On the relation of protein dynamics and exciton relaxation in pigment–protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra

De novo design of proteins housing excitonically coupled chlorophyll special pairs

Natural photosystems couple light harvesting to charge separation using a 'special pair' of chlorophyll molecules that accepts excitation energy from the antenna and initiates an electron-transfer cascade. To investigate the photophysics of special pairs independently of the complexities of native photosynthetic proteins, and as a first step toward creating synthetic photosystems for new energy conversion technologies, we designed C2-symmetric proteins that hold two chlorophyll molecules in closely juxtaposed arrangements. X-ray crystallography confirmed that one designed protein binds two chlorophylls in the same orientation as native special pairs, whereas a second designed protein positions them in a previously unseen geometry. Spectroscopy revealed that the chlorophylls are excitonically coupled, and fluorescence lifetime imaging demonstrated energy transfer. The cryo-electron microscopy structure of a designed 24-chlorophyll octahedral nanocage with a special pair on each edge closely matched the design model. The results suggest that the de novo design of artificial photosynthetic systems is within reach of current computational methods.

Probing the Effect of Mutations on Light Harvesting in CP29 by Transient Absorption and First-Principles Simulations

Natural light harvesting is exceptionally efficient thanks to the local energy funnel created within light-harvesting complexes (LHCs). To understand the design principles underlying energy transport in LHCs, ultrafast spectroscopy is often complemented by mutational studies that introduce perturbations into the excitonic structure of the natural complexes. However, such studies may fall short of identifying all excitation energy transfer (EET) pathways and their changes upon mutation. Here, we show that a synergistic combination of first-principles calculations and ultrafast spectroscopy can give unprecedented insight into the EET pathways occurring within LHCs. We measured the transient absorption spectra of the minor CP29 complex of plants and of two mutants, systematically mapping the kinetic components seen in experiments to the simulated exciton dynamics. With our combined strategy, we show that EET in CP29 is surprisingly robust to the changes in the exciton states induced by mutations, explaining the versatility of plant LHCs.

Ultrafast Energy Transfer in a Diatom Photosystem II Supercomplex

The light-harvesting complexes (LHCs) of diatoms, specifically fucoxanthin-Chl a/c binding proteins (FCPs), exhibit structural and functional diversity, as highlighted by recent structural studies of photosystem II-FCP (PSII-FCPII) supercomplexes from different diatom species. The excitation dynamics of PSII-FCPII supercomplexes isolated from the diatom Thalassiosira pseudonana was explored using time-resolved fluorescence spectroscopy and two-dimensional electronic spectroscopy at room temperature and 77 K. Energy transfer between FCPII and PSII occurred remarkably fast (<5 ps), emphasizing the efficiency of FCPII as a light-harvesting antenna. The presence of long-wavelength chlorophylls may further help concentrate excitations in the core complex and increase the efficiency of light harvesting. Structure-based calculations reveal remarkably strong excitonic couplings between chlorophylls in the FCP antenna and between FCP and the PSII core antenna that are the basis for the rapid energy transfer.

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.

Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

PigmentHunter: A point-and-click application for automated chlorophyll-protein simulations

Chlorophyll proteins (CPs) are the workhorses of biological photosynthesis, working together to absorb solar energy, transfer it to chemically active reaction centers, and control the charge-separation process that drives its storage as chemical energy. Yet predicting CP optical and electronic properties remains a serious challenge, driven by the computational difficulty of treating large, electronically coupled molecular pigments embedded in a dynamically structured protein environment. To address this challenge, we introduce here an analysis tool called PigmentHunter, which automates the process of preparing CP structures for molecular dynamics (MD), running short MD simulations on the nanoHUB.org science gateway, and then using electrostatic and steric analysis routines to predict optical absorption, fluorescence, and circular dichroism spectra within a Frenkel exciton model. Inter-pigment couplings are evaluated using point-dipole or transition-charge coupling models, while site energies can be estimated using both electrostatic and ring-deformation approaches. The package is built in a Jupyter Notebook environment, with a point-and-click interface that can be used either to manually prepare individual structures or to batch-process many structures at once. We illustrate PigmentHunter's capabilities with example simulations on spectral line shapes in the light harvesting 2 complex, site energies in the Fenna-Matthews-Olson protein, and ring deformation in photosystems I and II.

High-Resolution Frequency-Domain Spectroscopic and Modeling Studies of Photosystem I (PSI), PSI Mutants and PSI Supercomplexes

