Towards quantification of vibronic coupling in photosynthetic antenna complexes

Revealing Intermolecular Electronic and Vibronic Coherence with Polarization-Dependent Two-Dimensional Beating Maps

Two-dimensional electronic spectroscopy (2DES) has been widely employed as an efficient tool to reveal the impact of intermolecular electronic and/or vibronic quantum coherence on excitation energy transfer in light-harvesting complexes. However, intramolecular vibrational coherence would also contribute to oscillating signals in 2D spectra, along with the intermolecular coherence signals that are directly related to energy transfer. In this work, the possibility of screening the vibrational coherence signals is explored through polarization-dependent 2DES. The all-parallel (AP) and double-crossed (DC) polarization-dependent two-dimensional rephasing spectra (2DRS) are simulated for a minimalist heterodimer model with vibrational coupling. By combining the DC-2DRS and the 2D beating maps, we demonstrate that the population and vibrational coherence signals can be largely suppressed, resulting in highlighted intermolecular electronic and vibronic coherence signals. Moreover, the AP- and DC-2DBMs show rather different patterns at the vibrational frequency, indicating a possible way to identify pure vibrational coherence.

Symmetry-Breaking Enhanced Herzberg-Teller Effect with Brominated Polyacenes

Molecular symmetry is vital to the selection rule of vibrationally resolved electronic transition, particularly when the nuclear dependence of electronic wave function is explicitly treated by including Franck-Condon (FC) factor, Franck-Condon/Herzberg-Teller (FC/HT) interference, and Herzberg-Teller (HT) coupling. Our present study investigated the light absorption spectra of highly symmetric tetracene, pentacene, and hexacene molecules of point-group D_2h, as well as their monobrominated derivatives with a lower C_s symmetry. It was found that the symmetry-breaking monobromination allows more vibrational normal modes and their pairs to contribute to FC/HT interference and HT coupling, respectively. Through a projection of a molecule's vibrational normal modes to its irreducible representations, a linear relationship between the FC/HT intensity to the polyacene's size was deduced alongside a quadratic dependence of the HT intensity. Both theoretically derived correlations were well justified by our numerical simulations, which also demonstrated an approximately 20% improvement on the agreement with experimental line shape if the HT theory is adopted to replace the FC approximation. Moreover, for these low-symmetry monobrominated polyacenes, the FC intensity was even weaker than its FC/HT and HT counterparts at some excitation energies, making the HT theory imperative to decipher vibronic coupling, a fundamental driving force behind numerous chemical, biological, and photophysical processes.

Physiological Genetics Reformed: Bridging the Genome-to-Phenome Gap by Coherent Chemical Fingerprints - the Global Coordinator

Forward-focused molecular genetics is successfully framing DNA diversity and mapping primary gene functions. However, abandoning the classic Linnaean fingerprint link between the phenome and genome by suppressing gene interaction (pleiotropy), has resulted in a genome-to-phenome gap and poor utilization of molecular data. We demonstrate how to bridge this gap by using an example of a barley mutant seed model, where pleiotropy is observed as covarying global molecular patterns that define each endosperm. Global coherence was discovered as a covariate coordinator within and between local genotype specific fingerprints. This implies that any of these fingerprints can select its recombinant global phenotype variant, including composition. Introducing the law of coherence, and the movement of gene complexes by chemical fingerprint traits as selectors, introduces a revolution in understanding physiological molecular genetics and plant-breeding.

Intraband dynamics and exciton trapping in the LH2 complex of Rhodopseudomonas acidophila

Over the last several decades, the light-harvesting protein complexes of purple bacteria have been among the most popular model systems for energy transport in excitonic systems in the weak and intermediate intermolecular coupling regime. Despite this extensive body of scientific work, significant questions regarding the excitonic states and the photo-induced dynamics remain. Here, we address the low-temperature electronic structure and excitation dynamics in the light-harvesting complex 2 of Rhodopseudomonas acidophila by two-dimensional electronic spectroscopy. We find that, although at cryogenic temperature energy relaxation is very rapid, exciton mobility is limited over a significant range of excitation energies. This points to the presence of a sub-200 fs, spatially local energy-relaxation mechanism and suggests that local trapping might contribute substantially more in cryogenic experiments than under physiological conditions where the thermal energy is comparable to or larger than the static disorder.

