First-Principles Models for Biological Light-Harvesting: Phycobiliprotein Complexes from Cryptophyte Algae

General framework for quantifying dissipation pathways in open quantum systems. II. Numerical validation and the role of non-Markovianity

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1-214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics.

General framework for quantifying dissipation pathways in open quantum systems. I. Theoretical formulation

We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.

Insights into Energy Transfer in Light-Harvesting Complex II Through Machine-Learning Assisted Simulations

Light-harvesting complex II (LHCII) is the major antenna of higher plants. Energy transfer processes taking place inside its aggregate of chlorophylls have been experimentally investigated with time-resolved techniques, but a complete understanding of the most relevant energy transfer pathways and relative characteristic times remains elusive. Theoretical models to disentangle experimental data in LHCII have long been challenged by the large size and complex nature of the system. Here, we show that a fully first-principles approach combining molecular dynamics and machine learning can be successfully used to reproduce transient absorption spectra and characterize the EET pathways and the involved times.

Taming the third order cumulant approximation to linear optical spectroscopy

The second order cumulant method offers a promising pathway to predicting optical properties in condensed phase systems. It allows for the computation of linear absorption spectra from excitation energy fluctuations sampled along molecular dynamics (MD) trajectories, fully accounting for vibronic effects, direct solute-solvent interactions, and environmental polarization effects. However, the second order cumulant approximation only guarantees accurate line shapes for energy gap fluctuations obeying Gaussian statistics. A third order correction has recently been derived but often yields unphysical spectra or divergent line shapes for moderately non-Gaussian fluctuations due to the neglect of higher order terms in the cumulant expansion. In this work, we develop a corrected cumulant approach, where the collective effect of neglected higher order contributions is approximately accounted for through a dampening factor applied to the third order cumulant term. We show that this dampening factor can be expressed as a function of the skewness and kurtosis of energy gap fluctuations and can be parameterized from a large set of randomly sampled model Hamiltonians for which exact spectral line shapes are known. This approach is shown to systematically remove unphysical contributions in the form of negative absorbances from cumulant spectra in both model Hamiltonians and condensed phase systems sampled from MD and dramatically improves over the second order cumulant method in describing systems exhibiting Duschinsky mode mixing effects. We successfully apply the approach to the coumarin-153 dye in toluene, obtaining excellent agreement with experiment.

Intermolecular resonance energy transfer between two lutein pigments in light-harvesting complex II studied by frenkel exciton models

The energy transfer pathways in light-harvesting complex II are complicated and the discovery of the energy transfer between the two luteins revealed an unelucidated important role of carotenoids in the energy flow. This energy transfer between the two S2 states of luteins was for the first time investigated using Frenkel exciton models, using a hybrid scheme of molecular mechanics and quantum mechanics. The results show the energy flow between the two luteins under the Förster resonance energy transfer mechanism. The energy transfer caused by energy level resonance occurs in configurations with small energy gaps. This energy transfer pathway is particularly sensitive to conformation. Moreover, according to the statistical characteristics of the data of the energy gaps and coupling values between LUTs, we proposed stochastic exciton Hamiltonian models to facilitate clarification of the energy transfer among pigments in antenna complexes.

Unraveling the role of thermal fluctuations on the exciton structure of the cryptophyte PC612 and PC645 photosynthetic antenna complexes

Protein scaffolds play a crucial role in tuning the light harvesting properties of photosynthetic pigment-protein complexes, influencing pigment-protein and pigment-pigment excitonic interactions. Here, we investigate the influence of thermal dynamic effects on the protein tuning mechanisms of phycocyanin PC645 and PC612 antenna complexes of cryptophyte algae, featuring closed or open quaternary structures. We employ a dual molecular dynamics (MD) strategy that combines extensive classical MD simulations with multiple short Born-Oppenheimer quantum/molecular mechanical (QM/MM) simulations to accurately account for both static and dynamic disorder effects. Additionally, we compare the results with an alternative protocol based on multiple QM/MM geometry optimizations of the pigments. Subsequently, we employ polarizable QM/MM calculations using time-dependent density functional theory (TD-DFT) to compute the excited states, and we adopt the full cumulant expansion (FCE) formalism to describe the absorption and circular dichroism spectra. Our findings indicate that thermal effects have only minor impacts on the energy ladder in PC612, despite its remarkable flexibility owing to an open quaternary structure. In striking contrast, thermal effects significantly influence the properties of PC645 due to the absence of a hydrogen bond controlling the twist of ring D in PCB β82 bilins, as well as the larger impact of fluctuations on the excited states of MBV pigments, which possess a higher conjugation length compared to other bilin types. Overall, the dual MD protocol combined with the FCE formalism yields excellent spectral properties for PC612 and PC645, and the resultant excitonic Hamiltonians pave the way for future investigations concerning the implications of open and closed quaternary structures on phycocyanin light harvesting properties.

