Influence of weak vibrational-electronic couplings on 2D electronic spectra and inter-site coherence in weakly coupled photosynthetic complexes

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.

Quantum energy levels of glutamate modulate neural biophotonic signals

Glutamate is the most abundant excitatory neurotransmitter in the brain, and it plays an essential and important role in neural functions. Current studies have shown that glutamate can induce neural biophotonic activity and transmission, which may involve the mechanism of photon quantum brain; however, it is unclear whether such a mechanism follows the principle of quantum mechanics. Here we show that the action of glutamate on its receptors leads to a decrease in its quantum energy levels, and glutamate then partially or completely loses its function to further induce the biophotonic activity in mouse brain slices. The reduced quantum energy levels of glutamate can be restored by direct-current electrical discharges and the use of energy transfer of chloroplast photosynthesis; hence, the quantum energy recovered glutamate can again induce significant biophotonic activity. Furthermore, the changes in quantum energy levels of glutamate are related to the exchange and transfer of electron energy on its active hydrogen atom. These findings suggest that the glutamate-induced neural biophotonic signals may be involved in the transfer of the quantum energy levels of glutamate, which implies a quantum mechanism of neurotransmitter action.

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.

Effect of an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions on excitation energy transfer

A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton-phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton-phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.

Structural Tuning of Quantum Decoherence and Coherent Energy Transfer in Photosynthetic Light Harvesting

Photosynthetic organisms capture energy from solar photons by constructing light-harvesting proteins containing arrays of electronic chromophores. Collective excitations (excitons) arise when energy transfer between chromophores is coherent, or wavelike, in character. Here we demonstrate experimentally that coherent energy transfer to the lowest-energy excitons is principally controlled in a light-harvesting protein by the temporal persistence of quantum coherence rather than by the strength of vibronic coupling. In the peridinin-chlorophyll protein from marine dinoflagellates, broad-band two-dimensional electronic spectroscopy reveals that replacing the native chlorophyll a acceptor chromophores with chlorophyll b slows energy transfer from the carotenoid peridinin to chlorophyll despite narrowing the donor-acceptor energy gap. The formyl substituent on the chlorophyll b macrocycle hastens decoherence by sensing the surrounding electrostatic noise. These findings demonstrate how quantum coherence enhances the efficiency of energy transfer despite being very short lived in light-harvesting proteins at physiological temperatures.

Intramolecular Vibrations Complement the Robustness of Primary Charge Separation in a Dimer Model of the Photosystem II Reaction Center

The energy conversion of oxygenic photosynthesis is triggered by primary charge separation in proteins at the photosystem II reaction center. Here, we investigate the impacts of the protein environment and intramolecular vibrations on primary charge separation at the photosystem II reaction center. This is accomplished by combining the quantum dynamic theories of condensed phase electron transfer with quantum chemical calculations to evaluate the vibrational Huang-Rhys factors of chlorophyll and pheophytin molecules. We report that individual vibrational modes play a minor role in promoting charge separation, contrary to the discussion in recent publications. Nevertheless, these small contributions accumulate to considerably influence the charge separation rate, resulting in subpicosecond charge separation almost independent of the driving force and temperature. We suggest that the intramolecular vibrations complement the robustness of the charge separation in the photosystem II reaction center against the inherently large static disorder of the involved electronic energies.

The contributions of 49ers to the measurements and models of ultrafast photosynthetic energy transfer

Progress in measuring and understanding the mechanism of the elementary energy transfer steps in photosynthetic light harvesting from roughly 1949 to the present is sketched with a focus on the group of scientists born in 1949 ± 1. Improvements in structural knowledge, laser spectroscopic methods, and quantum dynamical theories have led to the ability to record and calculate with reasonable accuracy the timescales of elementary energy transfer steps. The significance of delocalized excited states and of near-field Coulombic coupling is noted. The microscopic understanding enables consistent coarse graining and should enable a much-improved understanding of the regulation of photosynthetic light harvesting.

Coherent wavepackets in the Fenna-Matthews-Olson complex are robust to excitonic-structure perturbations caused by mutagenesis

Femtosecond pulsed excitation of light-harvesting complexes creates oscillatory features in their response. This phenomenon has inspired a large body of work aimed at uncovering the origin of the coherent beatings and possible implications for function. Here we exploit site-directed mutagenesis to change the excitonic level structure in Fenna-Matthews-Olson (FMO) complexes and compare the coherences using broadband pump-probe spectroscopy. Our experiments detect two oscillation frequencies with dephasing on a picosecond timescale-both at 77 K and at room temperature. By studying these coherences with selective excitation pump-probe experiments, where pump excitation is in resonance only with the lowest excitonic state, we show that the key contributions to these oscillations stem from ground-state vibrational wavepackets. These experiments explicitly show that the coherences-although in the ground electronic state-can be probed at the absorption resonances of other bacteriochlorophyll molecules because of delocalization of the electronic excitation over several chromophores.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Angle-resolved coherent wave mixing using a 4 fs ultra-broad bandwidth laser

We demonstrate angle-resolved coherent (ARC) wave mixing using 4 fs light pulses derived from a laser source that spans 550-1000 nm. We believe this to be the shortest pulse duration used to date in coherent multi-dimensional spectroscopy. The marriage of this ultra-broad band, few-cycle coherent source with the ARC technique will permit new investigations of the interplay between energy transfers and quantum superposition states spanning 8200  cm^-1. We applied this configuration to measurements on the photosynthetic low light (LL) complex from Rhodopseudomonas palustris in solution at ambient temperature. We observe bi-exponential population dynamics for energy transfer across 5500  cm^-1 (0.65 eV), which we attribute to energy transfer from the Q_x transition of bacteriochlorophylls to the B850 pigment of the complex. We believe for the first time, to the best of our knowledge, we demonstrate that ARC maps can be recorded using a single laser pulse.

