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

Frequency-Dependent Vibronic Effects in Steady State Energy Transport

The interplay between electronic and intramolecular high-frequency vibrational degrees of freedom is ubiquitous in natural light-harvesting systems. Recent studies have indicated that an intramolecular vibrational donor-acceptor frequency difference can enhance energy transport. Here, we analyze the extent to which different intramolecular donor-acceptor vibrational frequencies affect excitation energy transport in the natural nonequilibrium steady state configuration. Comments are included on the less physical equilibrium case for comparison with the literature. It is found that for constant Huang-Rhys factors, whereas the acceptor population increases in the equilibrium case when the intramolecular vibrational frequency of the acceptor exceeds that of the donor, this increase is negligible for the nonequilibrium steady state. Therefore, these changes in acceptor population do not significantly enhance energy transport in the nonequilibrium steady state for the natural scenario of incoherent light excitation with biologically relevant parameters of typical photosynthetic complexes. Insight about a potential mechanism to optimize energy transfer in the nonequilibrium steady state based on increasing the harvesting time at the reaction center is analyzed.

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.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

Light-Harvesting Efficiency Cannot Depend on Optical Coherence in the Absence of Orientational Order

The coherence of light has been proposed as a quantum-mechanical control for enhancing light-harvesting efficiency. In particular, optical coherence can be manipulated by changing either the polarization state or the spectral phase of the light. Here, we show that, in weak light, light-harvesting efficiency cannot be controlled using any form of optical coherence in molecular light-harvesting systems and, more broadly, those comprising orientationally disordered subunits and operating on longer-than-ultrafast time scales. Under those conditions, optical coherence does not affect the light-harvesting efficiency, meaning that it cannot be used for control. Specifically, polarization-state control is lost in disordered samples or when the molecules reorient on the time scales of light harvesting, and spectral-phase control is lost when the efficiency is time-averaged over a period longer than the optical coherence time. In practice, efficiency is always averaged over long times, meaning that coherent optical control is only possible through polarization and only in systems with orientational order.

Observation of parallel intersystem crossing and charge transfer-state dynamics in [Fe(bpy)3]2+ from ultrafast 2D electronic spectroscopy

Transition metal-based charge-transfer complexes represent a broad class of inorganic compounds with diverse photochemical applications. Charge-transfer complexes based on earth-abundant elements have been of increasing interest, particularly the canonical [Fe(bpy)3]2+. Photoexcitation into the singlet metal-ligand charge transfer (1MLCT) state is followed by relaxation first to the ligand-field manifold and then to the ground state. While these dynamics have been well-studied, processes within the MLCT manifold that facilitate and/or compete with relaxation have been more elusive. We applied ultrafast two-dimensional electronic spectroscopy (2DES) to disentangle the dynamics immediately following MLCT excitation of this compound. First, dynamics ascribed to relaxation out of the initially formed 1MLCT state was found to correlate with the inertial response time of the solvent. Second, the additional dimension of the 2D spectra revealed a peak consistent with a ∼20 fs 1MLCT → 3MLCT intersystem crossing process. These two observations indicate that the complex simultaneously undergoes intersystem crossing and direct conversion to ligand-field state(s). Resolution of these parallel pathways in this prototypical earth-abundant complex highlights the ability of 2DES to deconvolve the otherwise obscured excited-state dynamics of charge-transfer complexes.

Ab initio simulation of peak evolutions and beating maps for electronic two-dimensional signals of a polyatomic chromophore

By employing the doorway-window (DW) on-the-fly simulation protocol, we performed ab initio simulations of peak evolutions and beating maps of electronic two-dimensional (2D) spectra of a polyatomic molecule in the gas phase. As the system under study, we chose pyrazine, which is a paradigmatic example of photodynamics dominated by conical intersections (CIs). From the technical perspective, we demonstrate that the DW protocol is a numerically efficient methodology suitable for simulations of 2D spectra for a wide range of excitation/detection frequencies and population times. From the information content perspective, we show that peak evolutions and beating maps not only reveal timescales of transitions through CIs but also pinpoint the most relevant coupling and tuning modes active at these CIs.

