The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae

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.

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.

Quantum phase synchronization via exciton-vibrational energy dissipation sustains long-lived coherence in photosynthetic antennas

The lifetime of electronic coherences found in photosynthetic antennas is known to be too short to match the energy transfer time, rendering the coherent energy transfer mechanism inactive. Exciton-vibrational coherence time in excitonic dimers which consist of two chromophores coupled by excitation transfer interaction, can however be much longer. Uncovering the mechanism for sustained coherences in a noisy biological environment is challenging, requiring the use of simpler model systems as proxies. Here, via two-dimensional electronic spectroscopy experiments, we present compelling evidence for longer exciton-vibrational coherence time in the allophycocyanin trimer, containing excitonic dimers, compared to isolated pigments. This is attributed to the quantum phase synchronization of the resonant vibrational collective modes of the dimer, where the anti-symmetric modes, coupled to excitonic states with fast dephasing, are dissipated. The decoupled symmetric counterparts are subject to slower energy dissipation. The resonant modes have a predicted nearly 50% reduction in the vibrational amplitudes, and almost zero amplitude in the corresponding dynamical Stokes shift spectrum compared to the isolated pigments. Our findings provide insights into the mechanisms for protecting coherences against the noisy environment.

Docosahexaenoic Acid Explains the Unexplained in Visual Transduction

In George Wald's Nobel Prize acceptance speech for "discoveries concerning the primary physiological and chemical visual processes in the eye", he noted that events after the activation of rhodopsin are too slow to explain visual reception. Photoreceptor membrane phosphoglycerides contain near-saturation amounts of the omega-3 fatty acid docosahexaenoic acid (DHA). The visual response to a photon is a retinal cis-trans isomerization. The trans-state is lower in energy; hence, a quantum of energy is released equivalent to the sum of the photon and cis-trans difference. We hypothesize that DHA traps this energy, and the resulting hyperpolarization extracts the energized electron, which depolarizes the membrane and carries a function of the photon's energy (wavelength) to the brain. There, it contributes to the creation of the vivid images of our world that we see in our consciousness. This proposed revision to the visual process provides an explanation for these previously unresolved issues around the speed of information transfer and the purity of conservation of a photon's wavelength and supports observations of the unique and indispensable role of DHA in the visual process.

Resonant vibrations produce quantum bridge over high-energy states in heterogeneous antenna

Photosynthetic light-harvesting complexes usually contain several pools of molecules with a big difference in transition energies, for example, chlorophylls a and b in plant antennas. Some pathways of the excitation energy transfer may include pigments from the low-energy pool separated by a site occupied by a high-energy molecule. We demonstrate that such pathways may be functional if high-frequency intramolecular vibrations fall in resonance with the energy gap between the neighboring molecules belonging to different pools. In this case, a vibration-assisted mixing of the excited states can produce delocalized vibronic states playing a role of 'quantum bridge' that facilitates a passage over high-energy barrier. We perform calculations of the excitation dynamics in the model three-state system with the parameters emerging from our previous studies of real antennas. Simulation of the dynamics in an explicit electron-vibrational basis demonstrates that the rate of transfer between the two chlorophylls a through the chlorophyll b intermediate is increased by a factor of 1.7-2 in the presence of resonant vibration. A possible influence of energetic disorder and other (non-resonant) vibrations on this effect is discussed.

Infrared Signatures of Phycobilins within the Phycocyanin 645 Complex

Aquatic photosynthetic organisms evolved to use a variety of light frequencies to perform photosynthesis. Phycobiliprotein phycocyanin 645 (PC645) is a light-harvesting complex in cryptophyte algae able to transfer the absorbed green solar light to other antennas with over 99% efficiency. The infrared signatures of the phycobilin pigments embedded in PC645 are difficult to access and could provide useful information to understand the mechanism behind the high efficiency of energy transfer in PC645. We use visible-pump IR-probe and two-dimensional electronic vibrational spectroscopy to study the dynamical evolution and assign the fingerprint mid-infrared signatures to each pigment in PC645. Here, we report the pigment-specific vibrational markers that enable us to track the spatial flow of excitation energy between the phycobilin pigment pairs. We speculate that two high-frequency modes (1588 and 1596 cm^-1) are involved in the vibronic coupling leading to fast (<ps) and direct energy transfer from the highest to lowest exciton, bypassing the intermediate excitons.

