Coherence Dynamics in Photosynthesis: Protein Protection of Excitonic Coherence

Conductance Channels in a Single-Entity Enzyme

For a long time, the prevailing view in the scientific community was that proteins, being complex macromolecules composed of amino acid chains linked by peptide bonds, adopt folded structure with insulating or semiconducting properties, with high bandgaps. However, recent discoveries of unexpectedly high conductance levels, reaching values in the range of dozens of nanosiemens (nS) in proteins, have challenged this conventional understanding. In this study, we used scanning tunneling microscopy (STM) to explore the single-entity conductance properties of enzymatic channels, focusing on bilirubin oxidase (BOD) as a model metalloprotein. By immobilizing BOD on a conductive carbon surface, we discern its preferred orientation, facilitating the formation of electronic and ionic channels. These channels show efficient electron transport (ETp), with apparent conductance up to the 15 nS range. Notably, these conductance pathways are localized, minimizing electron transport barriers due to solvents and ions, underscoring BOD's redox versatility. Furthermore, electron transfer (ET) within the BOD occurs via preferential pathways. The alignment of the conductance channels with hydrophilicity maps, molecular vacancies, and regions accessible to electrolytes explains the observed conductance values. Additionally, BOD exhibits redox activity, with its active center playing a critical role in the ETp process. These findings significantly advance our understanding of the intricate mechanisms that govern ETp processes in proteins, offering new insights into the conductance of metalloproteins.

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.

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.

Femtosecond Collisional Dissipation of Vibrating D_{2}^{+} in Helium Nanodroplets

We explored the collision-induced vibrational decoherence of singly ionized D_{2} molecules inside a helium nanodroplet. By using the pump-probe reaction microscopy with few-cycle laser pulses, we captured in real time the collision-induced ultrafast dissipation of vibrational nuclear wave packet dynamics of D_{2}^{+} ion embedded in the droplet. Because of the strong coupling of excited molecular cations with the surrounding solvent, the vibrational coherence of D_{2}^{+} in the droplet interior only lasts for a few vibrational periods and completely collapses within 140 fs. The observed ultrafast coherence loss is distinct from that of isolated D_{2}^{+} in the gas phase, where the vibrational coherence persists for a long time with periodic quantum revivals. Our findings underscore the crucial role of ultrafast collisional dissipation in shaping the molecular decoherence and solvation dynamics during solution chemical reactions, particularly when the solute molecules are predominantly in ionic states.

New classifications for quantum bioinformatics: Q-bioinformatics, QCt-bioinformatics, QCg-bioinformatics, and QCr-bioinformatics

Bioinformatics has revolutionized biology and medicine by using computational methods to analyze and interpret biological data. Quantum mechanics has recently emerged as a promising tool for the analysis of biological systems, leading to the development of quantum bioinformatics. This new field employs the principles of quantum mechanics, quantum algorithms, and quantum computing to solve complex problems in molecular biology, drug design, and protein folding. However, the intersection of bioinformatics, biology, and quantum mechanics presents unique challenges. One significant challenge is the possibility of confusion among scientists between quantum bioinformatics and quantum biology, which have similar goals and concepts. Additionally, the diverse calculations in each field make it difficult to establish boundaries and identify purely quantum effects from other factors that may affect biological processes. This review provides an overview of the concepts of quantum biology and quantum mechanics and their intersection in quantum bioinformatics. We examine the challenges and unique features of this field and propose a classification of quantum bioinformatics to promote interdisciplinary collaboration and accelerate progress. By unlocking the full potential of quantum bioinformatics, this review aims to contribute to our understanding of quantum mechanics in biological systems.

Investigating the dissipation of heat and quantum information from DNA-scaffolded chromophore networks

Scaffolded molecular networks are important building blocks in biological pigment-protein complexes, and DNA nanotechnology allows analogous systems to be designed and synthesized. System-environment interactions in these systems are responsible for important processes, such as the dissipation of heat and quantum information. This study investigates the role of nanoscale molecular parameters in tuning these vibronic system-environment dynamics. Here, genetic algorithm methods are used to obtain nanoscale parameters for a DNA-scaffolded chromophore network based on comparisons between its calculated and measured optical spectra. These parameters include the positions, orientations, and energy level characteristics within the network. This information is then used to compute the dynamics, including the vibronic population dynamics and system-environment heat currents, using the hierarchical equations of motion. The dissipation of quantum information is identified by the system's transient change in entropy, which is proportional to the heat currents according to the second law of thermodynamics. These results indicate that the dissipation of quantum information is highly dependent on the particular nanoscale characteristics of the molecular network, which is a necessary first step before gleaning the systematic optimization rules. Subsequently, the I-concurrence dynamics are calculated to understand the evolution of the vibronic system's quantum entanglement, which are found to be long-lived compared to these system-bath dissipation processes.