Photosystem I (PSI) is one of the two main pigment-protein complexes where the primary steps of oxygenic photosynthesis take place. This review describes low-temperature frequency-domain experiments (absorption, emission, circular dichroism, resonant and non-resonant hole-burned spectra) and modeling efforts reported for PSI in recent years. In particular, we focus on the spectral hole-burning studies, which are not as common in photosynthesis research as the time-domain spectroscopies. Experimental and modeling data obtained for trimeric cyanobacterial Photosystem I (PSI3), PSI3 mutants, and PSI3-IsiA18 supercomplexes are analyzed to provide a more comprehensive understanding of their excitonic structure and excitation energy transfer (EET) processes. Detailed information on the excitonic structure of photosynthetic complexes is essential to determine the structure-function relationship. We will focus on the so-called "red antenna states" of cyanobacterial PSI, as these states play an important role in photochemical processes and EET pathways. The high-resolution data and modeling studies presented here provide additional information on the energetics of the lowest energy states and their chlorophyll (Chl) compositions, as well as the EET pathways and how they are altered by mutations. We present evidence that the low-energy traps observed in PSI are excitonically coupled states with significant charge-transfer (CT) character. The analysis presented for various optical spectra of PSI3 and PSI3-IsiA18 supercomplexes allowed us to make inferences about EET from the IsiA18 ring to the PSI3 core and demonstrate that the number of entry points varies between sample preparations studied by different groups. In our most recent samples, there most likely are three entry points for EET from the IsiA18 ring per the PSI core monomer, with two of these entry points likely being located next to each other. Therefore, there are nine entry points from the IsiA18 ring to the PSI3 trimer. We anticipate that the data discussed below will stimulate further research in this area, providing even more insight into the structure-based models of these important cyanobacterial photosystems.

Application of density matrix Wigner transforms for ultrafast macromolecular and chemical x-ray crystallography

Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian.

Experimental and Theoretical Mutation of Exciton States on the Smallest Type-I Photosynthetic Reaction Center Complex of a Green Sulfur Bacterium Chlorobaclum tepidum

The exciton states on the smallest type-I photosynthetic reaction center complex of a green sulfur bacterium Chlorobaculum tepidum (GsbRC) consisting of 26 bacteriochlorophylls a (BChl a) and four chlorophylls a (Chl a) located on the homodimer of two PscA reaction center polypeptides were investigated. This analysis involved the study of exciton states through a combination of theoretical modeling and the genetic removal of BChl a pigments at eight sites. (1) A theoretical model of the pigment assembly exciton state on GsbRC was constructed using Poisson TrESP (P-TrESP) and charge density coupling (CDC) methods based on structural information. The model reproduced the experimentally obtained absorption spectrum, circular dichroism spectrum, and excitation transfer dynamics, as well as explained the effects of mutation. (2) Eight BChl a molecules at different locations on the GsbRC were selectively removed by genetic exchange of the His residue, which ligates the central Mg atom of BChl a, with the Leu residue on either one or two PscAs in the RC. His locations are conserved among all type-I RC plant polypeptide, cyanobacteria, and bacteria amino acid sequences. (3) Purified mutant-GsbRCs demonstrated distinct absorption and fluorescence spectra at 77 K, which were different from each other, suggesting successful pigment removal. (4) The same mutations were applied to the constructed theoretical model to analyze the outcomes of these mutations. (5) The combination of theoretical predictions and experimental mutations based on structural information is a new tool for studying the function and evolution of photosynthetic reaction centers.

Light-Harvesting Efficiency Cannot Depend on Optical Coherence in the Absence of Orientational Order

The coherence of light has been proposed as a quantum-mechanical control for enhancing light-harvesting efficiency. In particular, optical coherence can be manipulated by changing either the polarization state or the spectral phase of the light. Here, we show that, in weak light, light-harvesting efficiency cannot be controlled using any form of optical coherence in molecular light-harvesting systems and, more broadly, those comprising orientationally disordered subunits and operating on longer-than-ultrafast time scales. Under those conditions, optical coherence does not affect the light-harvesting efficiency, meaning that it cannot be used for control. Specifically, polarization-state control is lost in disordered samples or when the molecules reorient on the time scales of light harvesting, and spectral-phase control is lost when the efficiency is time-averaged over a period longer than the optical coherence time. In practice, efficiency is always averaged over long times, meaning that coherent optical control is only possible through polarization and only in systems with orientational order.

First-principles simulation of excitation energy transfer and transient absorption spectroscopy in the CP29 light-harvesting complex

The dynamics of delocalized excitons in light-harvesting complexes (LHCs) can be investigated using different experimental techniques, and transient absorption (TA) spectroscopy is one of the most valuable methods for this purpose. A careful interpretation of TA spectra is essential for the clarification of excitation energy transfer (EET) processes occurring during light-harvesting. However, even in the simplest LHCs, a physical model is needed to interpret transient spectra as the number of EET processes occurring at the same time is very large to be disentangled from measurements alone. Physical EET models are commonly built by fittings of the microscopic exciton Hamiltonians and exciton-vibrational parameters, an approach that can lead to biases. Here, we present a first-principles strategy to simulate EET and transient absorption spectra in LHCs, combining molecular dynamics and accurate multiscale quantum chemical calculations to obtain an independent estimate of the excitonic structure of the complex. The microscopic parameters thus obtained are then used in EET simulations to obtain the population dynamics and the related spectroscopic signature. We apply this approach to the CP29 minor antenna complex of plants for which we follow the EET dynamics and transient spectra after excitation in the chlorophyll b region. Our calculations reproduce all the main features observed in the transient absorption spectra and provide independent insight on the excited-state dynamics of CP29. The approach presented here lays the groundwork for the accurate simulation of EET and unbiased interpretation of transient spectra in multichromophoric systems.

