Impact of environmentally induced fluctuations on quantum mechanically mixed electronic and vibrational pigment states in photosynthetic energy transfer and 2D electronic spectra

Electronic-vibrational resonance damping time-dependent photosynthetic energy transfer acceleration revealed by 2D electronic spectroscopy

The effects of damping time of electronic-vibrational resonance modes on energy transfer in photosynthetic light-harvesting systems are examined. Using the hierarchical equations of motion (HEOM) method, we simulate the linear absorption and two-dimensional electronic spectra (2DES) for a dimer model based on bottleneck sites in the light-harvesting complex of photosystem II. A site-dependent spectral density is incorporated, with only the low-energy site being coupled to the resonance mode. Similar patterns are observed in linear absorption spectra and early time 2DES for various damping times, owing to the weak coupling strength. However, notable differences emerge in the dynamics of the high-energy diagonal and cross-peaks in the 2DES. It is found that the coupling of electronic-vibrational resonance modes accelerates the energy transfer process, with rates being increased as the damping time is extended, but the impact becomes negligible when the damping time exceeds a certain threshold. To evaluate the reliability of the perturbation method, the modified Redfield (MR) method is employed to simulate 2DES under the same conditions. The results from the MR method are aligned with those obtained from the HEOM method, but the MR method predicts faster dynamics.

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100 fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle

We have developed a computer code for the thermodynamic hierarchical equations of motion derived from a spin subsystem coupled to multiple Drude baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code can simulate the reduced dynamics of the subsystem under isothermal, isentropic, thermostatic, and entropic conditions. The extensive and intensive thermodynamic variables are calculated as physical observables, and Gibbs and Helmholtz energies are evaluated as intensive and extensive work. The energy contribution of the system-bath interaction is evaluated separately from the subsystem using the hierarchical elements of the hierarchical equations of motion. The accuracy of the calculated results for the equilibrium distribution and the two-body correlation functions is assessed by contrasting the results with those obtained from the time-convolution-less Redfield equation. It is shown that the Lindblad master equation is inappropriate for the thermodynamic description of a spin-boson system. Non-Markovian effects in thermostatic processes are investigated by sequentially turning on and off the baths at different temperatures with different switching times and system-bath coupling. In addition, the Carnot cycle is simulated under quasi-static conditions. To analyze the work performed for the subsystem in the cycle, thermodynamic work diagrams are plotted as functions of intensive and extensive variables. The C++ source codes are provided as supplementary material.

Role of Quantum Information in HEOM Trajectories

Open quantum systems often operate in the non-Markovian regime where a finite history of a trajectory is intrinsic to its evolution. The degree of non-Markovianity for a trajectory may be measured in terms of the amount of information flowing from the bath back into the system. In this study, we consider how information flows through the auxiliary density operators (ADOs) in the hierarchical equations of motion. We consider three cases for a range of baths, underdamped, intermediate, and overdamped. By understanding how information flows, we are able to determine the relative importance of different ADOs within the hierarchy. We show that ADOs sharing a common Matsubara axis behave similarly, while ADOs on different Matsubara axes behave differently. Using this knowledge, we are able to truncate hierarchies significantly, thus reducing the computation time, while obtaining qualitatively similar results. This is illustrated by comparing 2D electronic spectra for a molecule with an underdamped vibration subsumed into the bath spectral density.

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Pathway selectivity in time-resolved spectroscopy using two-photon coincidence counting with quantum entangled photons

Ultrafast optical spectroscopy is a powerful technique for studying the dynamic processes of molecular systems in condensed phases. However, in molecular systems containing many dye molecules, the spectra can become crowded and difficult to interpret owing to the presence of multiple nonlinear optical contributions. In this work, we theoretically propose time-resolved spectroscopy based on the coincidence counting of two entangled photons generated via parametric down-conversion with a monochromatic laser. We demonstrate that the use of two-photon counting detection of entangled photon pairs enables the selective elimination of the excited-state absorption signal. This selective elimination cannot be realized with classical coherent light. We anticipate that the proposed spectroscopy will help simplify the spectral interpretation of complex molecular and material systems comprising multiple molecules.

