Excitation Energy Transfer Dynamics Research Articles

Semiclassical approaches to perturbative time-convolution and time-convolutionless quantum master equations for electronic transitions in multistate systems.

Understanding the dynamics of photoinduced processes in complex systems is crucial for the development of advanced energy-conversion materials. In this study, we investigate the nonadiabatic dynamics using time-convolution (TC) and time-convolutionless (TCL) quantum master equations (QMEs) based on treating electronic couplings as perturbation within the framework of multistate harmonic (MSH) models. The MSH model Hamiltonians are mapped from all-atom simulations such that all pairwise reorganization energies are consistently incorporated, leading to a heterogeneous environment that couples to the multiple electronic states differently. Our exploration encompasses the photoinduced charge transfer dynamics in organic photovoltaic carotenoid-porphyrin-C60 triad dissolved in liquid solution and the excitation energy transfer (EET) dynamics in photosynthetic Fenna-Matthews-Olson complexes. By systematically comparing the perturbative TC and TCL QME approaches with exact quantum-mechanical and various semiclassical approximate kernels, we demonstrate their efficacy and accuracy in capturing the essential features of photoinduced dynamics. Our calculations show that TC QMEs generally yield more accurate results than TCL QMEs, especially in EET, although both methods offer versatile approaches adaptable across different systems. In addition, we investigate various semiclassical approximations featuring the Wigner-transformed and classical nuclear densities as well as the governing dynamics during the quantum coherence period, highlighting the trade-off between accuracy and computational cost. This work provides valuable insights into the applicability and performance of TC and TCL QME approaches via the MSH model, offering guidance for realistic applications to condensed-phase systems on the atomistic level.

Carotenoid-Mediated Long-Range Energy Transfer in the Light Harvesting-Reaction Center Complex from Photosynthetic Bacterium Roseiflexus castenholzii.

The light harvesting-reaction center complex (LH-RC) of Roseiflexus castenholzii binds bacteriochlorophylls a (BChls a), B800 and B880, absorbing around 800 and 880 nm, respectively. We comparatively investigated the interband excitation energy transfer (EET) dynamics of the wild-type LH-RC (wt-LH-RC) of Rfl. castenholzii and its carotenoid (Car)-less mutant (m-LH-RC) and found that Car can boost the B800 → B880 EET rate from (2.43 ps)-1 to (1.75 ps)-1, accounting for 38% acceleration of the EET process. Interestingly, photoexcitation of wt-LH-RC at 800 nm induced pronounced excitation dynamics of Car despite the insufficient photon energy for direct Car excitation, a phenomenon which is attributed to the BChl-Car exciplex 1[B800(↑↑)···Car(↓↓)]*. Such an exciplex is suggested to play an essential role in promoting the B800 → B880 EET process, as corroborated by the recently reported cryo-EM structures of wt-LH-RC and m-LH-RC. The mechanism of Car-mediated EET will be helpful to deepen the understanding of the role of Car in bacterial photosynthesis.

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.

Non-negligible roles of charge transfer excitons in ultrafast excitation energy transfer dynamics of a double-walled carbon nanotube.

Herein, we employed a developed linear response time dependent density functional theory-based nonadiabatic dynamics simulation method that explicitly takes into account the excitonic effects to investigate photoinduced excitation energy transfer dynamics of a double-walled carbon nanotube (CNT) model with different excitation energies. The E11 excitation of the outer CNT will generate a local excitation (LE) |out*〉 exciton due to its low energy, which does not induce any charge separation. In contrast, the E11 excitation of the inner CNT can generate four kinds of excitons with the LE exciton |in*〉 dominates. In the 500-fs dynamics simulation, the LE exciton |in*〉 and charge transfer (CT) excitons |out-in+〉 and |out+in-〉 are all gradually converted to the |out*〉 exciton, corresponding to a photoinduced excitation energy transfer, which is consistent with experimental studies. Finally, when the excitation energy is close to the E22 state of the outer CNT (∼1.05eV), a mixed population of different excitons, with the |out*〉 exciton dominated, is generated. Then, photoinduced energy transfer from the outer to inner CNTs occurs in the first 50fs, which is followed by an inner to outer excitation energy transfer that is completed in 400fs. The present work not only sheds important light on the mechanistic details of wavelength-dependent excitation energy transfer of a double-walled CNT model but also demonstrates the roles and importance of CT excitons in photoinduced excitation energy transfer. It also emphasized that explicitly including the excitonic effects in electronic structure calculations and nonadiabatic dynamics simulations is significant for correct understanding/rational design of optoelectronic properties of periodically extended systems.