Reconstruction of Nuclear Ensemble Approach Electronic Spectra Using Probabilistic Machine Learning

The theoretical prediction of molecular electronic spectra by means of quantum mechanical (QM) computations is fundamental to gain a deep insight into many photophysical and photochemical processes. A computational strategy that is attracting significant attention is the so-called Nuclear Ensemble Approach (NEA), that relies on generating a representative ensemble of nuclear geometries around the equilibrium structure and computing the vertical excitation energies (ΔE) and oscillator strengths (f) and phenomenologically broadening each transition with a line-shaped function with empirical full-width δ. Frequently, the choice of δ is carried out by visually finding the trade-off between artificial vibronic features (small δ) and over-smoothing of electronic signatures (large δ). Nevertheless, this approach is not satisfactory, as it relies on a subjective perception and may lead to spectral inaccuracies overall when the number of sampled configurations is limited due to an excessive computational burden (high-level QM methods, complex systems, solvent effects, etc.). In this work, we have developed and tested a new approach to reconstruct NEA spectra, dubbed GMM-NEA, based on the use of Gaussian Mixture Models (GMMs), a probabilistic machine learning algorithm, that circumvents the phenomenological broadening assumption and, in turn, the use of δ altogether. We show that GMM-NEA systematically outperforms other data-driven models to automatically select δ overall for small datasets. In addition, we report the use of an algorithm to detect anomalous QM computations (outliers) that can affect the overall shape and uncertainty of the NEA spectra. Finally, we apply GMM-NEA to predict the photolysis rate for HgBrOOH, a compound involved in Earth's atmospheric chemistry.

The atomistic modeling of light-harvesting complexes from the physical models to the computational protocol

The function of light-harvesting complexes is determined by a complex network of dynamic interactions among all the different components: the aggregate of pigments, the protein, and the surrounding environment. Complete and reliable predictions on these types of composite systems can be only achieved with an atomistic description. In the last few decades, there have been important advances in the atomistic modeling of light-harvesting complexes. These advances have involved both the completeness of the physical models and the accuracy and effectiveness of the computational protocols. In this Perspective, we present an overview of the main theoretical and computational breakthroughs attained so far in the field, with particular focus on the important role played by the protein and its dynamics. We then discuss the open problems in their accurate modeling that still need to be addressed. To illustrate an effective computational workflow for the modeling of light harvesting complexes, we take as an example the plant antenna complex CP29 and its H111N mutant.

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.

Three States Involving Vibronic Resonance is a Key to Enhancing Reverse Intersystem Crossing Dynamics of an Organoboron-Based Ultrapure Blue Emitter

The recently developed narrow-band blue-emitting organoboron chromophores based on the multiple-resonance (MR) effect have now become one of the most important components for constructing efficient organic light emitting diodes (OLEDs). While they basically emit through fluorescence, they are also known for showing substantial thermally activated delayed fluorescence (TADF) even with a relatively large singlet-triplet gap (ΔE _ST). Indeed, understanding the reverse intersystem crossing (RISC) dynamics behind this peculiar TADF will allow judicious molecular designs toward achieving better performing OLEDs. Explaining the underlying nonadiabatic spin-flip mechanism, however, has often been equivocal, and how the sufficiently fast RISC takes place even with the sizable ΔE _ST and vanishingly small spin-orbit coupling is not well understood. Here, we show that a vibronic resonance, namely the frequency matching condition between the vibration and the electronic energy gap, orchestrates three electronic states together and this effect plays a major role in enhancing RISC in a typical organoboron emitter. Interestingly, the mediating upper electronic state is quite high in energy to an extent that its thermal population is vanishingly small. Through semiclassical quantum dynamics simulations, we further show that the geometry dependent non-Condon coupling to the upper triplet state that oscillates with the frequency ΔE _ST/ℏ is the main driving force behind the peculiar resonance enhancement. The existence of an array of vibrational modes with strong vibronic rate enhancements provides the ability to sustain efficient RISC over a range of ΔE _ST in defiance of the energy gap law, which can render the MR-emitters peculiar in comparison with more conventional donor-acceptor type emitters. Our investigation may provide a new guide for future blue emitting molecule developments.