Energy transfer in N-component nanosystems enhanced by pulse-driven vibronic many-body entanglement

The processing of energy by transfer and redistribution, plays a key role in the evolution of dynamical systems. At the ultrasmall and ultrafast scale of nanosystems, quantum coherence could in principle also play a role and has been reported in many pulse-driven nanosystems (e.g. quantum dots and even the microscopic Light-Harvesting Complex II (LHC-II) aggregate). Typical theoretical analyses cannot easily be scaled to describe these general N-component nanosystems; they do not treat the pulse dynamically; and they approximate memory effects. Here our aim is to shed light on what new physics might arise beyond these approximations. We adopt a purposely minimal model such that the time-dependence of the pulse is included explicitly in the Hamiltonian. This simple model generates complex dynamics: specifically, pulses of intermediate duration generate highly entangled vibronic (i.e. electronic-vibrational) states that spread multiple excitons - and hence energy - maximally within the system. Subsequent pulses can then act on such entangled states to efficiently channel subsequent energy capture. The underlying pulse-generated vibronic entanglement increases in strength and robustness as N increases.

Probing exciton dynamics with spectral selectivity through the use of quantum entangled photons

Quantum light is increasingly recognized as a promising resource for developing optical measurement techniques. Particular attention has been paid to enhancing the precision of the measurements beyond classical techniques by using nonclassical correlations between quantum entangled photons. Recent advances in the quantum optics technology have made it possible to manipulate spectral and temporal properties of entangled photons, and photon correlations can facilitate the extraction of matter information with relatively simple optical systems compared to conventional schemes. In these respects, the applications of entangled photons to time-resolved spectroscopy can open new avenues for unambiguously extracting information on dynamical processes in complex molecular and materials systems. Here, we propose time-resolved spectroscopy in which specific signal contributions are selectively enhanced by harnessing nonclassical correlations of entangled photons. The entanglement time characterizes the mutual delay between an entangled twin and determines the spectral distribution of photon correlations. The entanglement time plays a dual role as the knob for controlling the accessible time region of dynamical processes and the degrees of spectral selectivity. In this sense, the role of the entanglement time is substantially equivalent to the temporal width of the classical laser pulse. The results demonstrate that the application of quantum entangled photons to time-resolved spectroscopy leads to monitoring dynamical processes in complex molecular and materials systems by selectively extracting desired signal contributions from congested spectra. We anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Synthetic Control of Exciton Dynamics in Bioinspired Cofacial Porphyrin Dimers

Understanding how the complex interplay among excitonic interactions, vibronic couplings, and reorganization energy determines coherence-enabled transport mechanisms is a grand challenge with both foundational implications and potential payoffs for energy science. We use a combined experimental and theoretical approach to show how a modest change in structure may be used to modify the exciton delocalization, tune electronic and vibrational coherences, and alter the mechanism of exciton transfer in covalently linked cofacial Zn-porphyrin dimers (meso-beta linked ABm-β and meso-meso linked AAm-m). While both ABm-β and AAm-m feature zinc porphyrins linked by a 1,2-phenylene bridge, differences in the interporphyrin connectivity set the lateral shift between macrocycles, reducing electronic coupling in ABm-β and resulting in a localized exciton. Pump-probe experiments show that the exciton dynamics is faster by almost an order of magnitude in the strongly coupled AAm-m dimer, and two-dimensional electronic spectroscopy (2DES) identifies a vibronic coherence that is absent in ABm-β. Theoretical studies indicate how the interchromophore interactions in these structures, and their system-bath couplings, influence excitonic delocalization and vibronic coherence-enabled rapid exciton transport dynamics. Real-time path integral calculations reproduce the exciton transfer kinetics observed experimentally and find that the linking-modulated exciton delocalization strongly enhances the contribution of vibronic coherences to the exciton transfer mechanism, and that this coherence accelerates the exciton transfer dynamics. These benchmark molecular design, 2DES, and theoretical studies provide a foundation for directed explorations of nonclassical effects on exciton dynamics in multiporphyrin assemblies.

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.