Signature of Quantum Coherence in the Exciton Energy Pathways of the LH2 Photosynthetic Complex

Unraveling the energy transfer pathways in photosynthetic complexes is an important step toward understanding their structure-function interplay. Here, we use an open quantum systems approach to investigate energy transfer within the LH2 photosynthetic apparatus and its dependence on environmental conditions. We find that energy transfer pathways strongly depend on the environment-induced dephasing time. A comparison between the computational results and experiments performed on similar systems demonstrates that quantum coherences are present in these systems under physiological conditions and have an important role in shaping the energy transfer pathways. Moreover, our calculations indicate that relatively simple spectroscopy experiments can be used to detect traces of quantum coherence. Finally, our results suggest that quantum coherence may play a role in photosynthesis, but not in enhancing the efficiency as was previously suggested.

Measuring the Ultrafast Correlation Dynamics of a Multilevel System Using the Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy

In a two-dimensional (2D) optical spectrum of a multilevel system, there are diagonal peaks and off-diagonal cross-peaks that correlate the different levels. The time-dependent properties of these diagonal peaks and cross-peaks contain much information about the dynamics of the multilevel system. The time-dependent diagonal peakshape that depends on the spectral diffusion dynamics of the associated transition and characterized by the frequency-fluctuation correlation function (FFCF) is well studied. However, the time-dependent peakshape of a cross-peak that provides the correlation dynamics between different transitions is much less studied or understood. We derived the third-order nonlinear response functions that describe the cross-peaks in a 2D electronic spectrum of a multilevel system that arise from processes sharing a common ground state and/or from internal conversion and population transfer. We can use the center line slope (CLS) analysis to characterize the cross-peaks in conjunction with the diagonal peaks. This allows us to recover the frequency-fluctuation cross-correlation functions (FXCFs) between two transitions. The FXCF and its subsidiary quantities such as the initial correlation and the initial covariance between different transitions are important for studying the correlation effects between states in complex systems, such as energy-transfer processes. Furthermore, knowledge of how various molecular processes over different timescales affect simultaneously different transitions can also be obtained from the measured FXCF. We validated and tested our derived equations and analysis process by studying, as an example, the 2D electronic spectra of metal-free phthalocyanine in solution. We measured and analyzed the diagonal peaks of the Qx and Qy transitions and the cross-peaks between these two transitions of this multilevel electronic system and obtained the associated FFCFs and FXCFs. In this model system, we measured negative components of FXCF over the tens of picosecond timescale. This suggests that in phthalocyanine, the Qx and Qy transitions coupling with the solvent molecule motion are anticorrelated to each other.

Tunable couplings between location-insensitive emitters mediated by an epsilon-near-zero plasmonic waveguide

This work demonstrates the efficient tuning of incoherent and coherent coupling between emitters embedded in an epsilon-near-zero (ENZ) waveguide coated with a multilayer graphene. As a result, a tunable two-qubit quantum phase gate based on the ENZ waveguide is realized at the cutoff frequency. Furthermore, due to the vanishingly small permittivity of the ENZ waveguide, all incoherent coupling between any two identical emitters located in the central area of the slit approaches a maximum, enabling near-ideal bipartite and multipartite entanglement. The coherent coupling between emitters is much larger at an operating frequency far from the ENZ resonance frequency than at the cutoff frequency, and the coherent coupling and resulting energy transfer efficiency can also be effectively tuned by the Fermi level of graphene. These results demonstrate an efficiently tunable electro-optical platform for quantum devices.

Tunable Non-Markovianity for Bosonic Quantum Memristors

We studied the tunable control of the non-Markovianity of a bosonic mode due to its coupling to a set of auxiliary qubits, both embedded in a thermal reservoir. Specifically, we considered a single cavity mode coupled to auxiliary qubits described by the Tavis-Cummings model. As a figure of merit, we define the dynamical non-Markovianity as the tendency of a system to return to its initial state, instead of evolving monotonically to its steady state. We studied how this dynamical non-Markovianity can be manipulated in terms of the qubit frequency. We found that the control of the auxiliary systems affects the cavity dynamics as an effective time-dependent decay rate. Finally, we show how this tunable time-dependent decay rate can be tuned to engineer bosonic quantum memristors, involving memory effects that are fundamental for developing neuromorphic quantum technologies.