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.

Dyads with tunable near-infrared donor-acceptor excited-state energy gaps: molecular design and Förster analysis for ultrafast energy transfer

Bacteriochlorophylls, nature's near-infrared absorbers, play an essential role in energy transfer in photosynthetic antennas and reaction centers. To probe energy-transfer processes akin to those in photosynthetic systems, nine synthetic bacteriochlorin-bacteriochlorin dyads have been prepared wherein the constituent pigments are joined at the meso-positions by a phenylethyne linker. The phenylethyne linker is an unsymmetric auxochrome, which differentially shifts the excited-state energies of the phenyl- or ethynyl-attached bacteriochlorin constituents in the dyad. Molecular designs utilized known effects of macrocycle substituents to engineer bacteriochlorins with S₀ → S₁ (Q_y) transitions spanning 725-788 nm. The design-predicted donor-acceptor excited-state energy gaps in the dyads agree well with those obtained from time dependent density functional theory calculations and with the measured range of 197-1089 cm^-1. Similar trends with donor-acceptor excited-state energy gaps are found for (1) the measured ultrafast energy-transfer rates of (0.3-1.7 ps)^-1, (2) the spectral overlap integral (J) in Förster energy-transfer theory, and (3) donor-acceptor electronic mixing manifested in the natural transition orbitals for the S₀ → S₁ transition. Subtle outcomes include the near orthogonal orientation of the π-planes of the bacteriochlorin macrocycles, and the substituent-induced shift in transition-dipole moment from the typical coincidence with the NH-NH axis; the two features together afforded the Förster orientation term κ² ranging from 0.55-1.53 across the nine dyads, a value supportive of efficient excited-state energy transfer. The molecular design and collective insights on the dyads are valuable for studies relevant to artificial photosynthesis and other processes requiring ultrafast energy transfer.

Probing the Effects of Electronic-Vibrational Resonance on the Rate of Excited-State Energy Transfer in Bacteriochlorin Dyads

The impact of vibrational-electronic resonances on the rate of excited-state energy transfer is examined in a set of bacteriochlorin dyads that employ the same phenylethyne linker. The donor/acceptor excited-state energy gap is tuned from ∼200 to ∼1100 cm^-1 using peripheral substituents on the donor and acceptor bacteriochlorin macrocycles. Ultrafast energy transfer is observed with rate constants of (0.3 ps)^-1 to (1.7 ps)^-1, which agree with those predicted by Förster theory to within a factor of 2. Furthermore, the measured rates follow a trend-line with only small deviations that do not correlate with the density of vibrations at the donor/acceptor excited-state energy gap. Thus, if vibrational-electronic resonances occur in any of these dyads, which seems likely, the impact on the rate of energy transfer is small.

Long-Range Nonequilibrium Coherent Tunneling Induced by Fractional Vibronic Resonances

We study the influence of a linear energy bias on a nonequilibrium excitation on a chain of molecules coupled to local vibrations (a tilted Holstein model) using both a random-walk rate kernel theory and a nonperturbative, massively parallelized adaptive-basis algorithm. We uncover structured and discrete vibronic resonance behavior fundamentally different from both linear response theory and homogeneous polaron dynamics. Remarkably, resonance between the phonon energy ℏω and the bias δ_ϵ occurs not only at integer but also fractional ratios δ_ϵ/(ℏω) = m/n, which effect long-range n-bond m-phonon tunneling. These observations are reproduced in a model calculation of a recently demonstrated Cy3 system, and the effect of dipole-dipole-type non-nearest-neighbor coupling and vibrationally relaxed initial states is also considered. Potential applications range from molecular electronics to optical lattices and artificial light harvesting via vibronic engineering of coherent quantum transport.

Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals

The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals. The nitrogencentered system ensures strong interchromophore interactions and, thus, the presence of coherences. Nevertheless, the multitude of non-deterministic photoinduced pathways during the ultrafast inter-branch migration of the excitation results in random confinement on some branches and, therefore, spatial exciton scrambling and loss of phase information at long times. We show that the vibronic coherence dynamics evolving into the incoherent scrambling mechanism on ultrafast 50 fs timescale, is accurately probed by the TRUECARS X-ray stimulated Raman signal. In combination with previous results, where the technique has revealed long-lived coherences in a rigid heterodimer, the signal is most valuable for detecting ultrafast molecular coherences or their absence. We demonstrate that X-ray Raman spectroscopy is a useful tool in the chemical design of functional molecular building blocks.

The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals.

Explaining the Efficiency of Photosynthesis: Quantum Uncertainty or Classical Vibrations?

Photosynthetic organisms are known to use a mechanism of vibrationally assisted exciton energy transfer to efficiently harvest energy from light. The importance of quantum effects in this mechanism is a long-standing topic of debate, which has traditionally focused on the role of excitonic coherences. Here, we address another recent claim: that the efficient energy transfer in the Fenna-Matthews-Olson complex relies on nuclear quantum uncertainty and would not function if the vibrations were classical. We present a counter-example to this claim, showing by trajectory-based simulations that a description in terms of quantum electrons and classical nuclei is indeed sufficient to describe the funneling of energy to the reaction center. We analyze and compare these findings to previous classical-nuclear approximations that predicted the absence of an energy funnel and conclude that the key difference and the reason for the discrepancy is the ability of the trajectories to properly account for Newton's third law.

Steady state in strong system-bath coupling regime: Reaction coordinate versus perturbative expansion

Motivated by the growing importance of strong system-bath coupling in several branches of quantum information and related technological applications, we analyze and compare two strategies currently used to obtain (approximately) steady states in strong-coupling regime. The first strategy is based on perturbative expansions while the second one uses reaction coordinate mapping. Focusing on the widely used spin-boson model, we show that the predictions of these two strategies coincide in many situations. This confirms and strengthens the relevance of both techniques. Beyond that, it is also crucial to know precisely their respective range of validity. In that perspective, thanks to their different limitations, we use one to benchmark the other. We introduce and successfully test some very simple validity criteria for both strategies, bringing some answers to the question of the validity range.

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.

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

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

Redox conditions correlated with vibronic coupling modulate quantum beats in photosynthetic pigment-protein complexes

Quantum coherences, observed as time-dependent beats in ultrafast spectroscopic experiments, arise when light-matter interactions prepare systems in superpositions of states with differing energy and fixed phase across the ensemble. Such coherences have been observed in photosynthetic systems following ultrafast laser excitation, but what these coherences imply about the underlying energy transfer dynamics remains subject to debate. Recent work showed that redox conditions tune vibronic coupling in the Fenna-Matthews-Olson (FMO) pigment-protein complex in green sulfur bacteria, raising the question of whether redox conditions may also affect the long-lived (>100 fs) quantum coherences observed in this complex. In this work, we perform ultrafast two-dimensional electronic spectroscopy measurements on the FMO complex under both oxidizing and reducing conditions. We observe that many excited-state coherences are exclusively present in reducing conditions and are absent or attenuated in oxidizing conditions. Reducing conditions mimic the natural conditions of the complex more closely. Further, the presence of these coherences correlates with the vibronic coupling that produces faster, more efficient energy transfer through the complex under reducing conditions. The growth of coherences across the waiting time and the number of beating frequencies across hundreds of wavenumbers in the power spectra suggest that the beats are excited-state coherences with a mostly vibrational character whose phase relationship is maintained through the energy transfer process. Our results suggest that excitonic energy transfer proceeds through a coherent mechanism in this complex and that the coherences may provide a tool to disentangle coherent relaxation from energy transfer driven by stochastic environmental fluctuations.