Effects of Heterogeneous Protein Environment on Excitation Energy Transfer Dynamics in the Fenna-Matthews-Olson Complex.

The Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has been serving as a prototypical light-harvesting protein for studying excitation energy transfer (EET) dynamics in photosynthesis. The most widely used Frenkel exciton model for FMO complex assumes that each excited bacteriochlorophyll site couples to an identical and isolated harmonic bath, which does not account for the heterogeneous local protein environment. To better describe the realistic environment, we propose to use the recently developed multistate harmonic (MSH) model, which contains a globally shared bath that couples to the different pigment sites according to the atomistic quantum mechanics/molecular mechanics simulations with explicit protein scaffold and solvent. In this work, the effects of heterogeneous protein environment on EET in FMO complexes from Prosthecochloris aestuarii and Chlorobium tepidum, specifically including realistic spectral density, site-dependent reorganization energies, and system-bath couplings are investigated. Semiclassical and mixed quantum-classical mapping dynamics were applied to obtain the nonadiabatic EET dynamics in several models ranging from the Frenkel exciton model to the MSH model and their variants. The MSH model with realistic spectral density and site-dependent system-bath couplings displays slower EET dynamics than the Frenkel exciton model. Our comparative study shows that larger average reorganization energy, heterogeneity in spectral densities, and low-frequency modes could facilitate energy dissipation, which is insensitive to the static disorder in reorganization energies. The effects of the spectral densities and system-bath couplings along with the MSH model can be used to optimize EET dynamics for artificial light-harvesting systems.

Machine learning for excitation energy transfer dynamics

A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through photosynthetic light harvesting complexes (LHCs). The hierarchical equations of motion (HEOM) was adapted by Ishizaki and Fleming (J. Chem. Phys., 2009) to simulate open quantum dynamics in the biological regime. We generate a set of time dependent observables that depict the coherent propagation of electronic excitations through the LHCs by solving the HEOM. We solve the inverse problem using classical machine learning (ML) models as this is a computationally intractable problem. The objective here is to determine whether a trained ML model can perform Hamiltonian tomography by using the time dependence of the observables as inputs. We demonstrate the capability of convolutional neural networks to tackle this research problem. The models developed here can predict Hamiltonian parameters such as excited state energies and inter-site couplings of a system up to 99.28\% accuracy and mean-squared error as low as 0.65.

Ultrafast Excitation Energy Transfer Dynamics in the LHCII–CP29–CP24 Subdomain of Plant Photosystem II

We measure the two-dimensional electronic spectra of the LHCII(M)-CP29-CP24 complex in photosystem II (PSII) and provide the first study of the ultrafast excitation energy transfer (EET) processes of an asymmetric and native light-harvesting assembly of the antenna of PSII. With comparisons to LHCII, we observe faster energy equilibrations in the intermediate levels of the LHCII(M)-CP29-CP24 complex at 662 and 670 nm. Notably, the putative "bottleneck" states in LHCII exhibit faster effective dynamics in the LHCII(M)-CP24-CP29 complex, with the average lifetime shortening from 2.5 ps in LHCII to 1.2 ps in the bigger assembly. The observations are supported by high-level structure-based calculations, and the accelerated dynamics can be attributed to the structural change of LHCII(M) in the bigger complex. This study shows that the biological functioning structures of the complexes are important to understand the overall EET dynamics of the PSII supercomplex.

Ultrafast excited state dynamics in the monomeric and trimeric photosystem I core complex of Spirulina platensis probed by two-dimensional electronic spectroscopy.

Photosystem I (PSI), a naturally occurring supercomplex composed of a core part and a light-harvesting antenna, plays an essential role in the photosynthetic electron transfer chain. Evolutionary adaptation dictates a large variability in the type, number, arrangement, and absorption of the Chlorophylls (Chls) responsible for the early steps of light-harvesting and charge separation. For example, the specific location of long-wavelength Chls (referred to as red forms) in the cyanobacterial core has been intensively investigated, but the assignment of the chromophores involved is still controversial. The most red-shifted Chl a form has been observed in the trimer of the PSI core of the cyanobacterium Spirulina platensis, with an absorption centered at ∼740nm. Here, we apply two-dimensional electronic spectroscopy to study photoexcitation dynamics in isolated trimers and monomers of the PSI core of S. platensis. By means of global analysis, we resolve and compare direct downhill and uphill excitation energy transfer (EET) processes between the bulk Chls and the red forms, observing significant differences between the monomer (lacking the most far red Chl form at 740nm) and the trimer, with the ultrafast EET component accelerated by five times, from 500 to 100fs, in the latter. Our findings highlight the complexity of EET dynamics occurring over a broad range of time constants and their sensitivity to energy distribution and arrangement of the cofactors involved. The comparison of monomeric and trimeric forms, differing both in the antenna dimension and in the extent of red forms, enables us to extract significant information regarding PSI functionality.