Recent progress in atomistic modeling of light-harvesting complexes: a mini review

In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as site energies, excitonic couplings, and spectral densities are key quantities which usually need to be extracted to be able to determine the exciton dynamics and spectroscopic properties. The recently developed multiscale approach based on the numerically efficient density functional tight-binding framework followed by excited state calculations has been shown to be superior to the scheme based on pure classical molecular dynamics simulations. The enhanced approach, which improves the description of the internal vibrational dynamics of the pigment molecules, yields spectral densities in good agreement with the experimental counterparts for various bacterial and plant LH systems. Here, we provide a brief overview of those results and described the theoretical foundation of the multiscale protocol.

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.

Analytical gradients and derivative couplings for the TDDFT-1D method

We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S₁/S₀ surfaces for a set of test cases.

Effects of Heterogeneous Protein Environment on Excitation Energy Transfer Dynamics in the Fenna-Matthews-Olson Complex

The Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has been serving as a prototypical light-harvesting protein for studying excitation energy transfer (EET) dynamics in photosynthesis. The most widely used Frenkel exciton model for FMO complex assumes that each excited bacteriochlorophyll site couples to an identical and isolated harmonic bath, which does not account for the heterogeneous local protein environment. To better describe the realistic environment, we propose to use the recently developed multistate harmonic (MSH) model, which contains a globally shared bath that couples to the different pigment sites according to the atomistic quantum mechanics/molecular mechanics simulations with explicit protein scaffold and solvent. In this work, the effects of heterogeneous protein environment on EET in FMO complexes from Prosthecochloris aestuarii and Chlorobium tepidum, specifically including realistic spectral density, site-dependent reorganization energies, and system-bath couplings are investigated. Semiclassical and mixed quantum-classical mapping dynamics were applied to obtain the nonadiabatic EET dynamics in several models ranging from the Frenkel exciton model to the MSH model and their variants. The MSH model with realistic spectral density and site-dependent system-bath couplings displays slower EET dynamics than the Frenkel exciton model. Our comparative study shows that larger average reorganization energy, heterogeneity in spectral densities, and low-frequency modes could facilitate energy dissipation, which is insensitive to the static disorder in reorganization energies. The effects of the spectral densities and system-bath couplings along with the MSH model can be used to optimize EET dynamics for artificial light-harvesting systems.

Beyond the Chlorophyll Molecule, Are There Other Organic Compounds Capable of Dissociating the Water Molecule? New and Unexpected Insights

In the XVII century, researchers throughout Europe began to study the composition of the atmosphere, discerning its physicochemical properties and composition. Since then, it has been observed that the concentration of oxygen in the air around us is relatively low. Lavoisier and Priestley, in the middle of XVII century, observed that plants leaves could replenish oxygen in an impoverished atmosphere. They concluded that chlorophyll possessed the intrinsic property of dissociating the molecule from water. At the XVIII century, the systematic study of human physiology began to deepen, and it was found that the oxygen levels inside the human body were five times higher than those of the atmosphere. The explanation given was that the lung, by means of some unknown mechanism like those of the swim bladder of some fish, was able to concentrate oxygen from the atmosphere and introduce it into the bloodstream. But such a theoretical mechanism has not been found after 200 years of searching. However, there is no way to explain how the concentration of oxygen rises substantially in the tiny distance between the alveolar space and the blood capillaries of the lung. Circumstantially, we found the mechanism during an observational study about the blood vessels entering and leaving the human optic nerve: Our body has several molecules capable of dissociating the molecule from water, such as plants.

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 Exciton-Phonon States in Stack-Engineered van der Waals Heterojunction Photodiodes

Stack engineering, an atomic-scale metamaterial strategy, enables the design of optical and electronic properties in van der Waals heterostructure devices. Here we reveal the optoelectronic effects of stacking-induced strong coupling between atomic motion and interlayer excitons in WSe₂/MoSe₂ heterojunction photodiodes. To do so, we introduce the photocurrent spectroscopy of a stack-engineered photodiode as a sensitive technique for probing interlayer excitons, enabling access to vibronic states typically found only in molecule-like systems. The vibronic states in our stack are manifest as a palisade of pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances and can be shifted "on demand" through the application of a perpendicular electric field via a source-drain bias voltage. The observation of multiple well-resolved sidebands as well as their ability to be shifted by applied voltages vividly demonstrates the emergence of interlayer exciton vibronic structure in a stack-engineered optoelectronic device.

