using the Dirac-Frenkel variational principle and Davydov D1 Ansatz. Using a two-site model system we show that a few qualitatively distinct relaxation regimes of an optically created exciton are possible, depending on the timescale of bath fluctuations. A slow bath always leads to adiabatic polaron formation. Non-adiabatic exciton self-trapping occurs when the system is strongly coupled to a fast bath. Weak coupling to such bath does not perturb the excitonic picture. The complex system-bath dynamics can then be mapped to an effective model where the resonant coupling between sites is quenched during relaxation. The timescale of the polaron formation can be defined by the timescale of resonant coupling quenching, and is found to directly correlate with the bath relaxation time.

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.

Homoleptic nickel(II) complexes of redox-tunable pincer-type ligands

Different synthetic methods have been developed to prepare eight new redox-active pincer-type ligands, H(X,Y), that have pyrazol-1-yl flanking donors attached to an ortho-position of each ring of a diarylamine anchor and that have different groups, X and Y, at the para-aryl positions. Together with four previously known H(X,Y) ligands, a series of 12 Ni(X,Y)2 complexes were prepared in high yields by a simple one-pot reaction. Six of the 12 derivatives were characterized by single-crystal X-ray diffraction, which showed tetragonally distorted hexacoordinate nickel(II) centers. The nickel(II) complexes exhibit two quasi-reversible one-electron oxidation waves in their cyclic voltammograms, with half-wave potentials that varied over a remarkable 700 mV range with the average of the Hammett σ(p) parameters of the para-aryl X, Y groups. The one- and two-electron oxidized derivatives [Ni(Me,Me)2](BF4)n (n = 1, 2) were prepared synthetically, were characterized by X-band EPR, electronic spectroscopy, and single-crystal X-ray diffraction (for n = 2), and were studied computationally by DFT methods. The dioxidized complex, [Ni(Me,Me)2](BF4)2, is an S = 2 species, with nickel(II) bound to two ligand radicals. The mono-oxidized complex [Ni(Me,Me)2](BF4), prepared by comproportionation, is best described as nickel(II) with one ligand centered radical. Neither the mono- nor the dioxidized derivative shows any substantial electronic coupling between the metal and their bound ligand radicals because of the orthogonal nature of their magnetic orbitals. On the other hand, weak electronic communication occurs between ligands in the mono-oxidized complex as evident from the intervalence charge transfer (IVCT) transition found in the near-IR absorption spectrum. Band shape analysis of the IVCT transition allowed comparisons of the strength of the electronic interaction with that in the related, previously known, Robin-Day class II mixed valence complex, [Ga(Me,Me)2](2+).

Long-wavelength limit of photochemical energy conversion in Photosystem I

In Photosystem I (PS I) long-wavelength chlorophylls (LWC) of the core antenna are known to extend the spectral region up to 750 nm for absorbance of light that drives photochemistry. Here we present clear evidence that even far-red light with wavelengths beyond 800 nm, clearly outside the LWC absorption bands, can still induce photochemical charge separation in PS I throughout the full temperature range from 295 to 5 K. At room temperature, the photoaccumulation of P700(+•) was followed by the absorbance increase at 826 nm. At low temperatures (T < 100 K), the formation of P700(+•)FA/B(-•) was monitored by the characteristic EPR signals of P700(+•) and FA/B(-•) and by the characteristic light-minus-dark absorbance difference spectrum in the QY region. P700 oxidation was observed upon selective excitation at 754, 785, and 808 nm, using monomeric and trimeric PS I core complexes of Thermosynechococcus elongatus and Arthrospira platensis, which differ in the amount of LWC. The results show that the LWC cannot be responsible for the long-wavelength excitation-induced charge separation at low temperatures, where thermal uphill energy transfer is frozen out. Direct energy conversion of the excitation energy from the LWC to the primary radical pair, e.g., via a superexchange mechanism, is excluded, because no dependence on the content of LWC was observed. Therefore, it is concluded that electron transfer through PS I is induced by direct excitation of a proposed charge transfer (CT) state in the reaction center. A direct signature of this CT state is seen in absorbance spectra of concentrated PS I samples, which reveal a weak and featureless absorbance band extending beyond 800 nm, in addition to the well-known bands of LWC (C708, C719 and C740) in the range between 700 and 750 nm. The present findings suggest that nature can exploit CT states for extending the long wavelength limit in PSI even beyond that of LWC. Similar mechanisms may work in other photosynthetic systems and in chemical systems capable of photoinduced electron transfer processes in general.