Influence of solution phase environmental heterogeneity and fluctuations on vibronic spectra: Perylene diimide molecular chromophore complexes in solution

Ensembles of ab initio parameterized Frenkel-exciton model Hamiltonians for different perylene diimide dimer systems are used, together with various dissipative quantum dynamics approaches, to study the influence of the solvation environment and fluctuations in chromophore relative orientation and packing on the vibronic spectra of two different dimer systems: a π-stacked dimer in aqueous solution in which the relative chromophore geometry is strongly confined by a phosphate bridge and a side-by-side dimer in dichloromethane involving a more flexible alkyne bridge that allows quasi-free rotation of the chromophores relative to one another. These entirely first-principles calculations are found to accurately reproduce the main features of the experimental absorption spectra, providing a detailed mechanistic understanding of how the structural fluctuations and environmental interactions influence the vibronic dynamics and spectroscopy of solutions of these multi-chromophore complexes.

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Theory of dissipation pathways in open quantum systems

We introduce a simple and effective method to decompose the energy dissipation in the dynamics of open quantum systems into contributions due to individual bath components. The method is based on a vibronic extension of the Förster resonance energy transfer theory that enables quantifying the energy dissipated by specific bath degrees of freedom. Its accuracy is determined by benchmarking against mixed quantum-classical simulations that reveal that the method provides a semi-quantitative frequency-dependent decomposition of the overall dissipation. The utility of the method is illustrated by using a model donor-acceptor pair interacting to a thermal harmonic bath with different coupling strengths. The method can be used to identify the key features of a bath that leads to energy dissipation as required to develop a deep understanding of the dynamics of open quantum systems and to engineer environments with desired dissipative features.

Absorption and Circular Dichroism Spectra of Molecular Aggregates With the Full Cumulant Expansion

The exciton Hamiltonian of multichromophoric aggregates can be probed by spectroscopic techniques such as linear absorption and circular dichroism. To compare calculated Hamiltonians to experiments, a lineshape theory is needed, which takes into account the coupling of the excitons with inter- and intramolecular vibrations. This coupling is normally introduced in a perturbative way through the cumulant expansion formalism and further approximated by assuming a Markovian exciton dynamics, for example with the modified Redfield theory. Here, we present the implementation of the full cumulant expansion (FCE) formalism (J. Chem. Phys.142, 2015, 09410625747060) to efficiently compute absorption and circular dichroism spectra of molecular aggregates beyond the Markov approximation, without restrictions on the form of exciton–phonon coupling. By employing the LH2 system of purple bacteria as a challenging test case, we compare the FCE lineshapes with the Markovian lineshapes obtained with the modified Redfield theory, showing that the latter presents a less satisfying agreement with experiments. The FCE approach instead accurately describes the lineshapes, especially in the vibronic sideband of the B800 peak. We envision that the FCE approach will become a valuable tool for accurately comparing model exciton Hamiltonians with optical spectroscopy experiments.

Exploiting Machine Learning to Efficiently Predict Multidimensional Optical Spectra in Complex Environments

The excited-state dynamics of chromophores in complex environments determine a range of vital biological and energy capture processes. Time-resolved, multidimensional optical spectroscopies provide a key tool to investigate these processes. Although theory has the potential to decode these spectra in terms of the electronic and atomistic dynamics, the need for large numbers of excited-state electronic structure calculations severely limits first-principles predictions of multidimensional optical spectra for chromophores in the condensed phase. Here, we leverage the locality of chromophore excitations to develop machine learning models to predict the excited-state energy gap of chromophores in complex environments for efficiently constructing linear and multidimensional optical spectra. By analyzing the performance of these models, which span a hierarchy of physical approximations, across a range of chromophore-environment interaction strengths, we provide strategies for the construction of machine learning models that greatly accelerate the calculation of multidimensional optical spectra from first principles.

