Quantum coherence as a witness of vibronically hot energy transfer in bacterial reaction center

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.

Diverse Transient Chiral Dynamics in Evolutionary Distinct Photosynthetic Reaction Centers

The evolution of photosynthetic reaction centers (RCs) from anoxygenic bacteria to higher-order oxygenic cynobacteria and plants highlights a remarkable journey of structural and functional diversification as an adaptation to environmental conditions. The role of chirality in these centers is important, influencing the arrangement and function of key molecules involved in photosynthesis. Investigating the role of chirality may provide a deeper understanding of photosynthesis and the evolutionary history of life on Earth. In this study, we explore chirality-related energy transfer in two evolutionarily distinct RCs: one from the anoxygenic purple sulfur bacterium Thermochromatium tepidum (BRC) and the other from the oxygenic cyanobacterium Thermosynechococcus vulcanus (PSII RC), utilizing two-dimensional electronic spectroscopy (2DES). By employing circularly polarized laser pulses, we can extract transient chiral dynamics within these RCs, offering a detailed view of their chiral contribution to energy transfer processes. We also compute traditional 2DES and compare these results with spectra related to circular dichroism. Our findings indicate that two-dimensional circular dichroism spectroscopy effectively reveals chiral dynamics, emphasizing the structural symmetries of pigments and their interactions with associated proteins. Despite having similar pigment-protein architectures, the BRC and PSII RC exhibit significantly different chiral dynamics on an ultrafast time scale. In the BRC, the complex contributions of pigments such as BChM, BPhL, BCh, and PM to key excitonic states lead to more pronounced chiral features and dynamic behavior. In contrast, the PSII RC, although significantly influenced by ChlD1 and ChlD2, shows less complex chiral effects and more subdued chiral dynamics. Notably, the PSII RC demonstrates a faster decay of coherence to localized excitonic populations compared to the BRC, which may represent an adaptive mechanism to minimize oxidative stress in oxygenic photosystems. By examining and comparing the chiral excitonic interactions and dynamics of BRC and PSII RC, this study offers valuable insights into the mechanisms of photosynthetic complexes. These findings could contribute to understanding how the functional optimization of photosynthetic proteins in ultrafast time scales is linked to biological evolution.

Antioxidative Triplet Excitation Energy Transfer in Bacterial Reaction Center Using a Screened Range Separated Hybrid Functional

Excess energy absorbed by photosystems (PSs) can result in photoinduced oxidative damage. Transfer of such energy within the core pigments of the reaction center in the form of triplet excitation is important in regulating and preserving the functionality of PSs. In the bacterial reaction center (BRC), the special pair (P) is understood to act as the electron donor in a photoinduced charge transfer process, triggering the charge separation process through the photoactive branch A pigments that experience a higher polarizing environment. At this work, triplet excitation energy transfer (TEET) in BRC is studied using a computational perspective to gain insights into the roles of the dielectric environment and interpigment orientations. We find in agreement with experimental observations that TEET proceeds through branch B. The TEET process toward branch B pigment is found to be significantly faster than the hypothetical process proceeding through branch A pigments with ps and ms time scales, respectively. Our calculations find that conformational differences play a major role in this branch asymmetry in TEET, where the dielectric environment asymmetry plays only a secondary role in directing the TEET to proceed through branch B. We also address TEET processes asserting the role of carotenoid as the final triplet energy acceptor and in a mutant form, where the branch pigments adjacent to P are replaced by bacteriopheophytins. The necessary electronic excitation energies and electronic state couplings are calculated by the recently developed polarization-consistent framework combining a screened range-separated hybrid functional and a polarizable continuum mode. The polarization-consistent potential energy surfaces are used to parametrize the quantum mechanical approach, implementing Fermi's golden rule expression of the TEET rate calculations.

Quantum phase synchronization via exciton-vibrational energy dissipation sustains long-lived coherence in photosynthetic antennas

The lifetime of electronic coherences found in photosynthetic antennas is known to be too short to match the energy transfer time, rendering the coherent energy transfer mechanism inactive. Exciton-vibrational coherence time in excitonic dimers which consist of two chromophores coupled by excitation transfer interaction, can however be much longer. Uncovering the mechanism for sustained coherences in a noisy biological environment is challenging, requiring the use of simpler model systems as proxies. Here, via two-dimensional electronic spectroscopy experiments, we present compelling evidence for longer exciton-vibrational coherence time in the allophycocyanin trimer, containing excitonic dimers, compared to isolated pigments. This is attributed to the quantum phase synchronization of the resonant vibrational collective modes of the dimer, where the anti-symmetric modes, coupled to excitonic states with fast dephasing, are dissipated. The decoupled symmetric counterparts are subject to slower energy dissipation. The resonant modes have a predicted nearly 50% reduction in the vibrational amplitudes, and almost zero amplitude in the corresponding dynamical Stokes shift spectrum compared to the isolated pigments. Our findings provide insights into the mechanisms for protecting coherences against the noisy environment.