Femtosecond Dynamics of Excited States of Chlorophyll Tetramer in Water-Soluble Chlorophyll-Binding Protein BoWSCP

The paper reports on the absorption dynamics of chlorophyll a in a symmetric tetrameric complex of the water-soluble chlorophyll-binding protein BoWSCP. It was measured by a broadband femtosecond laser pump-probe spectroscopy within the range from 400 to 750 nm and with a time resolution of 20 fs-200 ps. When BoWSCP was excited in the region of the Soret band at a wavelength of 430 nm, nonradiative intramolecular conversion S3→S1 was observed with a characteristic time of 83 ± 9 fs. When the complex was excited in the region of the Qy band at 670 nm, relaxation transition between two excitonic states of the chlorophyll dimer was observed in the range of 105 ± 10 fs. Absorption spectra of the excited singlet states S1 and S3 of chlorophyll a were obtained. The delocalization of the excited state between exciton-coupled Chl molecules in BoWSCP tetramer changed in time and depended on the excitation energy. When BoWSCP is excited in the Soret band region, an ultrafast photochemical reaction is observed. This could result from the reduction of tryptophan in the vicinity of chlorophyll.

Time-resolved circular dichroism of excitonic systems: theory and experiment on an exemplary squaraine polymer

Experimental and theoretical foundations for femtosecond time-resolved circular dichroism (TRCD) spectroscopy of excitonic systems are presented. In this method, the system is pumped with linearly polarized light and the signal is defined as the difference between the transient absorption spectrum probed with left and with right circularly polarized light. We present a new experimental setup with a polarization grating as key element to generate circularly polarized pulses. Herein the positive (negative) first order of the diffracted light is left-(right-)circularly polarized and serves as a probe pulse in a TRCD experiment. The grating is capable of transferring ultrashort broadband pulses ranging from 470 nm to 720 nm into two separate beams with opposite ellipticity. By applying a specific chopping scheme we can switch between left and right circular polarizations and detect transient absorption (TA) and TRCD spectra on a shot-to-shot basis simultaneously. We perform experiments on a squaraine polymer, investigating excitonic dynamics, and we develop a general theory for TRCD experiments of excitonically coupled systems that we then apply to describe the experimental data in this particular example. At a magic angle of 54.7° between the pump-pulse polarization and the propagation direction of the probe pulse, the TRCD and TA signals become particularly simple to analyze, since the orientational average over random orientations of complexes factorizes into that of the interaction with the pump and the probe pulse, and the intrinsic electric quadrupole contributions to the TRCD signal average to zero for isotropic samples. Application of exciton theory to linear absorption and to linear circular dichroism spectra of squaraine polymers reveals the presence of two fractions of polymer conformations, a dominant helical conformation with close interpigment distances that are suggested to lead to short-range contributions to site energy shifts and excitonic couplings of the squaraine molecules, and a fraction of unfolded random coils. Theory demonstrates that TRCD spectra of selectively excited helices can resolve state populations that are practically invisible in TA spectroscopy due to the small dipole strength of these states. A qualitative interpretation of TRCD and TA spectra in the spectral window investigated experimentally is offered. The 1 ps time component found in these spectra is related to the slow part of exciton relaxation obtained between states of the helix in the low-energy half of the exciton manifold. The dominant 140 ps time constant reflects the decay of excited states to the electronic ground state.

Excitonic interactions and Stark fluorescence spectra

We develop the theory for the Stark fluorescence (SF) of molecular aggregates by taking into account the mixing of the excited states [including the states with charge-transfer (CT) characters]. We use the sum-over-state approach and modified rotating wave approximation to describe interactions of the static and optical fields with the permanent and transition dipoles of the excited states. The SF spectral profiles are calculated using the standard and modified Redfield theories for the emission lineshapes. The resulting expression allows an interpretation of the SF response based on the calculation of only one-exciton states (i.e., the calculation of two-exciton states is not needed). The shape and amplitude of the SF spectrum can exhibit dramatic changes in the presence of the CT states, especially when the CT state is mixed with the red-most emitting exciton levels. In this case, the SF responses are much more sensitive to the exciton-CT mixing as compared with the usual Stark absorption. The limitation of the proposed theory is related to the simplified nature of the Redfield picture, which neglects the dynamic localization within the mixed exciton-CT configuration.

Signatures of intramolecular vibrational and vibronic Q[Formula: see text]-Q[Formula: see text] coupling effects in absorption and CD spectra of chlorophyll dimers

An electron-vibrational coupling model that includes the vibronic (non-adiabatic) coupling between the Q[Formula: see text] and Q[Formula: see text] transitions of chlorophyll (Chl), created by Reimers and coworkers (Scientific Rep. 3, 2761, 2013) is extended here to chlorophyll dimers with interchlorophyll excitonic coupling. The model is applied to a Chl a dimer of the water-soluble chlorophyll binding protein (WSCP). As for isolated chlorophyll, the vibronic coupling is found to have a strong influence on the high-frequency vibrational sideband in the absorption spectrum, giving rise to a band splitting. In contrast, in the CD spectrum the interplay of vibronic coupling and static disorder leads to a strong suppression of the vibrational sideband in excellent agreement with the experimental data. The conservative nature of the CD spectrum in the low-energy region is found to be caused by a delicate balance of the intermonomer excitonic coupling between the purely electronic Q[Formula: see text] transition and the Q[Formula: see text] transition involving intramolecular vibrational excitations on one hand and the coupling to higher-energy electronic transitions on the other hand.

