Vibronic resonances facilitate excited-state coherence in light-harvesting proteins at room temperature

Frequency-Dependent Vibronic Effects in Steady State Energy Transport

The interplay between electronic and intramolecular high-frequency vibrational degrees of freedom is ubiquitous in natural light-harvesting systems. Recent studies have indicated that an intramolecular vibrational donor-acceptor frequency difference can enhance energy transport. Here, we analyze the extent to which different intramolecular donor-acceptor vibrational frequencies affect excitation energy transport in the natural nonequilibrium steady state configuration. Comments are included on the less physical equilibrium case for comparison with the literature. It is found that for constant Huang-Rhys factors, whereas the acceptor population increases in the equilibrium case when the intramolecular vibrational frequency of the acceptor exceeds that of the donor, this increase is negligible for the nonequilibrium steady state. Therefore, these changes in acceptor population do not significantly enhance energy transport in the nonequilibrium steady state for the natural scenario of incoherent light excitation with biologically relevant parameters of typical photosynthetic complexes. Insight about a potential mechanism to optimize energy transfer in the nonequilibrium steady state based on increasing the harvesting time at the reaction center is analyzed.

Chirped Laser Pulse Control of Vibronic Wavepackets and Energy Transfer in Phycocyanin 645

Photosynthetic organisms use light-harvesting complexes to increase the spectrum of light that they absorb from solar photons. Recent ultrafast spectroscopic studies have revealed that efficient (sub-ps) energy transfer is mediated by vibronic coherence in the phycobiliprotein phycocyanin 645 (PC645). Here, we report studies that employ broadband pump-probe spectroscopy with linearly chirped excitation pulses to further investigate the relationship between vibronic state preparation and energy transfer dynamics in PC645. Negatively chirped pulse excitation is found to enhance wavepackets of a high-frequency mode (1580 cm-1) and increase the rate of downhill energy transfer, while on the other hand, positively chirped pulses suppress these oscillatory features and decrease this rate. Model calculations incorporating the influence of the chirped pump pulse are used to understand its effect on initial state preparation. These results provide mechanistic insight into how the overall nonequilibrium rate of energy transfer is influenced by initial state preparation.

Electronic-Vibrational Resonance Does Not Significantly Alter Steady-State Transport in Natural Light-Harvesting Systems

Oscillations in time-dependent two-dimensional electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state; therefore, the relevance of these arguments to the natural process is unclear. Here, we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. Specifically, we analyze the PEB dimer in the cryptophyte algae PE545 antenna protein. It is found that vibrations resonant with the energy difference between exciton states only marginally increase the quantum yield and the imaginary part of the intersite coherence that is relevant for transport compared to non-resonant vibrations in the natural non-equilibrium steady-state. That is, the electronic-vibrational resonance interaction does not significantly enhance energy transport under natural incoherent light excitation conditions.

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.

Role of Spatially Correlated Fluctuations in Photosynthetic Excitation Energy Transfer with an Equilibrium and a Nonequilibrium Initial Bath

The transfer of excitation energy in photosynthetic light-harvesting complexes has inspired growing interest for its scientific and engineering significance. Recent experimental findings have suggested that spatially correlated environmental fluctuations may account for the existence of long-lived quantum coherent energy transfer observed even at physiological temperature. In this paper, we investigate the effects of spatial correlations on the excitation energy transfer dynamics by including a nonequilibrium initial bath in a simulated donor-acceptor model. The initial bath state, which is assumed to be either equilibrium or nonequilibrium, is expanded in powers of coupling strength within the polaron formalism of a quantum master equation. The spatial correlations of bath fluctuations strongly influence the decay of coherence in the dynamics. The role of a nonequilibrium initial bath is also influenced by spatial correlations and becomes the most conspicuous for certain degrees of spatial correlations from which we propose a picture that the spatial correlations of bath fluctuations open up new energy transfer pathways, playing a role of protecting coherence. Besides, we apply the polaron master equation approach to study the dynamics in a two-site subsystem of the FMO complex and provide a practical example that shows the versatility of this approach.

Coherent Speedup of Excitation Energy Transfer in PC645

The fundamental principle governing the robust excitation energy transfer (EET) in the light-harvesting complexes remained elusive. Recent spectroscopic observations of the EET attract attention toward the role of the quantum effects in the biological systems. In this study, along with the time evolution, the distance between the quantum states of the pigments is also considered for a detailed illustration of the effect of the quantum coherence on the speed of the excitation transfer. The comparative analysis of the coherently delocalized EET with the incoherent discrete hopping reveals that the coherent superposition speedup the excitation transfer process, for instance, with the initially localized excitation, coherence provides a ∼4-fold enhancement to the excitation transfer rate.