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

Photopigment, Absorption, and Growth Responses of Marine Cryptophytes to Varying Spectral Irradiance

The underwater light field of lakes, estuaries, and oceans may vary greatly in spectral composition. Phytoplankton in these environments must contain pigments that absorb the available colors of light. If spectral quality changes, acclimation to the new spectral environment would confer an ecological advantage in terms of photosynthesis and growth. Here, we explored the capacity of eight marine cryptophytes to adjust pigmentation in response to changes in spectral irradiance and related effects on light absorption, photosynthetically useable radiation (PUR), and growth rate. The pigment composition of all species changed in some way in response to shifts in spectral irradiance, but not all pigment changes could be considered advantageous in the context of chromatic acclimation. For most species, absorption by chl-a and chl-c₂ resulted in highest absorption in the blue region, highest PUR values for blue-light grown cells, and highest growth rates in blue light. The exception was Chroomonas mesostigmatica (CCMP 1168), which contains a high percentage of Cryptophyte-Phycocyanin (Cr-PC) 645, absorbs strongly in the orange-to-red region of the spectrum, and grew fastest under red light. The position and magnitude of the maximum and secondary absorption peak of Cr-PC 569, the phycobiliprotein pigment of Hemiselmis cryptochromatica, varied with spectral irradiance. The underlying cause remains unknown, but may represent a mechanism by which cryptophytes optimize photon capture.

Modeling multidimensional spectral lineshapes from first principles: application to water-solvated adenine

We theoretically describe spectral lineshape from first principles, providing insight into solvent–solute interactions in terms of static and dynamic disorder and how these shape experimental signals in linear and non-linear optical spectroscopies.

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.

Quantum dynamics of vibration-assisted excitation energy transfer in phycobiliprotein light-harvesting complex

Phycobiliprotein is a light-harvesting complex containing linear tetrapyrrole bilin pigments that are responsible for absorption and funneling the sun's energy in cryptophytes algae. In particular, the protein structure determines relative positions and orientations of the pigments and thus controls energy transfer pathways. The present research reveals the impact of molecular vibrations (in the 850-2700 cm^-1 region) on excitation energy transfer in phycobiliprotein. The analysis of the excitation energy transfer pathways indicates a possibility of the coherent mechanism of energy transfer (delocalization) in central dihydrobiliverdin pigments and incoherent vibration-assisted energy transfer to peripheral phycocyanobilin pigments at a sub-picosecond time scale. A computational approach that enables modeling the dynamics of the excitation energy transfer with the quantum master equation formalism employing Huang-Rhys factors to describe electronic-vibrational coupling has been developed. The computational methodology has been implemented in PyFREC software.

Successes & challenges in the atomistic modeling of light-harvesting and its photoregulation

Light-harvesting is a crucial step of photosynthesis. Its mechanisms and related energetics have been revealed by a combination of experimental investigations and theoretical modeling. The success of theoretical modeling is largely due to the application of atomistic descriptions combining quantum chemistry, classical models and molecular dynamics techniques. Besides the important achievements obtained so far, a complete and quantitative understanding of how the many different light-harvesting complexes exploit their structural specificity is still missing. Moreover, many questions remain unanswered regarding the mechanisms through which light-harvesting is regulated in response to variable light conditions. Here we show that, in both fields, a major role will be played once more by atomistic descriptions, possibly generalized to tackle the numerous time and space scales on which the regulation takes place: going from the ultrafast electronic excitation of the multichromophoric aggregate, through the subsequent conformational changes in the embedding protein, up to the interaction between proteins.

Determination of the protonation preferences of bilin pigments in cryptophyte antenna complexes