Hidden vibronic and excitonic structure and vibronic coherence transfer in the bacterial reaction center

We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden vibronic and excitonic structure. Through analysis of the coherent dynamics of the BRC, we identify multiple quasi-resonances between pigment vibrations and excitonic energy gaps, and vibronic coherence transfer processes that are typically neglected in standard models of photosynthetic energy transfer and charge separation. We support our assignment with control experiments on bacteriochlorophyll and simulations of the coherent dynamics using a reduced excitonic model of the BRC. We find that specific vibronic coherence processes can readily reveal weak exciton transitions. While the functional relevance of such processes is unclear, they provide a spectroscopic tool that uses vibrations as a window for observing excited state structure and dynamics elsewhere in the BRC via vibronic coupling. Vibronic coherence transfer reveals the upper exciton of the “special pair” that was weakly visible in previous 2DES experiments.

Vibronic coupling in energy transfer dynamics and two-dimensional electronic-vibrational spectra

We introduce a heterodimer model in which multiple mechanisms of vibronic coupling and their impact on energy transfer can be explicitly studied. We consider vibronic coupling that arises through either Franck-Condon activity in which each site in the heterodimer has a local electron-phonon coupling or Herzberg-Teller activity in which the transition dipole moment coupling the sites has an explicit vibrational mode-dependence. We have computed two-dimensional electronic-vibrational (2DEV) spectra for this model while varying the magnitude of these two effects and find that 2DEV spectra contain static and dynamic signatures of both types of vibronic coupling. Franck-Condon activity emerges through a change in the observed excitonic structure, while Herzberg-Teller activity is evident in the appearance of significant side-band transitions that mimic the lower-energy excitonic structure. A comparison of quantum beating patterns obtained from analysis of the simulated 2DEV spectra shows that this technique can report on the mechanism of energy transfer, elucidating a means of experimentally determining the role of specific vibronic coupling mechanisms in such processes.

Achieving two-dimensional optical spectroscopy with temporal and spectral resolution using quantum entangled three photons

Recent advances in techniques for generating quantum light have stimulated research on novel spectroscopic measurements using quantum entangled photons. One such spectroscopy technique utilizes non-classical correlations among entangled photons to enable measurements with enhanced sensitivity and selectivity. Here, we investigate the spectroscopic measurement utilizing entangled three photons. In this measurement, time-resolved entangled photon spectroscopy with monochromatic pumping [A. Ishizaki, J. Chem. Phys. 153, 051102 (2020)] is integrated with the frequency-dispersed two-photon counting technique, which suppresses undesired accidental photon counts in the detector and thus allows one to separate the weak desired signal. This time-resolved frequency-dispersed two-photon counting signal, which is a function of two frequencies, is shown to provide the same information as that of coherent two-dimensional optical spectra. The spectral distribution of the phase-matching function works as a frequency filter to selectively resolve a specific region of the two-dimensional spectra, whereas the excited-state dynamics under investigation are temporally resolved in the time region longer than the entanglement time. The signal is not subject to Fourier limitations on the joint temporal and spectral resolution, and therefore, it is expected to be useful for investigating complex molecular systems in which multiple electronic states are present within a narrow energy range.

Modeling and Simulating the Excited-State Dynamics of a System with Condensed Phases: A Machine Learning Approach

Simulating the irreversible quantum dynamics of exciton- and electron-transfer problems poses a nontrivial challenge. Because the irreversibility of the system dynamics is a result of quantum thermal activation and dissipation caused by the surrounding environment, it is necessary to include infinite environmental degrees of freedom in the simulation. Because the capabilities of full quantum dynamics simulations that include the surrounding molecular degrees of freedom are limited, employing a system-bath model is a practical approach. In such a model, the dynamics of excitons or electrons are described by a system Hamiltonian, while the other degrees of freedom that arise from the environmental molecules are described by a harmonic oscillator bath (HOB) and system-bath interaction parameters. By extending on a previous study of molecular liquids [ J. Chem. Theory Comput. 2020, 16, 2099], here, we construct a system-bath model for exciton- and electron-transfer problems by means of a machine learning approach. We determine both the system and system-bath interaction parameters, including the spectral distribution of the bath, using the electronic excitation energies obtained from a quantum mechanics/molecular mechanics (QM/MM) simulation that is conducted as a function of time. Using the analytical expressions of optical response functions, we calculate linear and two-dimensional electronic spectra (2DES) for indocarbocyanine dimers in methanol. From these results, we demonstrate the capability of our approach to elucidate the nonequilibrium exciton dynamics of a quantum system in a nonintuitive manner.