On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation

Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg-Onuchic-Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrödinger picture coherences can be obtained from interaction picture electronic inputs.

Funneling dynamics in a phenylacetylene trimer: Coherent excitation of donor excitonic states and their superposition

Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.

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.

Vibration-mediated resonant charge separation across the donor-acceptor interface in an organic photovoltaic device

Examination of a recent open-system Ehrenfest dynamics simulation suggests that a vibration-mediate resonance may play a pivotal role in the charge transfer across a donor-acceptor interface in an organic solar cell. Based on this, a concise dissipative two-level electronic system coupled to a molecular vibrational mode is proposed and solved quantum mechanically. It is found that the charge transfer is enhanced substantially when the vibrational energy quanta is equal to the electronic energy loss across the interface. This vibration-mediate resonant charge transfer process is ultrafast, occurring within 100 fs, comparable to experimental findings. The open-system Ehrenfest dynamics simulation of the two-level model is carried out, and similar results are obtained, which confirms further that the earlier open-system Ehrenfest dynamics simulation indeed correctly predicted the occurrence of the resonant charge transfer across the donor-acceptor interface.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

Simulating Quantum Vibronic Dynamics at Finite Temperatures With Many Body Wave Functions at 0 K

For complex molecules, nuclear degrees of freedom can act as an environment for the electronic “system” variables, allowing the theory and concepts of open quantum systems to be applied. However, when molecular system-environment interactions are non-perturbative and non-Markovian, numerical simulations of the complete system-environment wave function become necessary. These many body dynamics can be very expensive to simulate, and extracting finite-temperature results—which require running and averaging over many such simulations—becomes especially challenging. Here, we present numerical simulations that exploit a recent theoretical result that allows dissipative environmental effects at finite temperature to be extracted efficiently from a single, zero-temperature wave function simulation. Using numerically exact time-dependent variational matrix product states, we verify that this approach can be applied to vibronic tunneling systems and provide insight into the practical problems lurking behind the elegance of the theory, such as the rapidly growing numerical demands that can appear for high temperatures over the length of computations.

Collective excitations in α-helical protein structures interacting with the water environment

Low-frequency vibrational excitations of protein macromolecules in the terahertz frequency region are suggested to contribute to many biological processes such as enzymatic catalysis, intra-protein energy/charge transport, recognition, and allostery. To explain high effectiveness of these processes, two possible mechanisms of the long-lived excitation were proposed by H. Fröhlich and A.S. Davydov, which relate to either vibrational modes or solitary waves, respectively. In this paper, we developed a quantum dynamic model of vibrational excitation in α-helical proteins interacting with the aqueous environment. In the model, we distinguished three coupled subsystems, i.e., (i) a chain of hydrogen-bonded peptide groups (PGs), interacting with (ii) the subsystem of the side-chain residuals which in turn interact with (iii) the environment, surrounding water responsible for dissipation and fluctuation in the system. It was shown that the equation of motion for phonon variables of the PG chain can be transformed to nonlinear Schrodinger equation which admits bifurcation into the solution corresponding to the weak-damped vibrational modes (Fröhlich-type regime) and Davydov solitons. A bifurcation parameter is derived through the strength of phonon-phonon interaction between the side-chains and hydration-shell water molecules. As shown, the energy of these excited states is pumped through the interaction of the side-chains with fluctuating water environment of the proteins. The suggested mechanism of the collective vibrational mode excitation is discussed in connection with the recent experiments on the long-lived collective protein excitations in the terahertz frequency region and vibrational energy transport pathways in proteins.

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.

