Effect of Underdamped Vibration on Excitation Energy Transfer: Direct Comparison between Two Different Partitioning Schemes

A Comprehensive Approach to Exciton Delocalization and Energy Transfer

Electrostatic intermolecular interactions lie at the heart of both the Förster model for resonance energy transfer (RET) and the exciton model for energy delocalization. In the Förster theory of RET, the excitation energy incoherently flows from the energy donor to a weakly coupled energy acceptor. The exciton model describes instead the energy delocalization in aggregates of identical (or nearly so) molecules. Here, we introduce a model that brings together molecular aggregates and RET. We will consider a couple of molecules, each described in terms of two diabatic electronic states, coupled to an effective molecular vibration. Electrostatic intermolecular interactions drive energy fluxes between the molecules, that, depending on model parameters, can be described as RET or energy delocalization. At variance with the standard Förster model for RET and of the exciton model for aggregates, our approach applies both in the weak and in the strong coupling regimes and fully accounts for the quantum nature of molecular vibrations in a nonadiabatic approach. Coupling the system to a thermal bath, we follow RET and energy delocalization in real time and simulate time-resolved emission spectra.

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

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

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.

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

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

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

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

Low-Frequency Vibronic Mixing Modulates the Excitation Energy Flow in Bacterial Light-Harvesting Complex II

Oscillatory features observed in two-dimensional electronic spectroscopy (2DES) manifest coherent vibrational and electronic dynamics and even the interplay of them. Recently, we developed a 2DES technique utilizing a pair of synchronized repetition-frequency-stabilized lasers, which enables the wide dynamic range measurements of 2DES signals rapidly. Here, we apply this dual-laser 2DES technique to investigate the electronic energy transfer (EET) process in bacterial light-harvesting complex II consisting of B800 and B850 circular aggregates at ambient temperature, and the coherent vibrational wavepakcet associated with the EET between the two aggregates are measured. Examining the principal component analysis of the time-resolved 2DES signal, we found that the EET from B800 to low-lying B850 states is modulated by a low-frequency (156 cm^-1) vibrational mode of the exciton donor (B800). This observation suggests that the donor transition density is modulated by this vibration, which, in turn, modulates the energy transfer dynamics.

Cooperation between Excitation Energy Transfer and Antisynchronously Coupled Vibrations

The effects of the environment in energy transfer systems have been continuously studied for decades. Here, we investigate how the energy transfer and the emergence of vibrational correlations cooperate with each other based on simulations with a few numerically approximate mixed quantum classical (MQC) methods. By adopting a two-state system with locally coupled underdamped vibrations that are resonant with the electronic energy gap, we observe prominent energy dissipations from the electronic system to the vibrations, rehighlighting the role of underdamped vibrations as a temporal electronic energy buffer. More importantly, this energy dissipation generates specific phase relations between the two vibrations. Namely, the vibrations become anticorrelated right after the initiation of the energy transfer but then synchronized as the transfer completes. These phase relations are interpreted as a selective activation of an anticorrelated motion of the vibrations and a subsequent deactivation by thermal energy redistribution. Furthermore, we show that a single vibration simultaneously coupled to the two electronic states with opposite phases induces a completely equivalent energy transfer dynamics as the two localized vibrations. Finally, we discuss how the vibrational energy dissipation dynamics is affected by the adopted MQC approaches and warn about the increased subtlety toward properly treating dissipation effects over having reliable population dynamics.

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

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

Theory of dissipation pathways in open quantum systems

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

Benchmarking the Surface Hopping Method to Include Nuclear Quantum Effects

We have benchmarked the surface hopping method to capture nuclear quantum effects in the spin-Boson model in the deep tunneling regime. The thermal populations and the rate constants calculated using the surface hopping method are compared with those calculated using Boltzmann theory and Fermi's golden rule, respectively. Additionally, we have proposed a simple kinetic model that partially includes nuclear quantum effects within Marcus theory, and the results of the surface hopping method are analyzed under the framework of this simple kinetic model. A broad range of parameters are investigated to identify the regimes for the successes and failures of the surface hopping method. This work shows that with the accurate treatment of decoherence and velocity reversal, surface hopping can generally capture the nuclear quantum effects in the deep tunneling and weak diabatic coupling regime.

Two-dimensional electronic spectroscopy of bacteriochlorophyll a with synchronized dual mode-locked lasers

How atoms and electrons in a molecule move during a chemical reaction and how rapidly energy is transferred to or from the surroundings can be studied with flashes of laser light. However, despite prolonged efforts to develop various coherent spectroscopic techniques, the lack of an all-encompassing method capable of both femtosecond time resolution and nanosecond relaxation measurement has hampered various applications of studying correlated electron dynamics and vibrational coherences in functional materials and biological systems. Here, we demonstrate that two broadband (>300 nm) synchronized mode-locked lasers enable two-dimensional electronic spectroscopy (2DES) study of chromophores such as bacteriochlorophyll a in condensed phases to measure both high-resolution coherent vibrational spectrum and nanosecond electronic relaxation. We thus anticipate that the dual mode-locked laser-based 2DES developed and demonstrated here would be of use for unveiling the correlation between the quantum coherence and exciton dynamics in light-harvesting protein complexes and semiconducting materials.

Toward monitoring the dissipative vibrational energy flows in open quantum systems by mixed quantum-classical simulations

In open quantum system dynamics, rich information about the major energy relaxation channels and corresponding relaxation rates can be elucidated by monitoring the vibrational energy flow among individual bath modes. However, such calculations often become tremendously difficult as the complexity of the subsystem-bath coupling increases. In this paper, we attempt to make this task feasible by using a mixed quantum-classical method, the Poisson-bracket mapping equation with non-Hamiltonian modification (PBME-nH) [H. W. Kim and Y. M. Rhee, J. Chem. Phys. 140, 184106 (2014)]. For a quantum subsystem bilinearly coupled to harmonic bath modes, we derive an expression for the mode energy in terms of the classical positions and momenta of the nuclei, while keeping consistency with the energy of the quantum subsystem. The accuracy of the resulting expression is then benchmarked against a numerically exact method by using relatively simple models. Although our expression predicts a qualitatively correct dissipation rate for a range of situations, cases involving a strong vibronic resonance are quite challenging. This is attributed to the inherent lack of quantum back reaction in PBME-nH, which becomes significant when the subsystem strongly interacts with a small number of bath modes. A rigorous treatment of such an effect will be crucial for developing quantitative simulation methods that can handle generic subsystem-bath coupling.