Nonadiabatic sunlight harvesting

Experimental and theoretical evidence points out the crucial role of specific intramolecular vibrational modes resonant with excitonic splittings in the interpretation of long-lived coherences observed in the two-dimensional spectra of some natural and synthetic light harvesting complexes. For the natural situation of illumination by incoherent (sun)light, the relevance of these vibrations is analyzed here for light-harvesting vibronic prototype dimers. The detailed analysis of the density matrix dynamics reveals that the inclusion of intramolecular vibrational modes reinforces the exciton coherence up to one order of magnitude and may increase the populations of lowest energy single exciton states, as well as populations and coherences in the site basis. In sharp contrast to the case of initial-state preparation by coherent (laser)light-sources, the initial thermal state of the local vibrational modes, as well as that of the anticorrelated vibrational mode, evolves devoid of non-classical correlations as confirmed by the absence of negative values of its phase-space quasi-probability distribution at all times. Therefore, not only the long-lived coherences observed in the two-dimensional spectra are induced by the coherent character of pulsed laser sources, but it is unambiguously shown here that the non-classical character generally assigned to the anticorrelated vibrational mode also comes as the result of the preparation of the initial state by coherent pulsed laser sources.

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.

Variety, the spice of life and essential for robustness in excitation energy transfer in light-harvesting complexes

For over a decade there has been some significant excitement and speculation that quantum effects may be important in the excitation energy transport process in the light harvesting complexes of certain bacteria and algae, in particular via the Fenna-Matthews-Olsen (FMO) complex. Whilst the excitement may have waned somewhat with the realisation that the observed long-lived oscillations in two-dimensional electronic spectra of FMO are probably due to vibronic coherences, it remains a question whether these coherences may play any important role. We review our recent work showing how important the site-to-site variation in coupling between chloroplasts in FMO and their protein scaffold environment is for energy transport in FMO and investigate the role of vibronic modes in this transport. Whilst the effects of vibronic excitations seem modest for FMO, we show that for bilin-based pigment-protein complexes of marine algae, in particular PC645, the site-dependent vibronic excitations seem essential for robust excitation energy transport, which may again open the door for important quantum effects to be important in these photosynthetic complexes.

Multicolor Quantum Control for Suppressing Ground State Coherences in Two-Dimensional Electronic Spectroscopy

The measured multidimensional spectral response of different light harvesting complexes exhibits oscillatory features which suggest an underlying coherent energy transfer. However, making this inference rigorous is challenging due to the difficulty of isolating excited state coherences in highly congested spectra. In this work, we provide a coherent control scheme that suppresses ground state coherences, thus making rephasing spectra dominated by excited state coherences. We provide a benchmark for the scheme using a model dimeric system and numerically exact methods to analyze the spectral response. We argue that combining temporal and spectral control methods can facilitate a second generation of experiments that are tailored to extract desired information and thus significantly advance our understanding of complex open many-body structure and dynamics.

Effect of an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions on excitation energy transfer

A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton-phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton-phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.

From Fundamental Theories to Quantum Coherences in Electron Transfer

Photoinduced electron transfer (ET) is a cornerstone of energy transduction from light to chemistry. The past decade has seen tremendous advances in the possible role of quantum coherent effects in the light-initiated energy and ET processes in chemical, biological, and materials systems. The prevalence of such coherence effects holds a promise to increase the efficiency and robustness of transport even in the face of energetic or structural disorder. A primary motive of this Perspective is to work out how to think about "coherence" in ET reactions. We will discuss how the interplay of basic parameters governing ET reactions-like electronic coupling, interactions with the environment, and intramolecular high-frequency quantum vibrations-impact coherences. This includes revisiting the insights from the seminal work on the theory of ET and time-resolved measurements on coherent dynamics to explore the role of coherences in ET reactions. We conclude by suggesting that in addition to optical spectroscopies, validating the functional role of coherences would require simultaneous mapping of correlated electron motion and atomically resolved nuclear structure.