Intramolecular Vibrations in Excitation Energy Transfer: Insights from Real-Time Path Integral Calculations.

Excitation energy transfer (EET) is fundamental to many processes in chemical and biological systems and carries significant implications for the design of materials suitable for efficient solar energy harvest and transport. This review discusses the role of intramolecular vibrations on the dynamics of EET in nonbonded molecular aggregates of bacteriochlorophyll, a perylene bisimide, and a model system, based on insights obtained from fully quantum mechanical real-time path integral results for a Frenkel exciton Hamiltonian that includes all vibrational modes of each molecular unit at finite temperature. Generic trends, as well as features specific to the vibrational characteristics of the molecules, are identified. Weak exciton-vibration (EV) interaction leads to compact, near-Gaussian densities on each electronic state, whose peak follows primarily a classical trajectory on a torus, while noncompact densities and nonlinear peak evolution are observed with strong EV coupling. Interaction with many intramolecular modes and increasing aggregate size smear, shift, and damp these dynamical features.

Time-dependent atomistic simulations of the CP29 light-harvesting complex.

Light harvesting as the first step in photosynthesis is of prime importance for life on earth. For a theoretical description of photochemical processes during light harvesting, spectral densities are key quantities. They serve as input functions for modeling the excitation energy transfer dynamics and spectroscopic properties. Herein, a recently developed procedure is applied to determine the spectral densities of the pigments in the minor antenna complex CP29 of photosystem II, which has recently gained attention because of its active role in non-photochemical quenching processes in higher plants. To this end, the density functional-based tight binding (DFTB) method has been employed to enable simulation of the ground state dynamics in a quantum-mechanics/molecular mechanics (QM/MM) scheme for each chlorophyll pigment. Subsequently, the time-dependent extension of the long-range corrected DFTB approach has been used to obtain the excitation energy fluctuations along the ground-state trajectories also in a QM/MM setting. From these results, the spectral densities have been determined and compared for different force fields and to spectral densities from other light-harvesting complexes. In addition, time-dependent and time-independent excitonic Hamiltonians of the system have been constructed and applied to the determination of absorption spectra as well as exciton dynamics.

Energy Transfer Dynamics in Light-Harvesting Complex 2 Variants Containing Oxidized B800 Bacteriochlorophyll a.

Excitation energy transfer (EET) in light-harvesting proteins is vital for photosynthetic activities. The pigment compositions and their organizations in these proteins are responsible for the EET functions. Thus, changing the pigment compositions in light-harvesting proteins contributes to a better understanding of EET mechanisms. In this study, we investigated the EET dynamics of two light-harvesting complex 2 (LH2) variants, in which nine B800 bacteriochlorophyll (BChl) a pigments were entirely or half converted to 3-acetyl chlorophyll (AcChl) a. The AcChl a pigments showed a Qy band, which was blue-shifted by 107 nm from B800 BChl a in the two variants. EET from AcChl a to B850 BChl a was observed in both fully oxidized and half-oxidized LH2 variants, but the EET rates were lower than that from B800 to B850 BChl a. EET from AcChl a to the co-present B800 was barely detected in the half-oxidized LH2. The preferential EET from AcChl a to B850 instead of B800 was rationalized by little spectral overlap of AcChl a with B800 BChl a and the pigment geometry in the protein. The EET rate from B800 to B850 BChl a in the half-oxidized LH2 was analogous to that in native LH2, indicating that partial oxidation of B800 did not disturb the EET channel from the residual B800 to B850.