Engineering giant excitonic coupling in bioinspired, covalently bridged BODIPY dyads

Strong excitonic coupling in photosynthetic systems is believed to enable efficient light absorption and quantitative charge separation, motivating the development of artificial multi-chromophore arrays with equally strong or even stronger excitonic coupling. However, large excitonic coupling strengths have typically been accompanied by fast non-radiative recombination, limiting the potential of the arrays for solar energy conversion as well as other applications such as fluorescent labeling. Here, we report giant excitonic coupling leading to broad optical absorption in bioinspired BODIPY dyads that have high photostability, excited-state lifetimes at the nanosecond scale, and fluorescence quantum yields of nearly 50%. Through the synthesis, spectroscopic characterization, and computational modeling of a series of dyads with different linking moieties, we show that the strongest coupling is obtained with diethynylmaleimide linkers, for which the coupling occurs through space between BODIPY units with small separations and slipped co-facial orientations. Other linkers allow for broad tuning of both the relative through-bond and through-space coupling contributions and the overall strength of interpigment coupling, with a tradeoff observed in general between the strength of the two coupling mechanisms. These findings open the door to the synthesis of molecular systems that function effectively as light-harvesting antennas and as electron donors or acceptors for solar energy conversion.

Electronic-Vibrational Resonance Does Not Significantly Alter Steady-State Transport in Natural Light-Harvesting Systems

Oscillations in time-dependent two-dimensional electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state; therefore, the relevance of these arguments to the natural process is unclear. Here, we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. Specifically, we analyze the PEB dimer in the cryptophyte algae PE545 antenna protein. It is found that vibrations resonant with the energy difference between exciton states only marginally increase the quantum yield and the imaginary part of the intersite coherence that is relevant for transport compared to non-resonant vibrations in the natural non-equilibrium steady-state. That is, the electronic-vibrational resonance interaction does not significantly enhance energy transport under natural incoherent light excitation conditions.

Beat-frequency-resolved two-dimensional electronic spectroscopy: disentangling vibrational coherences in artificial fluorescent proteins with sub-10-fs visible laser pulses

We perform a beat-frequency-resolved analysis for two-dimensional electronic spectroscopy using a high-speed and stable 2D electronic spectrometer and few-cycle visible laser pulses to disentangle the vibrational coherences in an artificial fluorescent protein. We develop a highly stable ultrashort light source that generates 5.3-fs visible pulses with a pulse energy of 4.7 µJ at a repetition rate of 10 kHz using multi-plate pulse compression and laser filamentation in a gas cell. The above-5.3-fs laser pulses together with a high-speed multichannel detector enable us to measure a series of 2D electronic spectra, which are resolved in terms of beat frequency related to vibrational coherence. We successfully extract the discrete vibrational peaks behind the inhomogeneous broadening in the absorption spectra and the vibrational quantum beats of the excited electronic state behind the strong incoherent population background in the typical 2D electronic spectra.

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.

Light-induced reversible reorganizations in closed Type II reaction centre complexes: physiological roles and physical mechanisms

The purpose of this review is to outline our understanding of the nature, mechanism and physiological significance of light-induced reversible reorganizations in closed Type II reaction centre (RC) complexes. In the so-called 'closed' state, purple bacterial RC (bRC) and photosystem II (PSII) RC complexes are incapable of generating additional stable charge separation. Yet, upon continued excitation they display well-discernible changes in their photophysical and photochemical parameters. Substantial stabilization of their charge-separated states has been thoroughly documented-uncovering light-induced reorganizations in closed RCs and revealing their physiological importance in gradually optimizing the operation of the photosynthetic machinery during the dark-to-light transition. A range of subtle light-induced conformational changes has indeed been detected experimentally in different laboratories using different bRC and PSII-containing preparations. In general, the presently available data strongly suggest similar structural dynamics of closed bRC and PSII RC complexes, and similar physical mechanisms, in which dielectric relaxation processes and structural memory effects of proteins are proposed to play important roles.