Coherent phenomena in photosynthetic light harvesting: part two-observations in biological systems

Considerable debate surrounds the question of whether or not quantum mechanics plays a significant, non-trivial role in photosynthetic light harvesting. Many have proposed that quantum superpositions and/or quantum transport phenomena may be responsible for the efficiency and robustness of energy transport present in biological systems. The critical experimental observations comprise the observation of coherent oscillations or "quantum beats" via femtosecond laser spectroscopy, which have been observed in many different light harvesting systems. Part Two of this review aims to provide an overview of experimental observations of energy transfer in the most studied light harvesting systems. Length scales, derived from crystallographic studies, are combined with energy and time scales of the beats observed via spectroscopy. A consensus is emerging that most long-lived (hundreds of femtoseconds) coherent phenomena are of vibrational or vibronic origin, where the latter may result in coherent excitation transport within a protein complex. In contrast, energy transport between proteins is likely to be incoherent in nature. The question of whether evolution has selected for these non-trivial quantum phenomena may be an unanswerable question, as dense packings of chromophores will lead to strong coupling and hence non-trivial quantum phenomena. As such, one cannot discern whether evolution has optimised light harvesting systems for high chromophore density or for the ensuing quantum effects as these are inextricably linked and cannot be switched off.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

Theory of Excitonic Delocalization for Robust Vibronic Dynamics in LH2

Nonlinear spectroscopy has revealed long-lasting oscillations in the optical response of a variety of photosynthetic complexes. Different theoretical models that involve the coherent coupling of electronic (excitonic) or electronic-vibrational (vibronic) degrees of freedom have been put forward to explain these observations. The ensuing debate concerning the relevance of either mechanism may have obscured their complementarity. To illustrate this balance, we quantify how the excitonic delocalization in the LH2 unit of Rhodopseudomonas acidophila purple bacterium leads to correlations of excitonic energy fluctuations, relevant coherent vibronic coupling, and importantly, a decrease in the excitonic dephasing rates. Combining these effects, we identify a feasible origin for the long-lasting oscillations observed in fluorescent traces from time-delayed two-pulse single-molecule experiments performed on this photosynthetic complex and use this approach to discuss the role of this complementarity in other photosynthetic systems.

Vibronic Wavepackets and Energy Transfer in Cryptophyte Light-Harvesting Complexes

Determining the key features of high-efficiency photosynthetic energy transfer remains an ongoing task. Recently, there has been evidence for the role of vibronic coherence in linking donor and acceptor states to redistribute oscillator strength for enhanced energy transfer. To gain further insights into the interplay between vibronic wavepackets and energy-transfer dynamics, we systematically compare four structurally related phycobiliproteins from cryptophyte algae by broad-band pump-probe spectroscopy and extend a parametric model based on global analysis to include vibrational wavepacket characterization. The four phycobiliproteins isolated from cryptophyte algae are two "open" structures and two "closed" structures. The closed structures exhibit strong exciton coupling in the central dimer. The dominant energy-transfer pathway occurs on the subpicosecond timescale across the largest energy gap in each of the proteins, from central to peripheral chromophores. All proteins exhibit a strong 1585 cm^-1 coherent oscillation whose relative amplitude, a measure of vibronic intensity borrowing from resonance between donor and acceptor states, scales with both energy-transfer rates and damping rates. Central exciton splitting may aid in bringing the vibronically linked donor and acceptor states into better resonance resulting in the observed doubled rate in the closed structures. Several excited-state vibrational wavepackets persist on timescales relevant to energy transfer, highlighting the importance of further investigation of the interplay between electronic coupling and nuclear degrees of freedom in studies on high-efficiency photosynthesis.

Local protein solvation drives direct down-conversion in phycobiliprotein PC645 via incoherent vibronic transport

The mechanisms controlling excitation energy transport (EET) in light-harvesting complexes remain controversial. Following the observation of long-lived beats in 2D electronic spectroscopy of PC645, vibronic coherence, the delocalization of excited states between pigments supported by a resonant vibration, has been proposed to enable direct excitation transport from the highest-energy to the lowest-energy pigments, bypassing a collection of intermediate states. Here, we instead show that for phycobiliprotein PC645 an incoherent vibronic transport mechanism is at play. We quantify the solvation dynamics of individual pigments using ab initio quantum mechanics/molecular mechanics (QM/MM) nuclear dynamics. Our atomistic spectral densities reproduce experimental observations ranging from absorption and fluorescence spectra to the timescales and selectivity of down-conversion observed in transient absorption measurements. We construct a general model for vibronic dimers and establish the parameter regimes of coherent and incoherent vibronic transport. We demonstrate that direct down-conversion in PC645 proceeds incoherently, enhanced by large reorganization energies and a broad collection of high-frequency vibrations. We suggest that a similar incoherent mechanism is appropriate across phycobiliproteins and represents a potential design principle for nanoscale control of EET.