Expanding the bandwidth of fluorescence-detected two-dimensional electronic spectroscopy using a broadband continuum probe pulse pair

We demonstrate fluorescence-detected two-dimensional electronic spectroscopy (F-2DES) with a broadband, continuum probe pulse pair in the pump-probe geometry. The approach combines a pump pulse pair generated by an acousto-optic pulse-shaper with precise control of the relative pump pulse phase and time delay with a broadband, continuum probe pulse pair created using the Translating Wedge-based Identical pulses eNcoding System (TWINS). The continuum probe expands the spectral range of the detection axis and lengthens the waiting times that can be accessed in comparison to implementations of F-2DES using a single pulse-shaper. We employ phase-cycling of the pump pulse pair and take advantage of the separation of signals in the frequency domain to isolate rephasing and non-rephasing signals and optimize the signal-to-noise ratio. As proof of principle, we demonstrate broadband F-2DES on a laser dye and bacteriochlorophyll a.

Coherent Phonon-Mediated Many-Body Interaction in Monolayer WSe2

Due to the strong Coulomb interaction, the optical and electrical properties of two-dimensional transition metal dichalcogenides (TMDCs) are greatly determined by the emergence of many-body complexes such as excitons or trions. To fully realize the potential functionalities of these atomically thin materials, a comprehensive understanding of their many-body interaction mechanism is essential. Here, using the advanced femtosecond two-dimensional electronic spectroscopy technique combined with broadband transient absorption spectroscopy, a strong electron-exciton coupling effect in monolayer WSe₂ following the ultrafast photoexcitation is revealed. We demonstrate that such many-body complexes can be generated effectively through the band-edge optical excitation, with a ∼1.5 ps stabilization process. The coherent optical phonon plays a dominant role in this electron-exciton interaction, and the coherence of the electron (exciton)-phonon coupling can last for ∼4.5 ps. This finding offers new insight into the formation mechanism of photoinduced many-body complexes in TMDCs.

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.

Dyads with tunable near-infrared donor-acceptor excited-state energy gaps: molecular design and Förster analysis for ultrafast energy transfer

Bacteriochlorophylls, nature's near-infrared absorbers, play an essential role in energy transfer in photosynthetic antennas and reaction centers. To probe energy-transfer processes akin to those in photosynthetic systems, nine synthetic bacteriochlorin-bacteriochlorin dyads have been prepared wherein the constituent pigments are joined at the meso-positions by a phenylethyne linker. The phenylethyne linker is an unsymmetric auxochrome, which differentially shifts the excited-state energies of the phenyl- or ethynyl-attached bacteriochlorin constituents in the dyad. Molecular designs utilized known effects of macrocycle substituents to engineer bacteriochlorins with S₀ → S₁ (Q_y) transitions spanning 725-788 nm. The design-predicted donor-acceptor excited-state energy gaps in the dyads agree well with those obtained from time dependent density functional theory calculations and with the measured range of 197-1089 cm^-1. Similar trends with donor-acceptor excited-state energy gaps are found for (1) the measured ultrafast energy-transfer rates of (0.3-1.7 ps)^-1, (2) the spectral overlap integral (J) in Förster energy-transfer theory, and (3) donor-acceptor electronic mixing manifested in the natural transition orbitals for the S₀ → S₁ transition. Subtle outcomes include the near orthogonal orientation of the π-planes of the bacteriochlorin macrocycles, and the substituent-induced shift in transition-dipole moment from the typical coincidence with the NH-NH axis; the two features together afforded the Förster orientation term κ² ranging from 0.55-1.53 across the nine dyads, a value supportive of efficient excited-state energy transfer. The molecular design and collective insights on the dyads are valuable for studies relevant to artificial photosynthesis and other processes requiring ultrafast energy transfer.

Extracting the excitonic Hamiltonian of a chlorophyll dimer from broadband two-dimensional electronic spectroscopy

We apply Frenkel exciton theory to model the entire Q-band of a tightly bound chlorophyll dimer inspired by the photosynthetic reaction center of photosystem II. The potential of broadband two-dimensional electronic spectroscopy experiment spanning the Q_x and Q_y regions to extract the parameters of the model dimer Hamiltonian is examined through theoretical simulations of the experiment. We find that the local nature of Q_x excitation enables identification of molecular properties of the delocalized Q_y excitons. Specifically, we demonstrate that the cross-peak region, where excitation energy is resonant with Q_y while detection is at Q_x, contains specific spectral signatures that can reveal the full real-space molecular Hamiltonian, a task that is impossible by considering the Q_y transitions alone. System-bath coupling and site energy disorder in realistic systems may limit the resolution of these spectral signatures due to spectral congestion.

