Hierarchical Equations of Motion Simulation of Temperature‐Dependent Two‐Dimensional Electronic Spectroscopy of the ChlorophyllaManifold in LHCII

Bioexcitons by Design: How Do We Get There?

Biological pigment-protein complexes (PPCs) exhibit a remarkable ability to tune the optical properties of biological excitons (bioexcitons) through specific pigment-protein interactions. While such fine-tuning allows natural systems (e.g., photosynthetic proteins) to carry out their native functions with near-optimal performance, native function itself is often suboptimal for applications such as biofuel production or quantum technology development. This perspective offers a look at near-term prospects for the rational reoptimization of PPC bioexcitons for new functions using site-directed mutagenesis. The primary focus is on the "structure-spectrum" challenge of understanding the relationships between structural features and spectroscopic properties. While recent examples demonstrate that site-directed mutagenesis can be used to tune nearly all key bioexciton parameters (e.g., site energies, interpigment couplings, and electronic-vibrational interactions), critical challenges remain before we achieve truly rational design of bioexciton properties.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Vibrational and vibronic coherences in the energy transfer process of light-harvesting complex II revealed by two-dimensional electronic spectroscopy

The presence of quantum coherence in light-harvesting complex II (LHCII) as a mechanism to understand the efficiency of the light-harvesting function in natural photosynthetic systems is still debated due to its structural complexity and weak-amplitude coherent oscillations. Here, we revisit the coherent dynamics and clarify different types of coherences in the energy transfer processes of LHCII using a joint method of the high-S/N transient grating and two-dimensional electronic spectroscopy. We find that the electronic coherence decays completely within 50 fs at room temperature. The vibrational coherences of chlorophyll a dominate over oscillations within 1 ps, whereas a low-frequency mode of 340 cm−1 with a vibronic mixing character may participate in vibrationally assisted energy transfer between chlorophylls a. Our results may suggest that vibronic mixing is relevant for rapid energy transfer processes among chlorophylls in LHCII.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer

We elucidate the influence of the system–bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Time-dependent simulation of photocurrent-detected two-dimensional spectroscopy of open systems

A new time-domain simulation protocol of two-dimensional electronic spectra with photocurrent detection is presented. Time-dependent density functional theory for open systems at finite temperature is applied to evaluate the photocurrent response to four laser pulses, and a non-perturbative phase-matching approach is implemented to extract the fourth-order photocurrent signal with a desired phase-matching condition. Simulations for an open three-level model indicates that transition dipoles interact resonantly with the incident pulses and that different sample-electrode couplings may be identified by appearance of different peaks/valleys in photocurrent spectra from different electrodes. Moreover, qualitative reproduction of experimental spectra of a PbS quantum dot photocell [Karki et al., Nat. Commun. 5(1), 5869 (2014)] reveals the stimulated electron dynamics.

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.

Characterization of the ultrafast spectral diffusion and vibronic coherence of TIPS-pentacene using 2D electronic spectroscopy

TIPS-pentacene is a small-molecule organic semiconductor that is widely used in optoelectronic devices. It has been studied intensely owing to its ability to undergo singlet fission. In this study, we aim to develop further understanding of the coupling between the electronic and nuclear degrees of freedom of TIPS-pentacene (TIPS-Pn). We measured and analyzed the 2D electronic spectra of TIPS-Pn in solutions. Using center line slope (CLS) analysis, we characterized the frequency-fluctuation correlation function of the 0-0 vibronic transition. Strong oscillations in the CLS values were observed for up to 5 ps with a frequency of 264 cm^-1, which are attributable to a large vibronic coupling with the TIPS-Pn ring-breathing vibrational mode. In addition, detailed analysis of the CLS values allowed us to retrieve two spectral diffusion lifetimes, which are attributed to the inertial and diffusive dynamics of solvent molecules. Amplitude beating analysis also uncovered couplings with another vibrational mode at 1173 cm^-1. The experimental results can be described using the displaced harmonic oscillator model. By comparing the CLS values of the simulated data with the experimental CLS values, we estimated a Huang-Rhys factor of 0.1 for the ring-breathing vibrational mode. The results demonstrated how CLS analysis can be a useful method for characterizing the strength of vibronic coupling.

A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics

We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

Excitation energy transfer kinetics of trimeric, monomeric and subunit-depleted Photosystem I from Synechocystis PCC 6803

Photosystem I is the most efficient photosynthetic enzyme with structure and composition highly conserved among all oxygenic phototrophs. Cyanobacterial Photosystem I is typically associated into trimers for reasons that are still debated. Almost universally, Photosystem I contains a number of long-wavelength-absorbing 'red' chlorophylls (Chls), that have a sizeable effect on the excitation energy transfer and trapping. Here we present spectroscopic comparison of trimeric Photosystem I from Synechocystis PCC 6803 with a monomeric complex from the ΔpsaL mutant and a 'minimal' monomeric complex ΔFIJL, containing only subunits A, B, C, D, E, K and M. The quantum yield of photochemistry at room temperature was the same in all complexes, demonstrating the functional robustness of this photosystem. The monomeric complexes had a reduced far-red absorption and emission equivalent to the loss of 1.5-2 red Chls emitting at 710-715 nm, whereas the longest-wavelength emission at 722 nm was not affected. The picosecond fluorescence kinetics at 77 K showed spectrally and kinetically distinct red Chls in all complexes and equilibration times of up to 50 ps. We found that the red Chls are not irreversible traps at 77 K but can still transfer excitations to the reaction centre, especially in the trimeric complexes. Structure-based Förster energy transfer calculations support the assignment of the lowest-energy state to the Chl pair B37/B38 and the trimer-specific red Chl emission to Chls A32/B7 located at the monomer-monomer interface. These intermediate-energy red Chls facilitate energy migration from the lowest-energy states to the reaction centre.