Coherent and incoherent theories for photosynthetic energy transfer

There is a remarkable characteristic of photosynthesis in nature, that is, the energy transfer efficiency is close to 100%. Recently, due to the rapid progress made in the experimental techniques, quantum coherent effects have been experimentally demonstrated. Traditionally, the incoherent theories are capable of calculating the energy transfer efficiency, e.g., (generalized) Förster theory and modified Redfield theory (MRT). However, in order to describe the quantum coherent effects in photosynthesis, one has to exploit coherent theories, such as hierarchical equation of motion (HEOM), quantum path integral, coherent modified Redfield theory (CMRT), small-polaron quantum master equation, and general Bloch-Redfield theory in addition to the Redfield theory. Here, we summarize the main points of the above approaches, which might be beneficial to the quantum simulation of quantum dynamics of exciton energy transfer (EET) in natural photosynthesis, and shed light on the design of artificial light-harvesting devices.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

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.

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.

Dissipation-Assisted Matrix Product Factorization

Charge and energy transfer in biological and synthetic organic materials are strongly influenced by the coupling of electronic states to a highly structured dissipative environment. Nonperturbative simulations of these systems require a substantial computational effort, and current methods can only be applied to large systems if environmental structures are severely coarse grained. Time evolution methods based on tensor networks are fundamentally limited by the times that can be reached due to the buildup of entanglement in time, which quickly increases the size of the tensor representation, i.e., the bond dimension. In this Letter, we introduce a dissipation-assisted matrix product factorization (DAMPF) method that combines a tensor network representation of the vibronic state within a pseudomode description of the environment where a continuous bosonic environment is mapped into a few harmonic oscillators under Lindblad damping. This framework is particularly suitable for a tensor network representation, since damping suppresses the entanglement growth among oscillators and significantly reduces the bond dimension required to achieve a desired accuracy. We show that dissipation removes the "time-wall" limitation of existing methods, enabling the long-time simulation of large vibronic systems consisting of 10-50 sites coupled to 100-1000 underdamped modes in total and for a wide range of parameter regimes. For these reasons, we believe that our formalism will facilitate the investigation of spatially extended systems with applications to quantum biology, organic photovoltaics, and quantum thermodynamics.

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.

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by Two-Dimensional Electronic Spectroscopy

Bacteriochlorophyll a (BChla) is the most abundant pigment found in the Bacterial Reaction Center (BRC) and light-harvesting proteins of photosynthetic purple and green bacteria. Recent two-dimensional electronic spectroscopy (2DES) studies of photosynthetic pigment-protein complexes including the BRC and the Fenna-Matthews-Olson (FMO) complex have shown oscillatory signals, or coherences, whose physical origin has been hotly debated. To better understand the observations of coherence in larger photosynthetic systems, it is important to carefully characterize the spectroscopic signatures of the monomeric pigments. Prior spectroscopic studies of BChla have differed significantly in their observations, with some studies reporting little to no coherence. Here we present evidence of strong coherences in monomeric BChla in isopropanol using 2DES at 77 K. We resolve many modes with frequencies that correspond well with known vibrational modes. We confirm their vibrational origin by comparing the 2D spectroscopic signatures with expectations based on a purely vibrational model.

High Magnetic Field Detunes Vibronic Resonances in Photosynthetic Light Harvesting

The origin and role of oscillatory features detected in recent femtosecond spectroscopy experiments of photosynthetic complexes remain elusive. A key hypothesis underneath of these observations relies on electronic-vibrational resonance, where vibrational levels of an acceptor chromophore match the donor-acceptor electronic gap, accelerating the downhill energy transfer. Here we identify and detune such vibronic resonances using a high magnetic field that exclusively shifts molecular exciton states. We implemented ultrafast pump-probe spectroscopy into a specialized 25 T magnetic field facility and studied the light-harvesting complex PC645 from a cryptophyte algae where strongly coupled chromophores form molecular exciton states. We detected a change in high-frequency coherent oscillations when the field was engaged. Quantum chemical calculations coupled with a vibronic model explain the experiment as a magnetic field-induced shift of the exciton states, which in turn affects the electronic-vibrational resonance between pigments within the protein. Our results demonstrate the delicate sensitivity of interpigment coherent oscillations of vibronic origin to electronic-vibrational resonance interactions in light-harvesting complexes.