Determining interchromophore effects for energy transport in molecular networks using machine-learning algorithms

Nature uses chromophore networks, with highly optimized structural and energetic characteristics, to perform important chemical functions. Due to its modularity, predictable aggregation characteristics, and established synthetic protocols, structural DNA nanotechnology is a promising medium for arranging chromophore networks with analogous structural and energetic controls. However, this high level of control creates a greater need to know how to optimize the systems precisely. This study uses the system's modularity to produce variations of a coupled 14-Site chromophore network. It uses machine-learning algorithms and spectroscopy measurements to reveal the energy-transport roles of these Sites, paying particular attention to the cooperative and inhibitive effects they impose on each other for transport across the network. The physical significance of these patterns is contextualized, using molecular dynamics simulations and energy-transport modeling. This analysis yields insights about how energy transfers across the Donor-Relay and Relay-Acceptor interfaces, as well as the energy-transport pathways through the homogeneous Relay segment. Overall, this report establishes an approach that uses machine-learning methods to understand, in fine detail, the role that each Site plays in an optoelectronic molecular network.

Calculation of exciton couplings based on density functional tight-binding coupled to state-interaction state-averaged ensemble-referenced Kohn-Sham approach

We introduce the combination of the density functional tight binding (DFTB) approach, including onsite correction (OC) and long-range corrected (LC) functional and the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method with extended active space involving four electrons and four orbitals [LC-OC-DFTB/SSR(4,4)], to investigate exciton couplings in multichromophoric systems, such as organic crystals and molecular aggregates. We employ the LC-OC-DFTB/SSR(4,4) method to calculate the excitonic coupling in anthracene and tetracene. As a result, the LC-OC-DFTB/SSR(4,4) method provides a reliable description of the locally excited (LE) state in a single chromophore and the excitonic couplings between chromophores with reasonable accuracy compared to the experiment and the conventional SSR(4,4) method. In addition, the thermal fluctuation of excitonic couplings from dynamic nuclear motion in an anthracene crystal with LC-OC-DFTB/SSR(4,4) shows a similar fluctuation of excitonic coupling and spectral density with those of first-principle calculations. We conclude that LC-OC-DFTB/SSR(4,4) is capable of providing reasonable features related to LE states, such as Frenkel exciton with efficient computational cost.

An efficient protocol for excited states of large biochromophores

Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Q_y transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies.

Digital Quantum Simulation of the Spin-Boson Model under Markovian Open-System Dynamics

Digital quantum computers have the potential to simulate complex quantum systems. The spin-boson model is one of such systems, used in disparate physical domains. Importantly, in a number of setups, the spin-boson model is open, i.e., the system is in contact with an external environment which can, for instance, cause the decay of the spin state. Here, we study how to simulate such open quantum dynamics in a digital quantum computer, for which we use an IBM hardware. We consider in particular how accurate different implementations of the evolution result as a function of the level of noise in the hardware and of the parameters of the open dynamics. For the regimes studied, we show that the key aspect is to simulate the unitary portion of the dynamics, while the dissipative part can lead to a more noise-resistant simulation. We consider both a single spin coupled to a harmonic oscillator, and also two spins coupled to the oscillator. In the latter case, we show that it is possible to simulate the emergence of correlations between the spins via the oscillator.

Frequency-Domain Spectroscopic Study of the Photosystem I Supercomplexes, Isolated IsiA Monomers, and the Intact IsiA Ring

The PSI₃-IsiA₁₈ supercomplex is one of the largest and most complicated assemblies in photosynthesis. The IsiA ring, composed of 18 IsiA monomers (IsiA₁₈) surrounding the PSI trimer (PSI₃), forms under iron-deficient conditions in cyanobacteria and acts as a peripheral antenna. Based on the supercomplex structure recently determined via cryo-EM imaging, we model various optical spectra of the IsiA monomers and IsiA₁₈ ring. Comparison of the absorption and emission spectra of the isolated IsiA monomers and the full ring reveals that about 2.7 chlorophylls (Chls) are lost in the isolated IsiA monomers. The best fits for isolated monomers spectra are obtained assuming the absence of Chl 508 and Chl 517 and 70% loss of Chl 511. The best model describing all three hexamers and the entire ring suggests that the lowest energy pigments are Chls 511, 514, and 517. Based on the modeling results presented in this work, we conclude that there are most likely three entry points for EET from the IsiA₆ hexamer to the PSI core monomer, with two of these entry points likely being located next to each other (i.e., nine entry points from IsiA₁₈ to the PSI₃ trimer). Finally, we show that excitation energy transfer inside individual monomers is fast (<2 ps at T = 5 K) and at least 20 times faster than intermonomer energy transfer.