Probing the Effects of Electronic-Vibrational Resonance on the Rate of Excited-State Energy Transfer in Bacteriochlorin Dyads

The impact of vibrational-electronic resonances on the rate of excited-state energy transfer is examined in a set of bacteriochlorin dyads that employ the same phenylethyne linker. The donor/acceptor excited-state energy gap is tuned from ∼200 to ∼1100 cm^-1 using peripheral substituents on the donor and acceptor bacteriochlorin macrocycles. Ultrafast energy transfer is observed with rate constants of (0.3 ps)^-1 to (1.7 ps)^-1, which agree with those predicted by Förster theory to within a factor of 2. Furthermore, the measured rates follow a trend-line with only small deviations that do not correlate with the density of vibrations at the donor/acceptor excited-state energy gap. Thus, if vibrational-electronic resonances occur in any of these dyads, which seems likely, the impact on the rate of energy transfer is small.

Beating signals in CdSe quantum dots measured by low-temperature 2D spectroscopy

Advances in ultrafast spectroscopy can provide access to dynamics involving nontrivial quantum correlations and their evolutions. In coherent 2D spectroscopy, the oscillatory time dependence of a signal is a signature of such quantum dynamics. Here we study such beating signals in electronic coherent 2D spectroscopy of CdSe quantum dots (CdSe QDs) at 77 K. The beating signals are analyzed in terms of their positive and negative Fourier components. We conclude that the beatings originate from coherent LO-phonons of CdSe QDs. No evidence for the quantum dot size dependence of the LO-phonon frequency was identified.

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.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

Dynamics of diverse coherences in primary charge separation of bacterial reaction center at 77 K revealed by wavelet analysis

To uncover the mechanism behind the high photo-electronic conversion efficiency in natural photosynthetic complexes it is essential to trace the dynamics of electronic and vibrational quantum coherences. Here we apply wavelet analysis to two-dimensional electronic spectroscopy data for three purple bacterial reaction centers with mutations that produce drastically different rates of primary charge separation. From the frequency distribution and dynamic evolution features of the quantum beating, electronic coherence with a dephasing lifetime of ~50 fs, vibronic coherence with a lifetime of ~150 fs and vibrational/vibronic coherences with a lifetime of 450 fs are distinguished. We find that they are responsible for, or couple to, different specific steps during the primary charge separation process, i.e., intradimer charge transfer inside the special bacteriochlorophyll pair followed by its relaxation and stabilization of the charge-transfer state. The results enlighten our understanding of how quantum coherences participate in, and contribute to, a biological electron transfer reaction.

Excited States and Their Dynamics in CdSe Quantum Dots Studied by Two-Color 2D Spectroscopy

Quantum dots (QDs) form a promising family of nanomaterials for various applications in optoelectronics. Understanding the details of the excited-state dynamics in QDs is vital for optimizing their function. We apply two-color 2D electronic spectroscopy to investigate CdSe QDs at 77 K within a broad spectral range. Analysis of the electronic dynamics during the population time allows us to identify the details of the excitation pathways. The initially excited high-energy electrons relax with the time constant of 100 fs. Simultaneously, the states at the band edge rise within 700 fs. Remarkably, the excited-state absorption is rising with a very similar time constant of 700 fs. This makes us reconsider the earlier interpretation of the excited-state absorption as the signature of a long-lived trap state. Instead, we propose that this signal originates from the excitation of the electrons that have arrived in the conduction-band edge.

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.

Vibration-mediated energy transport in bacterial reaction center: Simulation study

Exciton energy relaxation in a bacterial Reaction Center (bRC) pigment-protein aggregate presumably involves emission of high energy vibrational quanta to cover wide energy gaps between excitons. Here, we assess this hypothesis utilizing vibronic two-particle theory in modeling of the excitation relaxation process in bRC. Specific high frequency molecular vibrational modes are included explicitly one at a time in order to check which high frequency vibrations are involved in the excitation relaxation process. The low frequency bath modes are treated perturbatively within Redfield relaxation theory. The analysis of the population relaxation rate data indicates energy flow pathways in bRC and suggests that specific vibrations may be responsible for the excitation relaxation process.

Dynamic band-shift signal in two-dimensional electronic spectroscopy: A case of bacterial reaction center

Optical nonlinear spectroscopies carry a high amount of information about the systems under investigation; however, as they report polarization signals, the resulting spectra are often congested and difficult to interpret. To recover the landscape of energy states and physical processes such as energy and electron transfer, a clear interpretation of the nonlinear signals is prerequisite. Here, we focus on the interpretation of the electrochromic band-shift signal, which is generated when an internal electric field is established in the system following optical excitation. Whereas the derivative shape of the band-shift signal is well understood in transient absorption spectroscopy, its emergence in two-dimensional electronic spectroscopy (2DES) has not been discussed. In this work, we employed 2DES to follow the dynamic band-shift signal in reaction centers of purple bacteria Rhodobacter sphaeroides at 77 K. The prominent two-dimensional derivative-shape signal appears with the characteristic formation time of the charge separated state. To explain and characterize the band-shift signal, we use expanded double-sided Feynman diagram formalism. We propose to distinguish two types of Feynman diagrams that lead to signals with negative amplitude: excited state absorption and re-excitation. The presented signal decomposition and modeling analysis allows us to recover precise electrochromic shifts of accessory bacteriochlorophylls, identify additional signals in the B band range, and gain a further insight into the electron transfer mechanism. In a broader perspective, expanded Feynman diagram formalism will allow for interpretation of all 2D signals in a clearer and more intuitive way and therefore facilitate studying the underlying photophysics.