Interference among Multiple Vibronic Modes in Two-Dimensional Electronic Spectroscopy

Vibronic coupling between electronic and vibrational states in molecules plays a critical role in most photo-induced phenomena. Many key details about a molecule’s vibronic coupling are hidden in linear spectroscopic measurements, and therefore nonlinear optical spectroscopy methods such as two-dimensional electronic spectroscopy (2D ES) have become more broadly adopted. A single vibrational mode of a molecule leads to a Franck–Condon progression of peaks in a 2D spectrum. Each peak oscillates as a function of the waiting time, and Fourier transformation can produce a spectral slice known as a ‘beating map’ at the oscillation frequency. The single vibrational mode produces a characteristic peak structure in the beating map. Studies of single modes have limited utility, however, because most molecules have numerous vibrational modes that couple to the electronic transition. Interactions or interference among the modes may lead to complicated peak patterns in each beating map. Here, we use lineshape-function theory to simulate 2D ES arising from a system having multiple vibrational modes. The simulations reveal that the peaks in each beating map are affected by all of the vibrational modes and therefore do not isolate a single mode, which was anticipated.

Electronic coherence lifetimes of the Fenna-Matthews-Olson complex and light harvesting complex II

The study of coherence between excitonic states in naturally occurring photosynthetic systems offers tantalizing prospects for uncovering mechanisms of efficient energy transport.

The study of coherence between excitonic states in naturally occurring photosynthetic systems offers tantalizing prospects of uncovering mechanisms of efficient energy transport. However, experimental evidence of functionally relevant coherences in wild-type proteins has been tentative, leading to uncertainty in their importance at physiological conditions. Here, we extract the electronic coherence lifetime and frequency using a signal subtraction procedure in two model pigment-protein-complexes (PPCs), light harvesting complex II (LH2) and the Fenna–Matthews–Olson complex (FMO), and find that the coherence lifetimes occur at the same timescale (<100 fs) as energy transport between states at the energy level difference equal to the coherence energy. The pigment monomer bacteriochlorophyll a (BChla) shows no electronic coherences, supporting our methodology of removing long-lived vibrational coherences that have obfuscated previous assignments. This correlation of timescales and energy between coherences and energy transport reestablishes the time and energy scales that quantum processes may play a role in energy transport.

Orientational Dynamics of Transition Dipoles and Exciton Relaxation in LH2 from Ultrafast Two-Dimensional Anisotropy

Light-harvesting complexes in photosynthetic organisms display fast and efficient energy transfer dynamics, which depend critically on the electronic structure of the coupled chromophores within the complexes and their interactions with their environment. We present ultrafast anisotropy dynamics, resolved in both time and frequency, of the transmembrane light-harvesting complex LH2 from Rhodobacter sphaeroides in its native membrane environment using polarization-controlled two-dimensional electronic spectroscopy. Time-dependent anisotropy obtained from both experiment and modified Redfield simulation reveals an orientational preference for excited state absorption and an ultrafast equilibration within the B850 band in LH2. This ultrafast equilibration is favorable for subsequent energy transfer toward the reaction center. Our results also show a dynamic difference in excited state absorption anisotropy between the directly excited B850 population and the population that is initially excited at 800 nm, suggesting absorption from B850 states to higher-lying excited states following energy transfer from B850*. These results give insight into the ultrafast dynamics of bacterial light harvesting and the excited state energy landscape of LH2 in the native membrane environment.

Coherences of Bacteriochlorophyll a Uncovered Using 3D-Electronic Spectroscopy

Mapping the multidimensional energy landscape of photosynthetic systems is crucial for understanding their high efficiencies. Multidimensional coherent spectroscopy is well suited to this task but has difficulty distinguishing between vibrational and electronic degrees of freedom. In pigment-protein complexes, energy differences between vibrations within a single electronic manifold are similar to differences between electronic states, leading to ambiguous assignments of spectral features and diverging physical interpretations. An important control experiment is that of the pigment monomer, but previous attempts using multidimensional coherent spectroscopy lacked the sensitivity to capture the relevant spectroscopic signatures. Here we apply a variety of methods to rapidly acquire 3D electronic-vibrational spectra in seconds, leading to a mapping of the vibrational states of Bacteriochlorophyll a (BChl a) in solution. Using this information, we can distinguish features of proteins containing BChl a from the monomer subunit and show that many of the previously reported contentious spectral signatures are vibrations of individual pigments.

Coherent phenomena in photosynthetic light harvesting: part two-observations in biological systems

Considerable debate surrounds the question of whether or not quantum mechanics plays a significant, non-trivial role in photosynthetic light harvesting. Many have proposed that quantum superpositions and/or quantum transport phenomena may be responsible for the efficiency and robustness of energy transport present in biological systems. The critical experimental observations comprise the observation of coherent oscillations or "quantum beats" via femtosecond laser spectroscopy, which have been observed in many different light harvesting systems. Part Two of this review aims to provide an overview of experimental observations of energy transfer in the most studied light harvesting systems. Length scales, derived from crystallographic studies, are combined with energy and time scales of the beats observed via spectroscopy. A consensus is emerging that most long-lived (hundreds of femtoseconds) coherent phenomena are of vibrational or vibronic origin, where the latter may result in coherent excitation transport within a protein complex. In contrast, energy transport between proteins is likely to be incoherent in nature. The question of whether evolution has selected for these non-trivial quantum phenomena may be an unanswerable question, as dense packings of chromophores will lead to strong coupling and hence non-trivial quantum phenomena. As such, one cannot discern whether evolution has optimised light harvesting systems for high chromophore density or for the ensuing quantum effects as these are inextricably linked and cannot be switched off.