Accuracy of approximate methods for the calculation of absorption-type linear spectra with a complex system-bath coupling

The accuracy of approximate methods for calculating linear optical spectra depends on many variables. In this study, we fix most of these parameters to typical values found in photosynthetic light-harvesting complexes of plants and determine the accuracy of approximate spectra with respect to exact calculation as a function of the energy gap and interpigment coupling in a pigment dimer. We use a spectral density with the first eight intramolecular modes of chlorophyll a and include inhomogeneous disorder for the calculation of spectra. We compare the accuracy of absorption, linear dichroism, and circular dichroism spectra calculated using the Full Cumulant Expansion (FCE), coherent time-dependent Redfield (ctR), and time-independent Redfield and modified Redfield methods. As a reference we use spectra calculated with the Exact Stochastic Path Integral Evaluation method. We find the FCE method to be the most accurate for the calculation of all spectra. The ctR method performs well for the qualitative calculation of absorption and linear dichroism spectra when pigments are moderately coupled (∼15 cm-1), but ctR spectra may differ significantly from exact spectra when strong interpigment coupling (&gt;100 cm-1) is present. The dependence of the quality of Redfield and modified Redfield spectra on molecular parameters is similar, and these methods almost always perform worse than ctR, especially when the interpigment coupling is strong or the excitonic energy gap is small (for a given coupling). The accuracy of approximate spectra is not affected by resonance with intramolecular modes for typical system-bath coupling and disorder values found in plant light-harvesting complexes.

Theoretical Model of the Far-Red-Light-Adapted Photosystem I Reaction Center of Cyanobacterium Acaryochloris marina Using Chlorophyll d and the Effect of Chlorophyll Exchange

A theoretical model of the far-red-light-adapted photosystem I (PSI) reaction center (RC) complex of a cyanobacterium, Acaryochloris marina (AmPSI), was constructed based on the exciton theory and the recently identified molecular structure of AmPSI by Hamaguchi et al. (Nat. Commun., 2021, 12, 2333). A. marina performs photosynthesis under the visible to far-red light (400-750 nm), which is absorbed by chlorophyll d (Chl-d). It is in contrast to the situation of all the other oxygenic photosynthetic processes of cyanobacteria and plants, which contains chlorophyll a (Chl-a) that absorbs only 400-700 nm visible light. AmPSI contains 70 Chl-d, 1 Chl-d^', 2 pheophytin a (Pheo-a), and 12 carotenoids in the currently available structure. A special pair of Chl-d/Chl-d^' acts as the electron donor (P740) and two Pheo-a act as the primary electron acceptor A₀ as the counterparts of P700 and Chl-a, respectively, of Chl-a-type PSIs. The exciton Hamiltonian of AmPSI was constructed considering the excitonic coupling strength and site energy shift of individual pigments using the Poisson-TrESP (P-TrESP) and charge density coupling (CDC) methods. The model was constructed to fit the experimentally measured spectra of absorption and circular dichroism (CD) spectra during downhill/uphill excitation energy transfer processes. The constructed theoretical model of AmPSI was further compared with the Chl-a-type PSI of Thermosynechococcus elongatus (TePSI), which contains only Chl-a and Chl-a^'. The functional properties of AmPSI and TePSI were further examined by the in silico exchange of Chl-d by Chl-a in the models.

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.

Enhanced TEMPO Algorithm for Quantum Path Integrals with Off-Diagonal System-Bath Coupling: Applications to Photonic Quantum Networks

Multitime system correlation functions are relevant in various areas of physics and science, dealing with system-bath interaction including spectroscopy and quantum optics, where many of these schemes include an off-diagonal system bath interaction. Here we extend the enhanced time-evolving matrix product operator (eTEMPO) algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett. 123, 240602 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.240602 to open quantum systems with off-diagonal coupling beyond a single two level system. We exemplify the approach on a coupled cavity waveguide system with spatially separated quantum two-state emitters, though many other applications in material science are possible, including entangled photon propagation, photosynthesis spectroscopy, and on-chip quantum optics with realistic dissipation.

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.

Towards a quantitative description of excitonic couplings in photosynthetic pigment-protein complexes: quantum chemistry driven multiscale approaches

A structure-based quantitative calculation of excitonic couplings between photosynthetic pigments has to describe the dynamical polarization of the protein/solvent environment of the pigments, giving rise to reaction field and screening effects. Here, this challenging problem is approached by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM). The method is applied to compute excitonic couplings between chlorophyll a (Chl a) pigments of the water-soluble chlorophyll-binding protein (WSCP). By calibrating the vacuum dipole strength of the 0–0 transition of the Chl a chromophores according to experimental data, an excellent agreement between calculated and experimental linear absorption and circular dichroism spectra of WSCP is obtained. The effect of the mutual polarization of the pigment ground states is calculated to be very small. The simple Poisson-Transition-charge-from-Electrostatic-potential (Poisson-TrEsp) method is found to accurately describe the screening part of the excitonic coupling, obtained with FMO/PCM. Taking into account that the reaction field effects of the latter method can be described by a scalar constant leads to an improvement of Poisson-TrEsp that is expected to provide the basis for simple and realistic calculations of optical spectra and energy transfer in photosynthetic light-harvesting complexes. In addition, we present an expression for the estimation of Huang–Rhys factors of high-frequency pigment vibrations from experimental fluorescence line-narrowing spectra that takes into account the redistribution of oscillator strength by the interpigment excitonic coupling. Application to WSCP results in corrected Huang–Rhys factors that are less than one third of the original values obtained by the standard electronic two-state analysis that neglects the above redistribution. These factors are important for the estimation of the dipole strength of the 0–0 transition of the chromophores and for the development of calculation schemes for the spectral density of the exciton-vibrational coupling.