Excitonic structure and charge separation in the heliobacterial reaction center probed by multispectral multidimensional spectroscopy

Photochemical reaction centers are the engines that drive photosynthesis. The reaction center from heliobacteria (HbRC) has been proposed to most closely resemble the common ancestor of photosynthetic reaction centers, motivating a detailed understanding of its structure-function relationship. The recent elucidation of the HbRC crystal structure motivates advanced spectroscopic studies of its excitonic structure and charge separation mechanism. We perform multispectral two-dimensional electronic spectroscopy of the HbRC and corresponding numerical simulations, resolving the electronic structure and testing and refining recent excitonic models. Through extensive examination of the kinetic data by lifetime density analysis and global target analysis, we reveal that charge separation proceeds via a single pathway in which the distinct A₀ chlorophyll a pigment is the primary electron acceptor. In addition, we find strong delocalization of the charge separation intermediate. Our findings have general implications for the understanding of photosynthetic charge separation mechanisms, and how they might be tuned to achieve different functional goals.

The primary energy conversion step in photosynthesis, charge separation, takes place in the reaction center. Here the authors investigate the heliobacterial reaction center using multispectral two-dimensional electronic spectroscopy, identifying the primary electron acceptor and revealing the charge separation mechanism.

Singlet Fission Driven by Anisotropic Vibronic Coupling in Single-Crystalline Pentacene

Vibronic coupling is believed to play an important role in siglet fission, wherein a photoexcited singlet exciton is converted into two triplet excitons. In the present study, we examine the role of vibronic coupling in singlet fission using polarized transient absorption microscopy and ab initio simulations on single-crystalline pentacene. It was found that singlet fission in pentacene is greatly facilitated by the vibrational coherence of a 35.0 cm^-1 phonon, where anisotropic coherence persists extensively for a few picoseconds. This coherence-preserving phonon that drives the anisotropic singlet fission is made possible by a unique cross-axial charge-transfer intermediate state. In the same fashion, this phonon was also found to predominantly drive the quantum decohence of a correlated triplet pair to form a decoupled triplet dimer. Moreover, our transient kinetic experimental data illustrates notable directional anisotropicity of the singlet fission rate in single-crystalline pentacene.

Influence of Vibronic Coupling on Ultrafast Singlet Fission in a Linear Terrylenediimide Dimer

Singlet fission (SF) is a photophysical process capable of boosting the efficiency of solar cells. Recent experimental investigations into the mechanism of SF provide evidence for coherent mixing between the singlet, triplet, and charge transfer basis states. Up until now, this interpretation has largely focused on electronic interactions; however, nuclear motions resulting in vibronic coupling have been suggested to support rapid and efficient SF in organic chromophore assemblies. Further information about the complex interactions between vibronic excited states is needed to understand the potential role of this coupling in SF. Here, we report mixed singlet and correlated triplet pair states giving rise to sub-50 fs SF in a terrylene-3,4:11,12-bis(dicarboximide) (TDI) dimer in which the two TDI molecules are covalently linked by a direct N-N connection at one of their imide positions, leading to a linear dimer with perpendicular TDI π systems. We observe the transfer of low-frequency coherent wavepackets between the initial predominantly singlet states to the product triplet-dominated states. This implies a non-negligible dependence of SF on nonadiabatic coupling in this dimer. We interpret our experimental results in the framework of a modified Holstein Hamiltonian, which predicts that vibronic interactions between low-frequency singlet modes and high-frequency correlated triplet pair motions lead to mixing of the pure basis states. These results highlight how nonadiabatic mixing can shape the complex potential energy landscape underlying ultrafast SF.

Electronic State-Resolved Multimode-Coupled Vibrational Wavepackets in Oxazine 720 by Two-Dimensional Electronic Spectroscopy

The difference between the excited- and ground-state vibrational wavepackets remains to be fully explored when multiple vibrational modes are coherently excited simultaneously by femtosecond pulses. In this work, we present a series of one- and two-dimensional electronic spectroscopy for studying multimode wavepackets of oxazine 720 in solution. Fourier transform (FT) maps combined with time-frequency transform (TFT) are employed to unambiguously distinguish the origin of low-frequency vibrational wavepackets, that is, an excited-state vibrational wavepacket of 586 cm^-1 with a dephasing time of 0.7 ps and a ground-state vibrational wavepacket of 595 cm^-1 with a dephasing time of 1.3-1.7 ps. We also found the additional low-frequency vibrational wavepackets resulting from the coupling of the 595 cm^-1 mode to a series of high-frequency modes centered at 1150 cm^-1 via electronic transitions. The combined use of FT maps and TFT analysis allows us to reveal the potential vibrational coupling of wavepackets and offers the possibility of disentangling the coupling between the electronic and vibrational degrees of freedom in condensed-phase systems.