How Static Disorder Mimics Decoherence in Anisotropy Pump-Probe Experiments on Purple-Bacteria Light Harvesting Complexes

Anisotropy pump-probe experiments have provided insights into the character of excitons formed in photosynthetic complexes. Rapid decay in the observed anisotropy is cited as evidence of the strength of coupling of the excitonic degrees of freedom to their environment. Here we show that ensemble averaging over realistic model Hamiltonians leads to a rapid decay of anisotropy to a value close to the observed asymptote, and at a rate comparable to observed decay rates, even in the absence of coupling to the environment. While coupling to the environment will clearly play a role in the dynamics of such systems, our calculations suggest that caution is needed in deducing the strength of this coupling from anisotropy experiments. We also set out to clarify the nature of the quantum states and processes involved in the dynamics of such systems and the associated terminology.

Constructing an Interpolated Potential Energy Surface of a Large Molecule: A Case Study with Bacteriochlorophyll a Model in the Fenna-Matthews-Olson Complex

Constructing a reliable potential energy surface (PES) is a key step toward computationally studying the chemical dynamics of any molecular system. The interpolation scheme is a useful tool that can closely follow the accuracy of quantum chemical means at a dramatically reduced computational cost. However, applying interpolation to building a PES of a large molecule is not a straightforward black-box approach, as it frequently encounters practical difficulties associated with its large dimensionality. Here, we present detailed courses of applying interpolation toward building a PES of a large chromophore molecule. We take the example of S₀ and S₁ electronic states of bacteriochlorophyll a (BChla) molecules in the Fenna-Matthews-Olson light harvesting complex. With a reduced model molecule that bears BChla's main π-conjugated ring, various practical approaches are designed for improving the PES quality in a stable manner and for fine-tuning the final surface such that the surface can be adopted for long time molecular dynamics simulations. Combined with parallel implementation, we show that interpolated mechanics/molecular mechanics (IM/MM) simulations of the entire complex in the nanosecond time scale can be conducted readily without any practical issues. With 1500 interpolation data points for each chromophore unit, the PES error relative to the reference quantum chemical calculation is found to be ∼0.15 eV in the thermally accessible region of the conformational space, together with ∼0.01 eV error in S₀ - S₁ transition energies. The performance issue related to the use of a large interpolation database within the framework of our parallel routines is also discussed.

Isolated Ground-State Vibrational Coherence Measured by Fifth-Order Single-Shot Two-Dimensional Electronic Spectroscopy

Vibrations play a critical role in many photochemical and photophysical processes in which excitations reside on the electronically excited state. However, difficulty in assigning signals from spectroscopic measurements uniquely to a specific electronic state, ground or otherwise, has exposed limitations to their physical interpretation. Here, we demonstrate the selective excitation of vibrational coherences on the ground electronic state through impulsive Raman scattering, whose weak fifth-order signal is resonantly enhanced by coupling to strong electronic transitions. The six-wave mixing signals measured using this technique are free of lower-order cascades and represent correlations between zero-quantum vibrational coherences in the ground state and single-quantum coherences between the ground and electronic states. We believe that this technique has the potential to shed much-needed insight onto some of the mysteries regarding the origin of long-lived coherences observed in photosynthetic and other coupled chromophore systems.

Fluctuations in Electronic Energy Affecting Singlet Fission Dynamics and Mixing with Charge-Transfer State: Quantum Dynamics Study

Singlet fission is a spin-allowed process by which a singlet excited state is converted to two triplet states. To understand mechanisms of the ultrafast fission via a charge transfer (CT) state, one has investigated the dynamics through quantum-dynamical calculations with the uncorrelated fluctuation model; however, the electronic states are expected to experience the same fluctuations induced by the surrounding molecules because the electronic structure of the triplet pair state is similar to that of the singlet state except for the spin configuration. Therefore, the fluctuations in the electronic energies could be correlated, and the 1D reaction coordinate model may adequately describe the fission dynamics. In this work we develop a model for describing the fission dynamics to explain the experimentally observed behaviors. We also explore impacts of fluctuations in the energy of the CT state on the fission dynamics and the mixing with the CT state. The overall behavior of the dynamics is insensitive to values of the reorganization energy associated with the transition from the singlet state to the CT state, although the coherent oscillation is affected by the fluctuations. This result indicates that the mixing with the CT state is rather robust under the fluctuations in the energy of the CT state as well as the high-lying CT state.