The importance of reaction field and screening effects on the excitonic couplings is demonstrated, and from quantum-chemical calculations a single scaling factor is derived that can be used to improve simple models based on the Poisson equation.

Stark absorption and Stark fluorescence spectroscopies: Theory and simulations

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

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.

Understanding Disorder, Vibronic Structure, and Delocalization in Electronically Coupled Dimers on DNA Duplexes

Structural DNA nanotechnology is a promising approach to create chromophore networks with modular structures and Hamiltonians to control the material's functions. The functional behaviors of these systems depend on the interactions of the chromophores' vibronic states, as well as interactions with their environment. To optimize their functions, it is necessary to characterize the chromophore network's structural and energetic properties, including the electronic delocalization in some cases. In this study, parameters of interest are deduced in DNA-scaffolded Cyanine 3 and Cyanine 5 dimers. The methods include steady-state optical measurements, physical modeling, and a genetic algorithm approach. The parameters include the chromophore network's vibronic Hamiltonian, molecular positions, transition dipole orientations, and environmentally induced energy broadening. Additionally, the study uses temperature-dependent optical measurements to characterize the spectral broadening further. These combined results reveal the quantum mechanical delocalization, which is important for functions like coherent energy transport and quantum information applications.

Quantum-Classical Approach for Calculations of Absorption and Fluorescence: Principles and Applications

Absorption and fluorescence spectroscopy techniques provide a wealth of information on molecular systems. The simulations of such experiments remain challenging, however, despite the efforts put into developing the underlying theory. An attractive method of simulating the behavior of molecular systems is provided by the quantum-classical theory─it enables one to keep track of the state of the bath explicitly, which is needed for accurate calculations of fluorescence spectra. Unfortunately, until now there have been relatively few works that apply quantum-classical methods for modeling spectroscopic data. In this work, we seek to provide a framework for the calculations of absorption and fluorescence lineshapes of molecular systems using the methods based on the quantum-classical Liouville equation, namely, the forward-backward trajectory solution (FBTS) and the non-Hamiltonian variant of the Poisson bracket mapping equation (PBME-nH). We perform calculations on a molecular dimer and the photosynthetic Fenna-Matthews-Olson complex. We find that in the case of absorption, the FBTS outperforms PBME-nH, consistently yielding highly accurate results. We next demonstrate that for fluorescence calculations, the method of choice is a hybrid approach, which we call PBME-nH-Jeff, that utilizes the effective coupling theory [Gelzinis, A.; J. Chem. Phys. 2020, 152, 051103] to estimate the excited state equilibrium density operator. Thus, we find that FBTS and PBME-nH-Jeff are excellent candidates for simulating, respectively, absorption and fluorescence spectra of real molecular systems.

Two-Dimensional Electronic Spectroscopy of a Minimal Photosystem I Complex Reveals the Rate of Primary Charge Separation

Photosystem I (PSI), found in all oxygenic photosynthetic organisms, uses solar energy to drive electron transport with nearly 100% quantum efficiency, thanks to fast energy transfer among antenna chlorophylls and charge separation in the reaction center. There is no complete consensus regarding the kinetics of the elementary steps involved in the overall trapping, especially the rate of primary charge separation. In this work, we employed two-dimensional coherent electronic spectroscopy to follow the dynamics of energy and electron transfer in a monomeric PSI complex from Synechocystis PCC 6803, containing only subunits A-E, K, and M, at 77 K. We also determined the structure of the complex to 4.3 Å resolution by cryoelectron microscopy with refinements to 2.5 Å. We applied structure-based modeling using a combined Redfield-Förster theory to compute the excitation dynamics. The absorptive 2D electronic spectra revealed fast excitonic/vibronic relaxation on time scales of 50-100 fs from the high-energy side of the absorption spectrum. Antenna excitations were funneled within 1 ps to a small pool of chlorophylls absorbing around 687 nm, thereafter decaying with 4-20 ps lifetimes, independently of excitation wavelength. Redfield-Förster energy transfer computations showed that the kinetics is limited by transfer from these red-shifted pigments. The rate of primary charge separation, upon direct excitation of the reaction center, was determined to be 1.2-1.5 ps^-1. This result implies activationless electron transfer in PSI.