Synthetic non-classical luminescence generation by enhanced silica nanophotonics based on nano-bio-FRET

Fluorescent silica nanoparticles (NPs–(SiO₂–Fluo)) were synthesized based on the classical Störber method for cyanobacteria labelling. Modified mono-coloured SiO₂ NPs with fluorescein (Fl) and rhodamine B (RhB) were obtained (NPs–(SiO₂–Fl) and NPs–(SiO₂–RhB)). Moreover, multi-coloured SiO₂ NPs, via the incorporation of both emitters (NPs–(SiO₂–RhB–Fl)), were tuned for optimal emissions and the biodetection of cyanobacteria. NPs–(SiO₂–Fl) and NPs–(SiO₂–RhB–Fl) were optimized for detection via laser fluorescence microscopy and in-flow cytometry with laser excitation and fluorescence detection. By TEM, homogeneous SiO₂ NPs of 180.0 nm in diameter were recorded. These sizes were slightly increased due to the covalent linking incorporation of fluorescent dye emitters to 210.0 nm with mono-coloured fluorescent modified amine-organosilanes, and to 340.0 nm in diameter with multi-coloured dye incorporation. NPs–(SiO₂–Fluo) showed variable emission depending on the dye emitter concentration, quantum yield and applied luminescent pathway. Thus, mono-coloured NPs–(SiO₂–Fl) and NPs–(SiO₂–RhB) showed diminished emissions in comparison to multi-coloured NPs–(SiO₂–RhB–Fl). This enhancement was explained by fluorescence resonance energy transfer (FRET) between Fl as a fluorescent energy donor and RhB as an energy acceptor produced within the nanoarchitecture, produced only in the presence of both fluorophores with the appropriate laser excitation of the energy donor. The depositions of the nano-emitters on cyanobacteria by non-covalent interactions were observed by TEM and laser fluorescence microscopy. For multi-coloured NPs–(SiO₂–RhB–Fl) labelling, bio-FRET was observed between the emission of the nano-labellers and the natural fluorophores from the cyanobacteria that quenched the emission of the whole nano-biostructure in comparison to mono-coloured NPs–(SiO₂–Fl) labelling. This fact was explained and discussed in terms of different fluorescence energy transfer from the nanolabellers towards different natural chromophore coupling. In the presence of NPs–(SiO₂–RhB–Fl) and NPs–(SiO₂–RhB), the emission was coupled with lower quantum yield chromophores; while upon the application of NPs–(SiO₂–Fl), it was coupled with higher quantum yield chromophores. In this manner, for enhanced luminescent nanoplatform tracking, the multi-coloured NPs–(SiO₂–RhB–Fl) showed improved properties; but more highly luminescent bio-surfaces were generated with mono-coloured NPs–(SiO₂–Fl) that permitted faster cyanobacteria detection and counting by laser fluorescence microscopy, and by in-flow cytometry with laser excitation and fluorescence detection.

Fluorescent silica nanophotonics for cyanobacteria labelling.

Atomic fluctuations in electronic materials revealed by dephasing

The microscopic origin and timescale of the fluctuations of the energies of electronic states has a significant impact on the properties of interest of electronic materials, with implication in fields ranging from photovoltaic devices to quantum information processing. Spectroscopic investigations of coherent dynamics provide a direct measurement of electronic fluctuations. Modern multidimensional spectroscopy techniques allow the mapping of coherent processes along multiple time or frequency axes and thus allow unprecedented discrimination between different sources of electronic dephasing. Exploiting modern abilities in coherence mapping in both amplitude and phase, we unravel dissipative processes of electronic coherences in the model system of CdSe quantum dots (QDs). The method allows the assignment of the nature of the observed coherence as vibrational or electronic. The expected coherence maps are obtained for the coherent longitudinal optical (LO) phonon, which serves as an internal standard and confirms the sensitivity of the technique. Fast dephasing is observed between the first two exciton states, despite their shared electron state and common environment. This result is contrary to predictions of the standard effective mass model for these materials, in which the exciton levels are strongly correlated through a common size dependence. In contrast, the experiment is in agreement with ab initio molecular dynamics of a single QD. Electronic dephasing in these materials is thus dominated by the realistic electronic structure arising from fluctuations at the atomic level rather than static size distribution. The analysis of electronic dephasing thereby uniquely enables the study of electronic fluctuations in complex materials.

Quantum biology revisited

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.