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.

Coherent Speedup of Excitation Energy Transfer in PC645

The fundamental principle governing the robust excitation energy transfer (EET) in the light-harvesting complexes remained elusive. Recent spectroscopic observations of the EET attract attention toward the role of the quantum effects in the biological systems. In this study, along with the time evolution, the distance between the quantum states of the pigments is also considered for a detailed illustration of the effect of the quantum coherence on the speed of the excitation transfer. The comparative analysis of the coherently delocalized EET with the incoherent discrete hopping reveals that the coherent superposition speedup the excitation transfer process, for instance, with the initially localized excitation, coherence provides a ∼4-fold enhancement to the excitation transfer rate.

Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

Numerically "exact" simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

We present a scheme to evaluate thermodynamic variables for a system coupled to a heat bath under a time-dependent external force using the quasi-static Helmholtz energy from the numerically "exact" hierarchical equations of motion (HEOM). We computed the entropy produced by a spin system strongly coupled to a non-Markovian heat bath for various temperatures. We showed that when changes to the external perturbation occurred sufficiently slowly, the system always reached thermal equilibrium. Thus, we calculated the Boltzmann entropy and the von Neumann entropy for an isothermal process, as well as various thermodynamic variables, such as changes in internal energies, heat, and work, for a system in quasi-static equilibrium based on the HEOM. We found that although the characteristic features of the system entropies in the Boltzmann and von Neumann cases as a function of the system-bath coupling strength are similar, those for the total entropy production are completely different. The total entropy production in the Boltzmann case is always positive, whereas that in the von Neumann case becomes negative if we chose a thermal equilibrium state of the total system (an unfactorized thermal equilibrium state) as the initial state. This is because the total entropy production in the von Neumann case does not properly take into account the contribution of the entropy from the system-bath interaction. Thus, the Boltzmann entropy must be used to investigate entropy production in the fully quantum regime. Finally, we examined the applicability of the Jarzynski equality.

Importance of Intermonomer Couplings of the FMO Complex in Coherently Initiated Dynamics

In this work, the hierarchical equation of motion approach was employed to study the excitation transfer efficiency (ETE) from the Fenna-Matthews-Olson (FMO) complex to the reaction center core complex (RCC). Further, the realistic initial pure state (created by the interaction of femtosecond laser pulse with the isolated FMO complex) was used in the presence of an inhomogeneous protein environment. We observed the same amount of excitation transfer from the FMO to the RCC, in agreement with the experiment using femtosecond absorption spectroscopy. Simulation analysis shows weak intermonomer couplings are strongly affecting the dynamics of ETE, which implies that all the monomers of the FMO complex need to be considered as connected with the RCC pigment for a better estimate of the ETE.

Decoupling from a Thermal Bath via Molecular Polariton Formation

The coupling between an electronic system and an environmental bath plays a decisive role in the excited state dynamics of artificial/natural molecular condensed phases. Although it is generally difficult to control the coupling between the system and the thermal bath in condensed matter, a strong light-matter coupling can control system-bath coupling properties using the polaron decoupling effect, in which a coherent interaction between excitons and photons reduces the reorganization energy. Here we demonstrate that this polaron decoupling strongly reduces the fluctuations in electronic energy in tetraphenyldibenzoperiflanthene thin films embedded in an optical microcavity. Using two-dimensional electronic spectroscopy, the frequency-fluctuation correlation function of the lower polariton state was revealed, showing that the dynamic inhomogeneity due to bath coupling inside the microcavity almost vanishes completely. This was attributed to a significant delocalization of the lower polariton state over 10⁵ molecules in the cavity, reducing the effective coupling strength of the bath modes.

DNA Waves and Their Applications in Biology

AIM:

In this research, we show that DNA waves have many applications in biology. DNA is formed by the joining of quantum particles like electrons and charged atoms. DNA has different motions during transcription, translation, and replication, in which the charged particles move, accelerate, and emit waves. Thus, DNA could emit quantum waves.