Estimation of damped oscillation associated spectra from ultrafast transient absorption spectra

When exciting a complex molecular system with a short optical pulse, all chromophores present in the system can be excited. The resulting superposition of electronically and vibrationally excited states evolves in time, which is monitored with transient absorption spectroscopy. We present a methodology to resolve simultaneously the contributions of the different electronically and vibrationally excited states from the complete data. The evolution of the excited states is described with a superposition of damped oscillations. The amplitude of a damped oscillation cos(ω_nt)exp(-γ_nt) as a function of the detection wavelength constitutes a damped oscillation associated spectrum DOAS_n(λ) with an accompanying phase characteristic φ_n(λ). In a case study, the cryptophyte photosynthetic antenna complex PC612 which contains eight bilin chromophores was excited by a broadband optical pulse. Difference absorption spectra from 525 to 715 nm were measured until 1 ns. The population dynamics is described by four lifetimes, with interchromophore equilibration in 0.8 and 7.5 ps. We have resolved 24 DOAS with frequencies between 130 and 1649 cm^-1 and with damping rates between 0.9 and 12 ps^-1. In addition, 11 more DOAS with faster damping rates were necessary to describe the "coherent artefact." The DOAS contains both ground and excited state features. Their interpretation is aided by DOAS analysis of simulated transient absorption signals resulting from stimulated emission and ground state bleach.

Origin of long-lived quantum coherence and excitation dynamics in pigment-protein complexes

We explore the mechanism for the long-lived quantum coherence by considering the discrete phonon modes: these vibrational modes effectively weaken the exciton-environment interaction, due to the new composite (polaron) formed by excitons and vibrons. This subsequently demonstrates the role of vibrational coherence which greatly contributes to long-lived feature of the excitonic coherence that has been observed in femtosecond experiments. The estimation of the timescale of coherence elongated by vibrational modes is given in an analytical manner. To test the validity of our theory, we study the pigment-protein complex in detail by exploring the energy transfer and coherence dynamics. The ground-state vibrational coherence generated by incoherent radiations is shown to be long-survived and is demonstrated to be significant in promoting the excitation energy transfer. This is attributed to the nonequilibriumness of the system caused by the detailed-balance-breaking, which funnels the downhill migration of excitons.

Size-Independent Energy Transfer in Biomimetic Nanoring Complexes

Supramolecular antenna-ring complexes are of great interest due to their presence in natural light-harvesting complexes. While such systems are known to provide benefits through robust and efficient energy funneling, the relationship between molecular structure, strain (governed by nuclear coordinates and motion), and energy dynamics (arising from electronic behavior) is highly complex. We present a synthetic antenna-nanoring system based on a series of conjugated porphyrin chromophores ideally suited to explore such effects. By systematically varying the size of the acceptor nanoring, we reveal the interplay between antenna-nanoring binding, local strain, and energy dynamics on the picosecond time scale. Binding of the antenna unit creates a local strain in the nanoring, and this strain was measured as a function of the size of the nanoring, by UV-vis-NIR titration, providing information on the conformational flexibility of the system. Strikingly, the energy-transfer rate is independent of nanoring size, indicating the existence of strain-localized acceptor states, spread over about six porphyrin units, arising from the noncovalent antenna-nanoring association.

Locally Broken Crystal Symmetry Facilitates Singlet Exciton Fission

Photovoltaic yield is normally limited to at most two charge carriers per photon. In solid pentacene this limit may be potentially bypassed owing to singlet exciton fission into a pair of triplets. The process occurs via a superexchange mechanism mediated by charge-transfer (CT) configurations and is sensitive to their energies. As demonstrated recently, these strongly depend on the local environment of the two molecules on which the charges reside. Using a multiscale model, here we show that in the crystal bulk approximate local symmetry affects CT state energetics in a way unfavorable for fission, so that at the places where this symmetry is broken the fission probability is enhanced by up to an order of magnitude. These fission-favorable locations entail the vicinity of vacancies, specific impurities, and interfaces, such as crystallite boundaries. Hence, photovoltaic yield might be substantially increased by using nanoscopically disordered pentacene rather than highly ordered specimens.

The Role of Resonant Vibrations in Electronic Energy Transfer

Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.