Optimal efficiency of the Q-cycle mechanism around physiological temperatures from an open quantum systems approach

The Q-cycle mechanism entering the electron and proton transport chain in oxygenic photosynthesis is an example of how biological processes can be efficiently investigated with elementary microscopic models. Here we address the problem of energy transport across the cellular membrane from an open quantum system theoretical perspective. We model the cytochrome \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${b}_{6}\,f$$\end{document}b6f protein complex under cyclic electron flow conditions starting from a simplified kinetic model, which is hereby revisited in terms of a Markovian quantum master equation formulation and spin-boson Hamiltonian treatment. We apply this model to theoretically demonstrate an optimal thermodynamic efficiency of the Q-cycle around ambient and physiologically relevant temperature conditions. Furthermore, we determine the quantum yield of this complex biochemical process after setting the electrochemical potentials to values well established in the literature. The present work suggests that the theory of quantum open systems can successfully push forward our theoretical understanding of complex biological systems working close to the quantum/classical boundary.

Non-equilibrium relaxation of hot states in organic semiconductors: Impact of mode-selective excitation on charge transfer

The theoretical study of open quantum systems strongly coupled to a vibrational environment remains computationally challenging due to the strongly non-Markovian characteristics of the dynamics. We study this problem in the case of a molecular dimer of the organic semiconductor tetracene, the exciton states of which are strongly coupled to a few hundreds of molecular vibrations. To do so, we employ a previously developed tensor network approach, based on the formalism of matrix product states. By analyzing the entanglement structure of the system wavefunction, we can expand it in a tree tensor network state, which allows us to perform a fully quantum mechanical time evolution of the exciton-vibrational system, including the effect of 156 molecular vibrations. We simulate the dynamics of hot states, i.e., states resulting from excess energy photoexcitation, by constructing various initial bath states, and show that the exciton system indeed has a memory of those initial configurations. In particular, the specific pathway of vibrational relaxation is shown to strongly affect the quantum coherence between exciton states in time scales relevant for the ultrafast dynamics of application-relevant processes such as charge transfer. The preferential excitation of low-frequency modes leads to a limited number of relaxation pathways, thus "protecting" quantum coherence and leading to a significant increase in the charge transfer yield in the dimer structure.

Both electronic and vibrational coherences are involved in primary electron transfer in bacterial reaction center

Understanding the mechanism behind the near-unity efficiency of primary electron transfer in reaction centers is essential for designing performance-enhanced artificial solar conversion systems to fulfill mankind’s growing demands for energy. One of the most important challenges is distinguishing electronic and vibrational coherence and establishing their respective roles during charge separation. In this work we apply two-dimensional electronic spectroscopy to three structurally-modified reaction centers from the purple bacterium Rhodobacter sphaeroides with different primary electron transfer rates. By comparing dynamics and quantum beats, we reveal that an electronic coherence with dephasing lifetime of ~190 fs connects the initial excited state, P*, and the charge-transfer intermediate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}PA+PB-; this \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ \ast \to {\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}P*→PA+PB- step is associated with a long-lived quasi-resonant vibrational coherence; and another vibrational coherence is associated with stabilizing the primary photoproduct, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ + {\mathrm{B}}_{\mathrm{A}}^ -$$\end{document}P+BA-. The results show that both electronic and vibrational coherences are involved in primary electron transfer process and they correlate with the super-high efficiency.

Distinguishing electronic and vibrational coherences helps to clarify the near-unity efficiency of primary electron transfer in reaction centres. Here, the authors report their respective correlation with the electron transfer rate by comparing the 2D electronic spectra of three mutant reaction centres.

Coupled excitation energy and charge transfer dynamics in reaction centre inspired model systems

Functional operation conditions of reaction centre core complexes require the tight coupling of exciton states to concomitant charge separation. Rigorous theoretical treatment of such integrated excitation energy transfer (EET) and charge transfer (CT) dynamics is particularly challenging due to (i) appreciable system sizes, (ii) inter-site and system-bath couplings of similar magnitude that render the Born-Markov approximation invalid, (iii) substantial reorganization energies of CT states, and (iv) the presence of complex structured spectral densities due to vibrational modes of the surroundings. We present numerical simulations on bacterial reaction centre (bRC) inspired model systems that utilize the recently developed MACGIC-iQUAPI method [Richter et al., J. Chem. Phys., 2017, 146, 214101]. The simulations demonstrate that the method provides a rigorous framework for the investigation of such integrated EET-CT dynamics. First, the applicability of the MACGIC-iQUAPI method is explored for a transition from monotonically decaying to oscillatory system-bath influence coefficients, a behavior inherently imposed by structured bath spectral densities. Tightly coupled EET and CT dynamics is further addressed for an excitonic subsystem that resembles strong coupling of special pair states and serves as donor towards a generic bridge-acceptor system. By solving the dissipative quantum dynamics of such bRC inspired model systems, the quenching of excitonic coherence on the hundreds of femtoseconds timescale is explored via a variation of the bridge state energetics, resembling a continuous transition from sequential to superexchange mediated CT regimes. Further, the simulations explore the influence of resonant vibrational modes on the quenching of excitonic coherence via CT. The results reveal a moderate influence of vibrational mode on charge separation dynamics in regimes of biologically relevant EET and CT dynamics.