Accuracy of the Quantum Regression Theorem for Photon Emission from a Quantum Dot

The quantum regression theorem (QRT) is the most widely used tool for calculating multitime correlation functions for the assessment of quantum emitters. It is an approximate method based on a Markov assumption for environmental coupling. In this Letter we quantify properties of photons emitted from a single quantum dot coupled to phonons. For the single-photon purity and the indistinguishability, we compare numerically exact path-integral results with those obtained from the QRT. It is demonstrated that the QRT systematically overestimates the influence of the environment for typical quantum dots used in quantum information technology.

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.

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

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

Fully Quantum Modeling of Exciton Diffusion in Mesoscale Light Harvesting Systems

It has long been a challenge to accurately and efficiently simulate exciton-phonon dynamics in mesoscale photosynthetic systems with a fully quantum mechanical treatment due to extensive computational resources required. In this work, we tackle this seemingly intractable problem by combining the Dirac-Frenkel time-dependent variational method with Davydov trial states and implementing the algorithm in graphic processing units. The phonons are treated on the same footing as the exciton. Tested with toy models, which are nanoarrays of the B850 pigments from the light harvesting 2 complexes of purple bacteria, the methodology is adopted to describe exciton diffusion in huge systems containing more than 1600 molecules. The superradiance enhancement factor extracted from the simulations indicates an exciton delocalization over two to three pigments, in agreement with measurements of fluorescence quantum yield and lifetime in B850 systems. With fractal analysis of the exciton dynamics, it is found that exciton transfer in B850 nanoarrays exhibits a superdiffusion component for about 500 fs. Treating the B850 ring as an aggregate and modeling the inter-ring exciton transfer as incoherent hopping, we also apply the method of classical master equations to estimate exciton diffusion properties in one-dimensional (1D) and two-dimensional (2D) B850 nanoarrays using derived analytical expressions of time-dependent excitation probabilities. For both coherent and incoherent propagation, faster energy transfer is uncovered in 2D nanoarrays than 1D chains, owing to availability of more numerous propagating channels in the 2D arrangement.

Exciton Lifetime Distributions and Population Dynamics in the FMO Protein Complex from Prosthecochloris aestuarii

Significant protein rearrangement upon excitation and energy transfer in Fenna-Matthews-Olson protein of Prosthecochloris aestuarii results in a modified energy landscape, which induces more changes in pigment site energies than predicted by the "standard" hole-burning theory. The energy changes are elucidated by simulations while investigating the effects of site-dependent disorder, both static (site-energy distribution widths) and dynamic (spectral density shapes). The resulting optimized site energies and their fluctuations are consistent with relative differences observed in inhomogeneous widths calculated by recent molecular dynamic simulations. Two sets of different spectral densities reveal how their shapes affect the population dynamics and distribution of exciton lifetimes. Calculations revealed the wavelength-dependent distributions of exciton lifetimes (T ₁) in the femtosecond to picosecond time frame. We suggest that the calculated multimodal and asymmetric wavelength-dependent T ₁ distributions offer more insight into the interpretation of resonant hole-burned (HB) spectra, kinetic traces in two-dimensional (2D) electronic spectroscopy experiments, and widely used global analyses in fitting data from transient absorption experiments.

On wavelength-dependent exciton lifetime distributions in reconstituted CP29 antenna of the photosystem II and its site-directed mutants

To provide more insight into the excitonic structure and exciton lifetimes of the wild type (WT) CP29 complex of photosystem II, we measured high-resolution (low temperature) absorption, emission, and hole burned spectra for the A2 and B3 mutants, which lack chlorophylls a612 and b614 (Chls), respectively. Experimental and modeling results obtained for the WT CP29 and A2/B3 mutants provide new insight on the mutation-induced changes at the molecular level and shed more light on energy transfer dynamics. Simulations of the A2 and B3 optical spectra, using the second-order non-Markovian theory, and comparison with improved fits of WT CP29 optical spectra provide more insight into their excitonic structure, mutation induced changes, and frequency-dependent distributions of exciton lifetimes (T₁). A new Hamiltonian obtained for WT CP29 reveals that deletion of Chls a612 or b614 induces changes in the site energies of all remaining Chls. Hamiltonians obtained for A2 and B3 mutants are discussed in the context of the energy landscape of chlorophylls, excitonic structure, and transfer kinetics. Our data suggest that the lowest exciton states in A2 and B3 mutants are contributed by a611(57%), a610(17%), a615(15%) and a615(58%), a611(20%), a612(15%) Chls, respectively, although other compositions of lowest energy states are also discussed. Finally, we argue that the calculated exciton decay times are consistent with both the hole-burning and recent transient absorption measurements. Wavelength-dependent T₁ distributions offer more insight into the interpretation of kinetic traces commonly described by discrete exponentials in global analysis/global fitting of transient absorption experiments.