Theory of Excitonic Delocalization for Robust Vibronic Dynamics in LH2

Nonlinear spectroscopy has revealed long-lasting oscillations in the optical response of a variety of photosynthetic complexes. Different theoretical models that involve the coherent coupling of electronic (excitonic) or electronic-vibrational (vibronic) degrees of freedom have been put forward to explain these observations. The ensuing debate concerning the relevance of either mechanism may have obscured their complementarity. To illustrate this balance, we quantify how the excitonic delocalization in the LH2 unit of Rhodopseudomonas acidophila purple bacterium leads to correlations of excitonic energy fluctuations, relevant coherent vibronic coupling, and importantly, a decrease in the excitonic dephasing rates. Combining these effects, we identify a feasible origin for the long-lasting oscillations observed in fluorescent traces from time-delayed two-pulse single-molecule experiments performed on this photosynthetic complex and use this approach to discuss the role of this complementarity in other photosynthetic systems.

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.

Signatures of Herzberg-Teller coupling in three-dimensional electronic spectroscopy

The coupling between electronic and nuclear variables is a key consideration in molecular dynamics and spectroscopy. However, simulations that include detailed vibronic coupling terms are challenging to perform, and thus a variety of approximations can be used to model and interpret experimental results. Recent work shows that these simplified models can be inadequate. It is therefore important to understand spectroscopic signals that can identify failures of those approximations. Here we use an extended response-function method to simulate coherent three-dimensional electronic spectroscopy (3D ES) and study the sensitivity of this method to the breakdown of the Franck-Condon approximation. The simulations include a coordinate-dependent transition dipole operator that produces nodes, phase shifts, and peak patterns in 3D ES that can be used to identify Herzberg-Teller coupling. Guided by the simulation results, we interpret measurements on a molecular aggregate.

Correlated Fluctuations and Intraband Dynamics of J-Aggregates Revealed by Combination of 2DES Schemes

The intraband exciton dynamics of molecular aggregates is a crucial initial step to determine the possibly coherent nature of energy transfer and its implications for the ensuing interband relaxation pathways in strongly coupled excitonic systems. In this work, we fully characterize the intraband dynamics in linear J-aggregates of porphyrins, good model systems for multichromophoric assemblies in biological antenna complexes. Using different 2D electronic spectroscopy schemes together with Raman spectroscopy and theoretical modeling, we provide a full characterization of the inner structure of the main one-exciton band of the porphyrin aggregates. We find that the redistribution of population within the band occurs with a characteristic time of 280 fs and dominates the modulation of an electronic coherence. While we do not find that the coupling to vibrations significantly affects the dynamics of excitonic coherence, our results suggest that exciton fluctuations are nevertheless highly correlated.

Communication: Coherences observed in vivo in photosynthetic bacteria using two-dimensional electronic spectroscopy

Energy transfer through large disordered antenna networks in photosynthetic organisms can occur with a quantum efficiency of nearly 100%. This energy transfer is facilitated by the electronic structure of the photosynthetic antennae as well as interactions between electronic states and the surrounding environment. Coherences in time-domain spectroscopy provide a fine probe of how a system interacts with its surroundings. In two-dimensional electronic spectroscopy, coherences can appear on both the ground and excited state surfaces revealing detailed information regarding electronic structure, system-bath coupling, energy transfer, and energetic coupling in complex chemical systems. Numerous studies have revealed coherences in isolated photosynthetic pigment-protein complexes, but these coherences have not been observed in vivo due to the small amplitude of these signals and the intense scatter from whole cells. Here, we present data acquired using ultrafast video-acquisition gradient-assisted photon echo spectroscopy to observe quantum beating signals from coherences in vivo. Experiments were conducted on isolated light harvesting complex II (LH2) from Rhodobacter sphaeroides, whole cells of R. sphaeroides, and whole cells of R. sphaeroides grown in 30% deuterated media. A vibronic coherence was observed following laser excitation at ambient temperature between the B850 and the B850(∗) states of LH2 in each of the 3 samples with a lifetime of ∼40-60 fs.