Single-molecule nano-optoelectronics: insights from physics

Single-molecule optoelectronic devices promise a potential solution for miniaturization and functionalization of silicon-based microelectronic circuits in the future. For decades of its fast development, this field has made significant progress in the synthesis of optoelectronic materials, the fabrication of single-molecule devices and the realization of optoelectronic functions. On the other hand, single-molecule optoelectronic devices offer a reliable platform to investigate the intrinsic physical phenomena and regulation rules of matters at the single-molecule level. To further realize and regulate the optoelectronic functions toward practical applications, it is necessary to clarify the intrinsic physical mechanisms of single-molecule optoelectronic nanodevices. Here, we provide a timely review to survey the physical phenomena and laws involved in single-molecule optoelectronic materials and devices, including charge effects, spin effects, exciton effects, vibronic effects, structural and orbital effects. In particular, we will systematically summarize the basics of molecular optoelectronic materials, and the physical effects and manipulations of single-molecule optoelectronic nanodevices. In addition, fundamentals of single-molecule electronics, which are basic of single-molecule optoelectronics, can also be found in this review. At last, we tend to focus the discussion on the opportunities and challenges arising in the field of single-molecule optoelectronics, and propose further potential breakthroughs.

Local Phonon Environment as a Design Element for Long-Lived Excitonic Coherence: Dithia-anthracenophane Revisited

The purpose of this study is to investigate the role of a structured immediate phonon environment in determining the exciton dynamics and the possibility of using it as an optimal design element. Through the case study of dithia-anthracenophane, a bichromophore using the Hierarchical Equations Of Motion formalism, we show that the experimentally observed coherent exciton dynamics can be reproduced only by considering the actual structure of the phonon environment. While the slow dephasing of quantum coherence in dithia-anthracenophane can be attributed to strong vibronic coupling to high-frequency modes, vibronic quenching is the source of long oscillation periods in population transfer. This study sheds light on the crucial role of the structure of the immediate phonon environment in determining the exciton dynamics. We conclude by proposing some design principles for sustaining long-lived coherence in molecular systems.

Coherent response of the electronic system driven by non-interfering laser pulses

The strength of light–matter interaction in condensed matter is fundamentally linked to the orientation and oscillation strength of the materials’ optical transition dipoles. Structurally anisotropic materials, e.g., elongated molecules, exhibit optical transition dipoles with fixed orientations that govern the angular-dependent light–matter interaction. Contrary, free electron-like metals should exhibit isotropic light–matter interaction with the light fields dictating the orientation of the optical transition dipoles. Here, we demonstrate that an anisotropic direction of the optical transition dipoles even exists in highly free electron-like noble metal surfaces. Our time- and phase-resolved photoemission experiment reveals coherent interference effects on the (110)-oriented silver surface after optical excitation with two non-interfering cross-polarized pulses. We explain this coherent material response within the density matrix formalism by an intrinsic coupling of the non-interfering light fields mediated by optical transition dipoles with fixed orientations in silver.

Light–matter interaction is expected to be isotropic in free-electron-like materials. Here, by using time- and phase-resolved photoemission, the authors observe signatures of an anisotropic interaction on a noble metal surface, that can only be accounted for by optical transition dipoles with a fixed orientation.

Diagrammatic quantum Monte Carlo toward the calculation of transport properties in disordered semiconductors

A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron–phonon interactions) and static disorder of local or nonlocal nature in a unified and numerically exact way. The establishment of the whole framework relies on a general reciprocal-space expression and a generalized Wick’s theorem for the static disorder. Since the numerical cost is independent of the system size, various physical quantities, such as the thermally averaged coherence, Matsubara one-particle Green’s function, and current autocorrelation function, can be efficiently evaluated in the thermodynamic limit (infinite in the system size). The validity and performance of the proposed approach are systematically examined in a broad parameter regime. This approach, combined with proper numerical analytic continuation methods and first-principles calculations, is expected to be a versatile tool toward the calculation of various transport properties, such as mobilities in realistic semiconductors involving multiple electronic energy bands, high-frequency optical and low-frequency acoustic phonons, different forms of dynamic and static disorders, and anisotropy.