Double-crossed polarization transient grating for distinction and characterization of coherences

Coherent phenomena have been widely suggested to play a role in efficient photosynthetic light harvesting and charge separation processes. To substantiate these ideas, separation of intramolecular vibrational coherences from purely electronic or mixed vibronic coherences is essential. To this end, polarization-controlled two-dimensional electronic spectroscopy has been shown to provide an effective selectivity. We show that analogous discrimination can be achieved in a transient grating experiment by employing the double-crossed polarization scheme. This is demonstrated in a study of bacterial reaction centers. Significantly faster acquisition times of these experiments make longer population time scans feasible, thereby achieving improved frequency resolution and allowing for accurate extraction of coherence frequencies and dephasing times. These parameters are crucial for the discussion on relevance of the measured coherences to energy or electron transfer phenomena.

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by Two-Dimensional Electronic Spectroscopy

Bacteriochlorophyll a (BChla) is the most abundant pigment found in the Bacterial Reaction Center (BRC) and light-harvesting proteins of photosynthetic purple and green bacteria. Recent two-dimensional electronic spectroscopy (2DES) studies of photosynthetic pigment-protein complexes including the BRC and the Fenna-Matthews-Olson (FMO) complex have shown oscillatory signals, or coherences, whose physical origin has been hotly debated. To better understand the observations of coherence in larger photosynthetic systems, it is important to carefully characterize the spectroscopic signatures of the monomeric pigments. Prior spectroscopic studies of BChla have differed significantly in their observations, with some studies reporting little to no coherence. Here we present evidence of strong coherences in monomeric BChla in isopropanol using 2DES at 77 K. We resolve many modes with frequencies that correspond well with known vibrational modes. We confirm their vibrational origin by comparing the 2D spectroscopic signatures with expectations based on a purely vibrational model.

Spatially-resolved fluorescence-detected two-dimensional electronic spectroscopy probes varying excitonic structure in photosynthetic bacteria

Conventional implementations of two-dimensional electronic spectroscopy typically spatially average over ~10¹⁰ chromophores spread over ~10⁴ micron square area, limiting their ability to characterize spatially heterogeneous samples. Here we present a variation of two-dimensional electronic spectroscopy that is capable of mapping spatially varying differences in excitonic structure, with sensitivity orders of magnitude better than conventional spatially-averaged electronic spectroscopies. The approach performs fluorescence-detection-based fully collinear two-dimensional electronic spectroscopy in a microscope, combining femtosecond time-resolution, sub-micron spatial resolution, and the sensitivity of fluorescence detection. We demonstrate the approach on a mixture of photosynthetic bacteria that are known to exhibit variations in electronic structure with growth conditions. Spatial variations in the constitution of mixed bacterial colonies manifests as spatially varying peak intensities in the measured two-dimensional contour maps, which exhibit distinct diagonal and cross-peaks that reflect differences in the excitonic structure of the bacterial proteins.

2D electronic spectroscopy enables a spatially-averaged view of the electronic structure of a heterogeneous system. Here, the authors extend it to sub-micron resolution and ~10⁶ times better sensitivity, to resolve spatially varying excitonic structure in a heterogeneous mixture of photosynthetic cells.

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.

Electronic Interactions in the Bacterial Reaction Center Revealed by Two-Color 2D Electronic Spectroscopy

The bacterial reaction center (BRC) serves as an important model system for understanding the charge separation processes in photosynthesis. Knowledge of the electronic structure of the BRC is critical for understanding its charge separation mechanism. While it is well-accepted that the "special pair" pigments are strongly coupled, the degree of coupling among other BRC pigments has been thought to be relatively weak. Here we study the W(M250)V mutant BRC by two-color two-dimensional electronic spectroscopy to correlate changes in the Q _x region with excitation of the Q _y transitions. The resulting Q _y-Q _x cross-peaks provide a sensitive measure of the electronic interactions throughout the BRC pigment network and complement one-color 2D studies in which such interactions are often obscured by energy transfer and excited-state absorption signals. Our observations should motivate the refinement of electronic structure models of the BRC to facilitate improved understanding of the charge separation mechanism.

Ultrafast Intersystem Crossing vs Internal Conversion in α-Diimine Transition Metal Complexes: Quantum Evidence

Whereas third row transition metal carbonyl α-diimine complexes display luminescent properties and possess low-lying triplet metal-to-ligand charge transfer (MLCT) states efficiently accessible by a spin-vibronic mechanism, first row analogues hold low-lying metal-centered (MC) excited states that could quench these properties. Upon visible irradiation, different functions are potentially stimulated, namely, luminescence, electron transfer, or photoinduced CO release, the branching ratio of which is governed by the energetics, the character, and the early time dynamics of the photoactive excited states. Simulations of ultrafast nonadiabatic quantum dynamics, including spin-vibronic effects, of [M(imidazole)(CO)₃(phenanthroline)]⁺ (M = Mn, Re) highlight the role of the metal atom. An ultrafast intersystem crossing process, driven by spin-orbit coupling, populates the low-lying triplet states of [Re(imidazole)(CO)₃(phen)]⁺ within the first tens of fs. In contrast, efficient internal conversion between the two lowest ¹MLCT states of [Mn(imidazole)(CO)₃(phen)]⁺ is mediated within 50 fs by vibronic coupling with upper MC and MLCT states.