Theoretical study on the exciton dynamics of coherent excitation energy transfer in the phycoerythrin 545 light-harvesting complex

The experimental observation of long-lived quantum coherence in the excitation energy transfer (EET) process of the several photosynthetic light-harvesting complexes at low and room temperatures has aroused hot debate. It challenges the common perception in the field of complicated pigment molecular systems and evokes considerable theoretical efforts to seek reasonable explanations. In this work, we investigate the coherent exciton dynamics of the phycoerythrin 545 (PE545) complex. We use the dissipation equation of motion to theoretically investigate the effect of the local pigment vibrations on the population transfer process. The result indicates that the realistic local pigment vibrations do assist the energy transmission. We demonstrate the coherence between different pigment molecules in the PE545 system is an essential ingredient in the EET process among various sites. The coherence makes the excitation energy delocalized, which leads to the redistribution of the excitation among all the chromophores in the steady state. Furthermore, we investigate the effects of the complex high-frequency spectral density function on the exciton dynamics and find that the high-frequency Brownian oscillator model contributes most to the exciton dynamic process. The discussions on the local pigment vibrations of the Brownian oscillator model suggest that the local heterogeneous protein environments and the effects of active vibration modes play a significant role in coherent energy transport.

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

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

Ultrafast energy transfer dynamics of phycobilisome from Thermosynechococcus vulcanus, as revealed by ps fluorescence and fs pump-probe spectroscopies.

Cyanobacterial photosynthetic systems efficiently capture sunlight using the pigment-protein megacomplexes, phycobilisome (PBS). The energy is subsequently transferred to photosystem I (PSI) and II (PSII), to produce electrochemical potentials. In the present study, we performed picosecond (ps) time-resolved fluorescence and femtosecond (fs) pump-probe spectroscopies on the intact PBS from a thermophilic cyanobacterium, Thermosynechococcus vulcanus, to reveal excitation energy transfer dynamics in PBS. The photophysical properties of the intact PBS were well characterized by spectroscopic measurements covering wide temporal range from femtoseconds to nanoseconds. The ps fluorescence measurements excited at 570nm, corresponding to the higher energy of the phycocyanin (PC) absorption band, demonstrated the excitation energy transfer from the PC rods to the allophycocyanin (APC) core complex as well as the energy transfer in the APC core complex. Then, the fs pump-probe measurements revealed the detailed energy transfer dynamics in the PC rods taking place in an ultrafast time scale. The results obtained in this study provide the full picture of the funnel-type excitation energy transfer with rate constants of (0.57ps)-1 → (7.3ps)-1 → (53ps)-1 → (180ps)-1 → (1800ps)-1.

Efficient propagation of the hierarchical equations of motion using the Tucker and hierarchical Tucker tensors.

We develop new methods to efficiently propagate the hierarchical equations of motion (HEOM) by using the Tucker and hierarchical Tucker (HT) tensors to represent the reduced density operator and auxiliary density operators. We first show that by employing the split operator method, the specific structure of the HEOM allows a simple propagation scheme using the Tucker tensor. When the number of effective modes in the HEOM increases and the Tucker representation becomes intractable, the split operator method is extended to the binary tree structure of the HT representation. It is found that to update the binary tree nodes related to a specific effective mode, we only need to propagate a short matrix product state constructed from these nodes. Numerical results show that by further employing the mode combination technique commonly used in the multi-configuration time-dependent Hartree approaches, the binary tree representation can be applied to study excitation energy transfer dynamics in a fairly large system including over 104 effective modes. The new methods may thus provide a promising tool in simulating quantum dynamics in condensed phases.

Direct Evidence for Excitation Energy Transfer Limitations Imposed by Low-Energy Chlorophylls in Photosystem I-Light Harvesting Complex I of Land Plants.

The overall efficiency of photosynthetic energy conversion depends both on photochemical and excitation energy transfer processes from extended light-harvesting antenna networks. Understanding the trade-offs between increase in the antenna cross section and bandwidth and photochemical conversion efficiency is of central importance both from a biological perspective and for the design of biomimetic artificial photosynthetic complexes. Here, we employ two-dimensional electronic spectroscopy to spectrally resolve the excitation energy transfer dynamics and directly correlate them with the initial site of excitation in photosystem I–light harvesting complex I (PSI-LHCI) supercomplex of land plants, which has both a large antenna dimension and a wide optical bandwidth extending to energies lower than the peak of the reaction center chlorophylls. Upon preferential excitation of the low-energy chlorophylls (red forms), the average relaxation time in the bulk supercomplex increases by a factor of 2–3 with respect to unselective excitation at higher photon energies. This slowdown is interpreted in terms of an excitation energy transfer limitation from low-energy chlorophyll forms in the PSI-LHCI. These results aid in defining the optimum balance between the extension of the antenna bandwidth to the near-infrared region, which increases light-harvesting capacity, and high photoconversion quantum efficiency.