Exact simulation of pigment-protein complexes unveils vibronic renormalization of electronic parameters in ultrafast spectroscopy

The primary steps of photosynthesis rely on the generation, transport, and trapping of excitons in pigment-protein complexes (PPCs). Generically, PPCs possess highly structured vibrational spectra, combining many discrete intra-pigment modes and a quasi-continuous of protein modes, with vibrational and electronic couplings of comparable strength. The intricacy of the resulting vibronic dynamics poses significant challenges in establishing a quantitative connection between spectroscopic data and underlying microscopic models. Here we show how to address this challenge using numerically exact simulation methods by considering two model systems, namely the water-soluble chlorophyll-binding protein of cauliflower and the special pair of bacterial reaction centers. We demonstrate that the inclusion of the full multi-mode vibronic dynamics in numerical calculations of linear spectra leads to systematic and quantitatively significant corrections to electronic parameter estimation. These multi-mode vibronic effects are shown to be relevant in the longstanding discussion regarding the origin of long-lived oscillations in multidimensional nonlinear spectra.

Multimode vibronic mixing in model photosynthetic systems revealed by numerically exact simulations is shown to strongly modify linear and non-linear optical responses and facilitate the persistence of coherent dynamics.

Transforming Dyes into Fluorophores: Exciton-Induced Emission with Chain-like Oligo-BODIPY Superstructures

Herein we present a systematic study demonstrating to which extent exciton formation can amplify fluorescence based on a series of ethylene-bridged oligo-BODIPYs. A set of non- and weakly fluorescent BODIPY motifs was selected and transformed into discrete, chain-like oligomers by linkage via a flexible ethylene tether. The prepared superstructures constitute excitonically active entities with non-conjugated, Coulomb-coupled oscillators. The non-radiative deactivation channels of Internal Conversion (IC), also combined with an upstream reductive Photoelectron Transfer (rPET) and Intersystem Crossing (ISC) were addressed at the monomeric state and the evolution of fluorescence and (non-)radiative decay rates studied along the oligomeric series. We demonstrate that a "masked" fluorescence can be fully reactivated irrespective of the imposed conformational rigidity. This work challenges the paradigm that a collective fluorescence enhancement is limited to sterically induced motional restrictions.

Predicting the future of excitation energy transfer in light-harvesting complex with artificial intelligence-based quantum dynamics

Exploring excitation energy transfer (EET) in light-harvesting complexes (LHCs) is essential for understanding the natural processes and design of highly-efficient photovoltaic devices. LHCs are open systems, where quantum effects may play a crucial role for almost perfect utilization of solar energy. Simulation of energy transfer with inclusion of quantum effects can be done within the framework of dissipative quantum dynamics (QD), which are computationally expensive. Thus, artificial intelligence (AI) offers itself as a tool for reducing the computational cost. Here we suggest AI-QD approach using AI to directly predict QD as a function of time and other parameters such as temperature, reorganization energy, etc., completely circumventing the need of recursive step-wise dynamics propagation in contrast to the traditional QD and alternative, recursive AI-based QD approaches. Our trajectory-learning AI-QD approach is able to predict the correct asymptotic behavior of QD at infinite time. We demonstrate AI-QD on seven-sites Fenna-Matthews-Olson (FMO) complex.

The coherence time of sunlight in the context of natural and artificial light-harvesting

The suggestion that quantum coherence might enhance biological processes such as photosynthesis is not only of fundamental importance but also leads to hopes of developing bio-inspired 'green' quantum technologies that mimic nature. A key question is how the timescale of coherent processes in molecular systems compare to that of the driving light source-the Sun. Across the quantum biology literature on light-harvesting, the coherence time quoted for sunlight spans about two orders of magnitude, ranging from 0.6 to '10s' of femtoseconds. This difference can potentially be significant in deciding whether the induced light-matter coherence is long enough to affect dynamical processes following photoexcitation. Here we revisit the historic calculations of sunlight coherence starting with the black-body spectrum and then proceed to provide values for the more realistic case of atmospherically filtered light. We corroborate these values with interferometric measurements of the complex degree of temporal coherence from which we calculate the coherence time of atmospherically filtered sunlight as [Formula: see text], as well as the coherence time in a chlorophyll analogous filtered case as [Formula: see text].

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.