Strongly coupled bacteriochlorin dyad studied using phase-modulated fluorescence-detected two-dimensional electronic spectroscopy

Fluorescence-detected two-dimensional electronic spectroscopy (F-2DES) projects the third-order non-linear polarization in a system as an excited electronic state population which is incoherently detected as fluorescence. Multiple variants of F-2DES have been developed. Here, we report phase-modulated F-2DES measurements on a strongly coupled symmetric bacteriochlorin dyad, a relevant 'toy' model for photosynthetic energy and charge transfer. Coherence map analysis shows that the strongest frequency observed in the dyad is well-separated from the excited state electronic energy gap, and is consistent with a vibrational frequency readily observed in bacteriochlorin monomers. Kinetic rate maps show a picosecond relaxation timescale between the excited states of the dyad. To our knowledge this is the first demonstration of coherence and kinetic analysis using the phase-modulation approach to F-2DES.

Coherence in carotenoid-to-chlorophyll energy transfer

The subtle details of the mechanism of energy flow from carotenoids to chlorophylls in biological light-harvesting complexes are still not fully understood, especially in the ultrafast regime. Here we focus on the antenna complex peridinin–chlorophyll a–protein (PCP), known for its remarkable efficiency of excitation energy transfer from carotenoids—peridinins—to chlorophylls. PCP solutions are studied by means of 2D electronic spectroscopy in different experimental conditions. Together with a global kinetic analysis and multiscale quantum chemical calculations, these data allow us to comprehensively address the contribution of the potential pathways of energy flow in PCP. These data support dominant energy transfer from peridinin S₂ to chlorophyll Q_y state via an ultrafast coherent mechanism. The coherent superposition of the two states is functional to drive population to the final acceptor state, adding an important piece of information in the quest for connections between coherent phenomena and biological functions.

Energy transfer from carotenoids to chlorophylls in light-harvesting is still not fully understood, especially in the ultrafast regime. Here, the authors investigate the coherent dynamics of this process in peridinin-chlorophyll a-protein complex via 2D electronic spectroscopy and quantum chemical calculations.

Identification and characterization of diverse coherences in the Fenna-Matthews-Olson complex

The idea that excitonic (electronic) coherences are of fundamental importance to natural photosynthesis gained popularity when slowly dephasing quantum beats (QBs) were observed in the two-dimensional electronic spectra of the Fenna-Matthews-Olson (FMO) complex at 77 K. These were assigned to superpositions of excitonic states, a controversial interpretation, as the strong chromophore-environment interactions in the complex suggest fast dephasing. Although it has been pointed out that vibrational motion produces similar spectral signatures, a concrete assignment of these oscillatory signals to distinct physical processes is still lacking. Here we revisit the coherence dynamics of the FMO complex using polarization-controlled two-dimensional electronic spectroscopy, supported by theoretical modelling. We show that the long-lived QBs are exclusively vibrational in origin, whereas the dephasing of the electronic coherences is completed within 240 fs even at 77 K. We further find that specific vibrational coherences are produced via vibronically coupled excited states. The presence of such states suggests that vibronic coupling is relevant for photosynthetic energy transfer.

Vibronic Coherence in the Charge Separation Process of the Rhodobacter sphaeroides Reaction Center

Two-dimensional electronic spectroscopy was applied to a variant of the reaction center (RC) of purple bacterium Rhodobacter sphaeroides lacking the primary acceptor ubiquinone in order to understand the ultrafast separation and transfer of charge between the bacteriochlorin cofactors. For the first time, characteristic 2D spectra were obtained for the participating excited and charge-transfer states, and the electron-transfer cascade (including two different channels, the P* and B* channels) was fully mapped. By analyzing quantum beats using 2D frequency maps, excited-state vibrational modes at 153 and 33 cm-1 were identified. We speculate that these modes couple to the charge separation (CS) process and collectively optimize the CS and are responsible for the superhigh efficiency.

Ultrafast coherence transfer in DNA-templated silver nanoclusters

DNA-templated silver nanoclusters of a few tens of atoms or less have come into prominence over the last several years due to very strong absorption and efficient emission. Applications in microscopy and sensing have already been realized, however little is known about the excited-state structure and dynamics in these clusters. Here we report on a multidimensional spectroscopy investigation of the energy-level structure and the early-time relaxation cascade, which eventually results in the population of an emitting state. We find that the ultrafast intramolecular relaxation is strongly coupled to a specific vibrational mode, resulting in the concerted transfer of population and coherence between excited states on a sub-100 fs timescale.

DNA-templated silver nanoclusters possess desirable optical properties, but their excited state dynamics remain poorly understood. Here the authors show that intracluster relaxations in such clusters are strongly coupled to a vibrational mode, resulting in ultrafast concerted transfer of population and coherence between excited states.