Elucidation of near-resonance vibronic coherence lifetimes by nonadiabatic electronic-vibrational state character mixing

Recent work suggests that the long-lived coherences observed in both natural and artificial light-harvesting systems (such as the Fenna-Matthews-Olson complex) could be attributed to the mixing of the pigments' electronic and vibrational degrees of freedom. To investigate the underlying mechanism of these long coherence lifetimes, a sophisticated description of interactions between the molecular aggregates and the nonequilibrium fluctuations in the surrounding environment is necessary. This is done by implementing the hierarchical equations of motion approach on model homodimers, a method used in the intermediate coupling regime for many molecular aggregates wherein the nonequilibrium environment phonons play nontrivial roles in exciton dynamics. Here we report a character change in the vibronic states-reflective of property mixing between the electronic and vibrational states-induced by an interplay between system coupling parameters within the exciton-vibrational near-resonance regime. This mixing dictates vital aspects of coherence lifetime; by tracking the degree of mixing, we are able to elucidate the relationship between coherence lifetime and both the electronic energy fluctuation and the vibrational relaxation dephasing pathways.

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.

Coherent exciton-vibrational dynamics and energy transfer in conjugated organics

Coherence, signifying concurrent electron-vibrational dynamics in complex natural and man-made systems, is currently a subject of intense study. Understanding this phenomenon is important when designing carrier transport in optoelectronic materials. Here, excited state dynamics simulations reveal a ubiquitous pattern in the evolution of photoexcitations for a broad range of molecular systems. Symmetries of the wavefunctions define a specific form of the non-adiabatic coupling that drives quantum transitions between excited states, leading to a collective asymmetric vibrational excitation coupled to the electronic system. This promotes periodic oscillatory evolution of the wavefunctions, preserving specific phase and amplitude relations across the ensemble of trajectories. The simple model proposed here explains the appearance of coherent exciton-vibrational dynamics due to non-adiabatic transitions, which is universal across multiple molecular systems. The observed relationships between electronic wavefunctions and the resulting functionalities allows us to understand, and potentially manipulate, excited state dynamics and energy transfer in molecular materials.

Mechanistic Regimes of Vibronic Transport in a Heterodimer and the Design Principle of Incoherent Vibronic Transport in Phycobiliproteins

Following the observation of coherent oscillations in nonlinear spectra of photosynthetic pigment protein complexes, in particular, phycobilliproteins such as PC645, coherent vibronic transport has been suggested as a design principle for novel light-harvesting materials. Vibronic transport between energetically remote pigments is coherent when the presence of a vibration resonant with the electronic energy gap supports transient delocalization between the electronic excited states. We establish the mechanism of vibronic transport for a model heterodimer across a wide range of molecular parameter values. The resulting mechanistic map demonstrates that the molecular parameters of phycobiliproteins in fact support incoherent vibronic transport. This result points to an important design principle: Incoherent vibronic transport is more efficient than a coherent mechanism when energetic disorder exceeds the coupling between the donor and vibrationally excited acceptor states. Finally, our results suggest that the role of coherent vibronic transport in pigment protein complexes should be reevaluated.

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.

Quantum Redirection of Antenna Absorption to Photosynthetic Reaction Centers

The early steps of photosynthesis involve the photoexcitation of reaction centers (RCs) and light-harvesting (LH) units. Here, we show that the historically overlooked excitonic delocalization across RC and LH pigments results in a redistribution of absorption amplitudes that benefits the absorption cross section of the optical bands associated with the RC of several species. While we prove that this redistribution is robust to the microscopic details of the dephasing between these units in the purple bacterium Rhodospirillum rubrum, we are able to show that the redistribution witnesses a more fragile, but persistent, coherent population dynamics which directs excitations from the LH toward the RC units under incoherent illumination and physiological conditions. Even though the redirection does not seem to affect importantly the overall efficiency in photosynthesis, stochastic optimization allows us to delineate clear guidelines and develop simple analytic expressions in order to amplify the coherent redirection in artificial nanostructures.