Coherent excitation energy transfer in model photosynthetic reaction center: Effects of non-Markovian quantum environment

Excitation energy transfer (EET) and electron transfer (ET) are crucially involved in photosynthetic processes. In reality, the photosynthetic reaction center constitutes an open quantum system of EET and ET, which manifests an interplay of pigments, solar light and phonon baths. So far theoretical studies have been mainly based on master equation approaches in the Markovian condition. The non-Markovian environmental effect, which may play a crucial role, has not been sufficiently considered. In this work, we propose a mixed dynamic approach to investigate this open system. The influence of phonon bath is treated via the exact dissipaton equation of motion (DEOM) while that of photon bath is via the Lindblad master equation. Specifically, we explore the effect of non-Markovian quantum phonon bath on the coherent transfer dynamics and its manipulation on the current--voltage behavior. Distinguished from the results of completely Markovian Lindblad equation and those adopting classical environment description, the mixed DEOM--Lindblad simulations exhibittransfer coherence up to a few hundreds femtosecondsand the related environmental manipulation effect on current.These non-Markovian quantum coherent effects may be extended tomore complex and realistic systems and be helpful to thedesign of organic photovoltaic devices.

Vibronic resonance along effective modes mediates selective energy transfer in excitonically coupled aggregates

We recently proposed effective normal modes for excitonically coupled aggregates that exactly transform the energy transfer Hamiltonian into a sum of one-dimensional Hamiltonians along the effective normal modes. Identifying physically meaningful vibrational motions that maximally promote vibronic mixing suggested an interesting possibility of leveraging vibrational-electronic resonance for mediating selective energy transfer. Here, we expand on the effective mode approach, elucidating its iterative nature for successively larger aggregates, and extend the idea of mediated energy transfer to larger aggregates. We show that energy transfer between electronically uncoupled but vibronically resonant donor-acceptor sites does not depend on the intermediate site energy or the number of intermediate sites. The intermediate sites simply mediate electronic coupling such that vibronic coupling along specific promoter modes leads to direct donor-acceptor energy transfer, bypassing any intermediate uphill energy transfer steps. We show that the interplay between the electronic Hamiltonian and the effective mode transformation partitions the linear vibronic coupling along specific promoter modes to dictate the selectivity of mediated energy transfer with a vital role of interference between vibronic couplings and multi-particle basis states. Our results suggest a general design principle for enhancing energy transfer through synergistic effects of vibronic resonance and weak mediated electronic coupling, where both effects individually do not promote efficient energy transfer. The effective mode approach proposed here paves a facile route toward four-wavemixing spectroscopy simulations of larger aggregates without severely approximating resonant vibronic coupling.

The fate of molecular excited states: modeling donor-acceptor dyes

We investigate the relaxation of a coherently excited molecule in the Redfield approximation. The molecular model, parametrized to describe donor-acceptor dyes that represent a large family of molecules of interest...

Redox conditions correlated with vibronic coupling modulate quantum beats in photosynthetic pigment-protein complexes

Quantum coherences, observed as time-dependent beats in ultrafast spectroscopic experiments, arise when light-matter interactions prepare systems in superpositions of states with differing energy and fixed phase across the ensemble. Such coherences have been observed in photosynthetic systems following ultrafast laser excitation, but what these coherences imply about the underlying energy transfer dynamics remains subject to debate. Recent work showed that redox conditions tune vibronic coupling in the Fenna-Matthews-Olson (FMO) pigment-protein complex in green sulfur bacteria, raising the question of whether redox conditions may also affect the long-lived (>100 fs) quantum coherences observed in this complex. In this work, we perform ultrafast two-dimensional electronic spectroscopy measurements on the FMO complex under both oxidizing and reducing conditions. We observe that many excited-state coherences are exclusively present in reducing conditions and are absent or attenuated in oxidizing conditions. Reducing conditions mimic the natural conditions of the complex more closely. Further, the presence of these coherences correlates with the vibronic coupling that produces faster, more efficient energy transfer through the complex under reducing conditions. The growth of coherences across the waiting time and the number of beating frequencies across hundreds of wavenumbers in the power spectra suggest that the beats are excited-state coherences with a mostly vibrational character whose phase relationship is maintained through the energy transfer process. Our results suggest that excitonic energy transfer proceeds through a coherent mechanism in this complex and that the coherences may provide a tool to disentangle coherent relaxation from energy transfer driven by stochastic environmental fluctuations.