METHODS:

Two methods are proposed to observe the effect of DNA waves. The first proposed method measures DNA waves emitted by bacteria suspended in the milk. The vessel of milk is placed in the interior of an inductor. One side of the vessel is connected to a generator and another side to a scope. By sending a current to the inductor, an input electromagnetic field is produced. Bacteria interact with the input field, change it and produce new output signals. Using the scope, the output signals are observed and compared with the input signals. The number of DNA waves produced also depends on temperature.

RESULTS:

At lower temperatures, bacterial replication is less, and fewer DNA waves are produced. Conversely, more bacteria are generated at higher temperatures, and more DNA waves are produced. The second proposed method acquires and images of DNA signals of chick embryos. In this method, a circuit is constructed that consists of a graphene or metal tube, generator, inductor, scope, DNA in the interior of eggs and DNA exterior to the eggs. Magnetic waves pass the interior and exterior DNA as well as the graphene. The DNA is excited and the exciting interior/exterior DNA exchanges waves. Some of these waves interact with electrons in the graphene tube, and a current is generated. Properties of the chick embryo DNA can be explored by analysing changes in the waves that emerge from the eggs.

CONCLUSION:

It is concluded that DNA waves could be used extensively in imaging and provide for us the exact information about evolutions of DNAs interior of biological systems.

Origin of Unexpectedly Simple Oscillatory Responses in the Excited-State Dynamics of Disordered Molecular Aggregates

Unraveling the many facets of coherent and incoherent exciton motion in an ensemble of chromophores is an inherently complex quantum mechanical problem that has triggered a vivid debate on the role of quantum effects in molecular materials and biophysical systems. Here the dynamics of a statistical ensemble of molecular aggregates consisting of identical chromophores is investigated within a new theoretical framework. Taking account of intrinsic properties of the system, the Hamiltonian of the aggregate is partitioned into two mutually commuting vibrational and vibronic operators. This representation paves the way for an analysis that reveals the role of static disorder in ensembles of aggregates. Using analytical methods, it is demonstrated that after a critical time τ_D ≃ 2π/σ (σ being the dispersion of the disorder) any dynamic variable of the aggregate exhibits purely vibrational dynamics. This result is confirmed by exact numerical calculations of the time-dependent site populations of the aggregate. These findings may be useful for the interpretation of recent femtosecond spectroscopic experiments on molecular aggregates.

Two-Dimensional Electronic-Vibrational Spectroscopy of Coupled Molecular Complexes: A Near-Analytical Approach

This work presents theoretical calculations of the two-dimensional electronic-vibrational (2DEV) spectrum of a vibronically coupled molecular dimer using a near-analytical method. In strongly coupled dimers, where the IR mode is resonant with the electronic energy gap between the excitons, multiple infrared transitions become allowed that are forbidden in weakly coupled systems that have a nonresonant IR mode. This formalism enables the coherences and population contributions to be explored separately and allows efficient calculation of relaxation rates between the vibronic states. At short times, we find strong contributions of vibronic coherences to the 2DEV spectra. They decay fairly rapidly, giving rise to strong population signals. Although the interpretation of 2DEV spectra is considerably more complex than that for weakly coupled systems, the richness of the spectra and the necessity to consider both visible and infrared transition moments suggest that such analysis will be very valuable in characterizing the role of vibronic effects in ultrafast molecular dynamics.

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.

Two-dimensional electronic vibrational spectroscopy and ultrafast excitonic and vibronic photosynthetic energy transfer

2-Dimensional electronic vibrational spectroscopy presents a novel experimental and theoretical approach to study energy transfer.

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.

Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies

Two-Dimensional Electronic-Vibrational (2D EV) spectroscopy and Two-Dimensional Vibrational-Electronic (2D VE) spectroscopy are new coherent four-wave mixing spectroscopies that utilize both electronically resonant and vibrationally resonant field-matter interactions to elucidate couplings between electronic and vibrational degrees of freedom. A system Hamiltonian is developed here to lay a foundation for interpreting the 2D EV and 2D VE signals that arise from a vibronically coupled molecular system in the condensed phase. A molecular system consisting of one anharmonic vibration and two electronic states is modeled. Equilibrium displacement of the vibrational coordinate and vibrational frequency shifts upon excitation to the first electronic excited state are included in our Hamiltonian through linear and quadratic vibronic coupling terms. We explicitly consider the nuclear dependence of the electronic transition dipole moment and demonstrate that these spectroscopies are sensitive to non-Condon effects. A series of simulations of 2D EV and 2D VE spectra obtained by varying parameters of the system, system-bath, and interaction Hamiltonians demonstrate that one of the following conditions must be met to observe signals: (1) non-zero linear and/or quadratic vibronic coupling in the electronic excited state, (2) vibrational-coordinate dependence of the electronic transition dipole moment, or (3) electronic-state-dependent vibrational dephasing dynamics. We explore how these vibronic interactions are manifested in the positions, amplitudes, and line shapes of the peaks in 2D EV and 2D VE spectroscopies.