The light-harvesting mechanisms of cryptophyte antenna complexes have attracted considerable attention due to their ability to exhibit maximal photosynthetic activity under very low-light conditions and to display several colors, as well as the observation of vibronic coherent features in their two-dimensional electronic spectra. However, detailed investigations on the interplay between the protein environment and their light-harvesting properties are hampered by the uncertainty related to the protonation state of the underlying bilin pigments. Here we study the protonation preferences of four types of bilin pigments including 15,16-dihydrobiliverdin (DBV), phycoerythrobilin (PEB), phycocyanobilin (PCB) and mesobiliverdin (MBV), which are found in phycoerythrin PE545 and phycocyanin PC577, PC612, PC630 and PC645 complexes. We apply quantum chemical calculations coupled to continuum solvation calculations to predict the intrinsic acidity of bilins in aqueous solution, and then combine molecular dynamics simulations with empirical pKa estimates to investigate the impact of the local protein environment on the acidity of the pigments. We also report measurements of the absorption spectra of the five complexes in a wide range of pH in order to validate our simulations and investigate possible changes in the light harvesting properties of the complexes in the range of physiological pH found in the lumen (pH ∼ 5-7). The results suggest a pKa > 7 for DBV and MBV pigments in the α polypeptide chains of PE545 and PC630/PC645 complexes, which are not coordinated to a negatively charged amino acid. For the other PEB, DBV and PCB pigments, which interact with a Glu or Asp side chain, higher pKa values (pKa > 8) are estimated. Overall, the results support a preferential population of the fully protonated state for bilins in cryptophyte complexes under physiological conditions regardless of the specific type of pigment and local protein environment.

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.

Tracing feed-back driven exciton dynamics in molecular aggregates

Excitation, exciton transport, dephasing and energy relaxation, and finally detection processes shift molecular systems into a specific superposition of quantum states causing localization, local heating and finally excitonic polaronic effects.

How fine-tuned for energy transfer is the environmental noise produced by proteins around biological chromophores?

Analysis of intermolecular motions of pigment–protein complexes shows no significant difference in influence of local environment despite different biological functions.

Coherence Spectroscopy in the Condensed Phase: Insights into Molecular Structure, Environment, and Interactions

The role of coherences, or coherently excited superposition states, in complex condensed-phase systems has been the topic of intense interest and debate for a number of years. In many cases, coherences have been utilized as spectators of ultrafast dynamics or for identifying couplings between electronic states. In rare cases, they have been found to drive excited state dynamics directly. Interestingly though, the utilization of coherences as a tool for high-detail vibronic spectroscopy has largely been overlooked until recently, despite their encoding of key information regarding molecular structure, electronically sensitive vibrational modes, and intermolecular interactions. Furthermore, their detection in the time domain makes for a highly comprehensive spectroscopic technique wherein the phase and dephasing times are extracted in addition to amplitude and intensity, an element not afforded in analogous frequency domain "steady-state" measurements. However, practical limitations arise in disentangling the large number of coherent signals typically accessed in broadband nonlinear spectroscopic experiments, often complicating assignment of the origin and type of coherences generated. Two-dimensional electronic spectroscopy (2DES) affords an avenue by which to disperse and decompose the large number of coherent signals generated in nonlinear experiments, facilitating the assignment of various types of quantum coherences. 2DES takes advantage of the broad bandwidth necessary for achieving the high time resolution desired for ultrafast dynamics and coherence generation by resolving the excitation axis to detect all excitation channels independently. This feature is beneficial for following population dynamics such as electronic energy transfer, and 2DES has become the choice method for such studies. Simultaneously, coherences arise as oscillations at well-defined coordinates across the 2D map often atop those evolving population signals. By isolating the coherent contribution to the 2DES data and Fourier transforming along the population time, a 3D spectral representation of the coherent 2D data is generated, and coherences are then ordered by their oscillation frequency, ν₂. Individual coherences can then be selected by their frequency and evaluated via their distinct "2D coherence" spectra, yielding a significantly more distinctive set of spectroscopic signatures over other 1D methodologies and single-point 2DES analysis. Given that coherences of different origin result in unique 2D coherence spectra, these characteristics can be catalogued and compared directly against experiment for prompt assignment, a strategy not afforded by traditional 2DES analysis. In this Account, a structure-driven time-independent spectral model is discussed and employed to compare the 2D fingerprints of various coherences to experimental 2D coherence spectra. The frequency-domain approach can easily integrate ab initio derived vibronic parameters, and its correspondence with experimental coherence spectra of a model compound is demonstrated. Several examples and applications are discussed herein, from 2D Franck-Condon analysis of a model compound, to identifying the signatures of interpigment vibronic coupling in a photosynthetic light-harvesting complex. The 3D spectral approach to 2DES provides remarkable spectroscopic detail, in turn leading to new insights in molecular structure and interactions, which complement the time-resolved dynamics simultaneously recorded. The approach presented herein has the potential to distill down the convoluted set of nonlinear signals appearing in 2D coherent spectra, making the technique more amenable to high-detail vibronic spectroscopy in inherently complex condensed phase systems.