Static Disorder in Excitation Energies of the Fenna-Matthews-Olson Protein: Structure-Based Theory Meets Experiment

Inhomogeneous broadening of optical lines of the Fenna-Matthews-Olson (FMO) light-harvesting protein is investigated by combining a Monte Carlo sampling of low-energy conformational substates of the protein with a quantum chemical/electrostatic calculation of local transition energies (site energies) of the pigments. The good agreement between the optical spectra calculated for the inhomogeneous ensemble and the experimental data demonstrates that electrostatics is the dominant contributor to static disorder in site energies. Rotamers of polar amino acid side chains are found to cause bimodal distribution functions of site energy shifts, which can be probed by hole burning and single-molecule spectroscopy. When summing over the large number of contributions, the resulting distribution functions of the site energies become Gaussians, and the correlations in site energy fluctuations at different sites practically average to zero. These results demonstrate that static disorder in the FMO protein is in the realm of the central limit theorem of statistics.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

Delocalization Effects in Chlorophyll Fluorescence: Nonperturbative Line Shape Analysis of a Vibronically Coupled Dimer

Non-adiabatic vibrational/electronic (vibronic) interactions in photosynthetic pigment/protein complexes (PPCs) have recently attracted considerable interest as a potential source for long-lived dynamic coherence and optimized light harvesting. The analysis of such effects is limited, however, by the complexity of the vibrational spectrum of biological pigments such as chlorophyll (Chl) molecules, which often makes numerical calculations prohibitively expensive and complicates the interpretation of experimental spectroscopic data. This work contributes to both challenges by using numerically exact computational methods to systematically examine vibronic mixing effects in the low-temperature fluorescence spectra of a Chl dimer possessing a full complement of local vibrations, using parameters extracted from experimental data. The results highlight the varying roles local vibrations can play in energy-transfer dynamics, both enhancing delocalization through vibronic resonance and, conversely, inducing dynamic localization by acting as a "self-bath" for local electronic transitions. In the specific context of line-narrowed fluorescence, the results indicate that, while low-frequency features are strongly suppressed by delocalization, high-frequency modes are likely to be dynamically localized in the parameter regime relevant to most photosynthetic complexes.

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.

Entropy Reorders Polariton States

The main result is that the long-range phase coherence of the polariton states formed by strong coupling between a photon mode in a cavity and an ensemble of molecules leads to exceptionally low entropy of the upper and lower polariton states, starkly contrasting with the dark states. That result means that spectroscopy does not correctly order the free energy of the excited states because there is a significant entropic contribution to the free energy, which turns out to comparable to the electronic energy gap between the lower polariton state and the dark-state manifold. The reordered states, according to their free energy, is important to predict the potential of polariton states for reactivity, to predict spontaneous photophysical dynamics, or to understand their decoherence. The entropic contribution adds to the polariton electronic gap, rendering states surprisingly more reactive than anticipated from the input excitation energy. This apparently "additional" reactivity, evident from the thermodynamics, suggests how the low entropy of highly coherent states can be exploited as a resource.

Excitation quenching in chlorophyll-carotenoid antenna systems: 'coherent' or 'incoherent'

Plants possess an essential ability to rapidly down-regulate light-harvesting in response to high light. This photoprotective process involves the formation of energy-quenching interactions between the chlorophyll and carotenoid pigments within the antenna of Photosystem II (PSII). The nature of these interactions is currently debated, with, among others, 'incoherent' or 'coherent' quenching models (or a combination of the two) suggested by a range of time-resolved spectroscopic measurements. In 'incoherent quenching', energy is transferred from a chlorophyll to a carotenoid and is dissipated due to the intrinsically short excitation lifetime of the latter. 'Coherent quenching' would arise from the quantum mechanical mixing of chlorophyll and carotenoid excited state properties, leading to a reduction in chlorophyll excitation lifetime. The key parameters are the energy gap, [Formula: see text] and the resonance coupling, J, between the two excited states. Coherent quenching will be the dominant process when [Formula: see text] i.e., when the two molecules are resonant, while the quenching will be largely incoherent when [Formula: see text] One would expect quenching to be energetically unfavorable for [Formula: see text] The actual dynamics of quenching lie somewhere between these limiting regimes and have non-trivial dependencies of both J and [Formula: see text] Using the Hierarchical Equation of Motion (HEOM) formalism we present a detailed theoretical examination of these excitation dynamics and their dependence on slow variations in J and [Formula: see text] We first consider an isolated chlorophyll-carotenoid dimer before embedding it within a PSII antenna sub-unit (LHCII). We show that neither energy transfer, nor the mixing of excited state lifetimes represent unique or necessary pathways for quenching and in fact discussing them as distinct quenching mechanisms is misleading. However, we do show that quenching cannot be switched 'on' and 'off' by fine tuning of [Formula: see text] around the resonance point, [Formula: see text] Due to the large reorganization energy of the carotenoid excited state, we find that the presence (or absence) of coherent interactions have almost no impact of the dynamics of quenching. Counter-intuitively significant quenching is present even when the carotenoid excited state lies above that of the chlorophyll. We also show that, above a rather small threshold value of [Formula: see text]quenching becomes less and less sensitive to J (since in the window [Formula: see text] the overall lifetime is independent of it). The requirement for quenching appear to be only that [Formula: see text] Although the coherent/incoherent character of the quenching can vary, the overall kinetics are likely robust with respect to fluctuations in J and [Formula: see text] This may be the basis for previous observations of NPQ with both coherent and incoherent features.

Quantum biology revisited

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.