Selective and differential optical spectroscopies in photosynthesis

Photosynthetic pigments are inherently intense optical absorbers and have strong polarisation characteristics. They can also luminesce strongly. These properties have led optical spectroscopies to be, quite naturally, key techniques in photosynthesis. However, there are typically many pigments in a photosynthetic assembly, which when combined with the very significant inhomogeneous and homogeneous linewidths characteristic of optical transitions, leads to spectral congestion. This in turn has made it difficult to provide a definitive and detailed electronic structure for many photosynthetic assemblies. An electronic structure is, however, necessary to provide a foundation for any complete description of fundamental processes in photosynthesis, particularly those in reaction centres. A wide range of selective and differential spectral techniques have been developed to help overcome the problems of spectral complexity and congestion. The techniques can serve to either reduce spectral linewidths and/or extract chromophore specific information from unresolved spectral features. Complementary spectral datasets, generated by a number of techniques, may then be combined in a 'multi-dimensional' theoretical analysis so as to constrain and define effective models of photosynthetic assemblies and their fundamental processes. A key example is the work of Renger and his group (Raszewski, Biophys J 88(2):986-998, 2005) on PS II reaction centre assemblies. This article looks to provide an overview of some of these techniques and indicate where their strengths and weaknesses may lie. It highlights some of our own contributions and indicates areas where progress may be possible.

Excitation energy transfer in a classical analogue of photosynthetic antennae

We formulate a classical pure dephasing system-bath interaction model in a full correspondence to the well-studied quantum model of natural light-harvesting antennae. The equations of motion of our classical model not only represent the correct classical analogy to the quantum description of excitonic systems, but they also have exactly the same functional form. We demonstrate derivation of classical dissipation and relaxation tensor in second order perturbation theory. We find that the only difference between the classical and quantum descriptions is in the interpretation of the state and in certain limitations imposed on the parameters of the model by classical physics. The effects of delocalization, transfer pathway interference, and the transition from coherent to diffusive transfer can be found already in the classical realm. The only qualitatively new effect occurring in quantum systems is the preference for a downhill energy transfer and the resulting possibility of trapping the energy in the lowest energy state.

Nonlinear spectroscopic theory of displaced harmonic oscillators with differing curvatures: a correlation function approach

We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.

Understanding photosynthetic light-harvesting: a bottom up theoretical approach

We discuss a bottom up approach for modeling photosynthetic light-harvesting. Methods are reviewed for a full structure-based parameterization of the Hamiltonian of pigment-protein complexes (PPCs). These parameters comprise (i) the local transition energies of the pigments in their binding sites in the protein, the site energies; (ii) the couplings between optical transitions of the pigments, the excitonic couplings; and (iii) the spectral density characterizing the dynamic modulation of pigment transition energies and excitonic couplings by protein vibrations. Starting with quantum mechanics perturbation theory, we provide a microscopic foundation for the standard PPC Hamiltonian and relate the expressions obtained for its matrix elements to quantities that can be calculated with classical molecular mechanics/electrostatics approaches including the whole PPC in atomic detail and using charge and transition densities obtained with quantum chemical calculations on the isolated building blocks of the PPC. In the second part of this perspective, the Hamiltonian is utilized to describe the quantum dynamics of excitons. Situations are discussed that differ in the relative strength of excitonic and exciton-vibrational coupling. The predictive power of the approaches is demonstrated in application to different PPCs, and challenges for future work are outlined.

Normal mode analysis of the spectral density of the Fenna-Matthews-Olson light-harvesting protein: how the protein dissipates the excess energy of excitons

We report a method for the structure-based calculation of the spectral density of the pigment-protein coupling in light-harvesting complexes that combines normal-mode analysis with the charge density coupling (CDC) and transition charge from electrostatic potential (TrEsp) methods for the computation of site energies and excitonic couplings, respectively. The method is applied to the Fenna-Matthews-Olson (FMO) protein in order to investigate the influence of the different parts of the spectral density as well as correlations among these contributions on the energy transfer dynamics and on the temperature-dependent decay of coherences. The fluctuations and correlations in excitonic couplings as well as the correlations between coupling and site energy fluctuations are found to be 1 order of magnitude smaller in amplitude than the site energy fluctuations. Despite considerable amplitudes of that part of the spectral density which contains correlations in site energy fluctuations, the effect of these correlations on the exciton population dynamics and dephasing of coherences is negligible. The inhomogeneous charge distribution of the protein, which causes variations in local pigment-protein coupling constants of the normal modes, is responsible for this effect. It is seen thereby that the same building principle that is used by nature to create an excitation energy funnel in the FMO protein also allows for efficient dissipation of the excitons' excess energy.