Origin of vibrational features in the excitation energy transfer dynamics of perylene bisimide J-aggregates.

We investigate the role of intramolecular normal mode vibrations in the excitation energy transfer (EET) dynamics of perylene bisimide J-aggregates composed of 2 or 25 units using numerically exact methods. The calculations employ a Frenkel exciton Hamiltonian where the ground and excited electronic states of each molecular unit are coupled to 28 intramolecular normal mode vibrations at various temperatures. The electronic populations exhibit strong damping effects, a lengthening of the EET time scale, and complex dynamical patterns, which depend on aggregate length, temperature, as well as electronic and vibrational initial conditions and which are not additive. The early evolution is dominated by high-frequency vibrational modes, but all modes are responsible for the observed dynamics after the initial 25 fs. Overall, we observe significant changes in the electronic populations upon varying the temperature between 0 and 600 K. With a Franck-Condon (FC) initial excitation, a strongly coupled vibrational mode introduces new peaks to the dimer populations, which show very weak temperature sensitivity. The first of these peaks is also seen in the long aggregate, but subsequent recurrences appear strongly quenched and merged. These structures are drastically altered if a non-FC initial condition is assumed. Additional insights are obtained from the diagonal elements of the dimer electronic-vibrational reduced density matrix. We find that the vibronic peaks result from depletion of the crossing region during the early coherent evolution of the vibrational density away from the crossing point, which allows the premature back-transfer of excitation to the initially excited unit.

Excitation Energy Transfer Dynamics in a Low-Band-Gap Copolymer: Two-Dimensional Electronic Spectroscopy of PTB7 in Solution

A series of donor–acceptor (D–A)-linked copolymers has been used extensively in organic photovoltaics. Poly({4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-b:4,5-b′]dithiophene-2,6-diyl}3-fluoro-2-[(2-ethylhe...

Theoretical study of excitation energy transfer and nonlinear spectroscopy of photosynthetic light‐harvesting complexes using the nonperturbative reduced dynamics method

AbstractThe highly efficient excitation energy transfer (EET) processes in photosynthetic light‐harvesting complexes have attracted much recent research interests. Experimentally, spectroscopic studies have provided important information on the energetics and EET dynamics. Theoretically, due to the large number of degrees of freedom and the complex interaction between the pigments and the protein environment, it is impossible to simulate the whole system quantum mechanically. Effective Hamiltonian models are often used, in which the most important degrees of freedom are treated explicitly and all the other degrees of freedom are treated as a thermal bath. However, even with such simplifications, solving the real‐time quantum dynamics could still be a difficult task. A particular challenging case in simulating the EET dynamics and related spectroscopic phenomena lies in the so‐called intermediate coupling regime, where the intermolecular electronic couplings and the electronic–vibrational couplings are of similar strength. In this article, we review theoretical studies of linear and nonlinear spectroscopic signals of photosynthetic light‐harvesting complexes, using the nonperturbative hierarchical equations of motion (HEOM) approach. Simulations were performed for the EET dynamics, various types of linear spectra, two‐dimensional electronic spectra, and pump–probe spectra. Benchmark tests of several approximate methods related to the HEOM approach were also discussed. The results show that the nonperturbative HEOM approach is an effective method in simulating the EET dynamics and spectroscopic signals of photosynthetic light‐harvesting complexes. Important insights into EET pathways, quantum effects including quantum delocalization, and quantum coherence in photosynthetic light‐harvesting complexes were also obtained through such simulations.This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods

Effects of intramolecular vibrations on excitation energy transfer dynamics of the Fenna-Matthews-Olson complex

The role of vibrational coherence in photosynthetic pigment-proteins has been controversial. The present article investigates theoretically how the intramolecular vibrations of bacteriochlorophyll (BChl) influence the excitation energy transfer (EET) dynamics in the Fenna-Matthews-Olson complex (FMO). To this end, we use an exciton model incorporating recent experimental data and treat the vibrations as both coherent and incoherent. We simulate the transfer phenomena numerically with non-Markovian quantum dynamics. Our results at 300 K indicate that incoherent vibrations can moderately improve the efficiency of EET between FMO and a reaction center. With a vibronic model, we show that the coherent vibrations in either strongly or resonantly coupled BChl pairs can generate characteristic oscillations in their electronic populations which persist for several picoseconds even at 300 K. Despite such robust coherences, no significant improvement in the efficiency of EET is observed.