Finite-temperature time-dependent variation with multiple Davydov states

The Dirac-Frenkel time-dependent variational approach with Davydov Ansätze is a sophisticated, yet efficient technique to obtain an accurate solution to many-body Schrödinger equations for energy and charge transfer dynamics in molecular aggregates and light-harvesting complexes. We extend this variational approach to finite temperature dynamics of the spin-boson model by adopting a Monte Carlo importance sampling method. In order to demonstrate the applicability of this approach, we compare calculated real-time quantum dynamics of the spin-boson model with that from numerically exact iterative quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows that our variational approach with the single Davydov Ansätze is in excellent agreement with the QUAPI method at high temperatures, while the two differ at low temperatures. Accuracy in dynamics calculations employing a multitude of Davydov trial states is found to improve substantially over the single Davydov Ansatz, especially at low temperatures. At a moderate computational cost, our variational approach with the multiple Davydov Ansatz is shown to provide accurate spin-boson dynamics over a wide range of temperatures and bath spectral densities.

Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath

Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.

Mechanistic Regimes of Vibronic Transport in a Heterodimer and the Design Principle of Incoherent Vibronic Transport in Phycobiliproteins

Following the observation of coherent oscillations in nonlinear spectra of photosynthetic pigment protein complexes, in particular, phycobilliproteins such as PC645, coherent vibronic transport has been suggested as a design principle for novel light-harvesting materials. Vibronic transport between energetically remote pigments is coherent when the presence of a vibration resonant with the electronic energy gap supports transient delocalization between the electronic excited states. We establish the mechanism of vibronic transport for a model heterodimer across a wide range of molecular parameter values. The resulting mechanistic map demonstrates that the molecular parameters of phycobiliproteins in fact support incoherent vibronic transport. This result points to an important design principle: Incoherent vibronic transport is more efficient than a coherent mechanism when energetic disorder exceeds the coupling between the donor and vibrationally excited acceptor states. Finally, our results suggest that the role of coherent vibronic transport in pigment protein complexes should be reevaluated.

Local protein solvation drives direct down-conversion in phycobiliprotein PC645 via incoherent vibronic transport

The mechanisms controlling excitation energy transport (EET) in light-harvesting complexes remain controversial. Following the observation of long-lived beats in 2D electronic spectroscopy of PC645, vibronic coherence, the delocalization of excited states between pigments supported by a resonant vibration, has been proposed to enable direct excitation transport from the highest-energy to the lowest-energy pigments, bypassing a collection of intermediate states. Here, we instead show that for phycobiliprotein PC645 an incoherent vibronic transport mechanism is at play. We quantify the solvation dynamics of individual pigments using ab initio quantum mechanics/molecular mechanics (QM/MM) nuclear dynamics. Our atomistic spectral densities reproduce experimental observations ranging from absorption and fluorescence spectra to the timescales and selectivity of down-conversion observed in transient absorption measurements. We construct a general model for vibronic dimers and establish the parameter regimes of coherent and incoherent vibronic transport. We demonstrate that direct down-conversion in PC645 proceeds incoherently, enhanced by large reorganization energies and a broad collection of high-frequency vibrations. We suggest that a similar incoherent mechanism is appropriate across phycobiliproteins and represents a potential design principle for nanoscale control of EET.

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.

Tracing feed-back driven exciton dynamics in molecular aggregates

Excitation, exciton transport, dephasing and energy relaxation, and finally detection processes shift molecular systems into a specific superposition of quantum states causing localization, local heating and finally excitonic polaronic effects.