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H₃trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an "envelope effect" in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C₃ symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

Testing quantum speedups in exciton transport through a photosynthetic complex using quantum stochastic walks

Photosynthesis is a highly efficient process, nearly 100 percent of the red photons falling on the surface of leaves reach the reaction center and get transformed into energy. Most theoretical studies on photosynthetic complexes focus mainly on the Fenna-Matthews-Olson complex obtained from green-sulfur bacteria. Quantum coherence was speculated to play a significant role in this very efficient transport process. However, recent reports indicate quantum coherence via exciton transport may not be as relevant as coherence originating via vibronic processes to photosynthesis. Regardless of the origin, there has been a debate on whether quantum coherence results in any speedup of the exciton transport process. To address this we model exciton transport in FMO using a quantum stochastic walk (QSW) with only incoherence, pure dephasing and with both dephasing and incoherence. We find that the QSW model with pure dephasing leads to a substantial speedup in exciton transport as compared to a QSW model which includes both dephasing and incoherence and one which includes only incoherence, both of which experience slowdowns.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.

Dynamics and mechanism of dimer dissociation of photoreceptor UVR8

Photoreceptors are a class of light-sensing proteins with critical biological functions. UVR8 is the only identified UV photoreceptor in plants and its dimer dissociation upon UV sensing activates UV-protective processes. However, the dissociation mechanism is still poorly understood. Here, by integrating extensive mutations, ultrafast spectroscopy, and computational calculations, we find that the funneled excitation energy in the interfacial tryptophan (Trp) pyramid center drives a directional Trp-Trp charge separation in 80 ps and produces a critical transient Trp anion, enabling its ultrafast charge neutralization with a nearby positive arginine residue in 17 ps to destroy a key salt bridge. A domino effect is then triggered to unzip the strong interfacial interactions, which is facilitated through flooding the interface by channel and interfacial water molecules. These detailed dynamics reveal a unique molecular mechanism of UV-induced dimer monomerization.

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.

Active control of strong plasmon-exciton coupling in biomimetic pigment-polymer antenna complexes grown by surface-initiated polymerisation from gold nanostructures

Plexcitonic antenna complexes, inspired by photosynthetic light-harvesting complexes, are formed by attachment of chlorophylls (Chl) to poly(cysteine methacrylate) (PCysMA) scaffolds grown by atom-transfer radical polymerisation from gold nanostructure arrays. In these pigment–polymer antenna complexes, localised surface plasmon resonances on gold nanostructures are strongly coupled to Chl excitons, yielding hybrid light–matter states (plexcitons) that are manifested in splitting of the plasmon band. Modelling of the extinction spectra of these systems using a simple coupled oscillator model indicates that their coupling energies are up to twice as large as those measured for LHCs from plants and bacteria. Coupling energies are correlated with the exciton density in the grafted polymer layer, consistent with the collective nature of strong plasmon–exciton coupling. Steric hindrance in fully-dense PCysMA brushes limits binding of bulky chlorophylls, but the chlorophyll concentration can be increased to ∼2 M, exceeding that in biological light-harvesting complexes, by controlling the grafting density and polymerisation time. Moreover, synthetic plexcitonic antenna complexes display pH- and temperature-responsiveness, facilitating active control of plasmon–exciton coupling. Because of the wide range of compatible polymer chemistries and the mild reaction conditions, plexcitonic antenna complexes may offer a versatile route to programmable molecular photonic materials.

Excitons in pigment–polymer antenna complexes formed by attachment of chlorophyll to surface grafted polymers are coupled strongly to plasmon modes, with coupling energies twice those for biological light-harvesting complexes and active control of plasmon–exciton coupling.

Efficient long-range triplet exciton transport by metal-metal interaction at room temperature

Efficient and long-range exciton transport is critical for photosynthesis and opto-electronic devices, and for triplet-harvesting materials, triplet exciton diffusion length ( [[EQUATION]] ) and coefficient ( [[EQUATION]] ) are key parameters in determining their performances. Herein, we observed that PtII and PdII organometallic nanowires exhibit long-range anisotropic triplet exciton LD of 5-7 μm along the M-M direction using direct photoluminescence (PL) imaging technique by low-power continuous wave (CW) laser excitation. At room temperature, via a combined triplet-triplet annihilation (TTA) analysis and spatial PL imaging, an efficient triplet exciton diffusion was observed for the PtII and PdII nanowires with extended close M-M contact, while is absent in nanowires without close M-M contact. Two-dimensional electronic spectroscopy (2DES) and calculations revealed a significant contribution of the delocalized 1/3[dσ*(M-M)→π*] excited state during the exciton diffusion modulated by the M-M distance.

Quantum transfer through small networks coupled to phonons: Effects of topology versus phonons

Particle or energy transfer through quantum networks is determined by network topology and couplings to environments. This study examines the combined effect of topology and external couplings on the efficiency of directional quantum transfer through quantum networks. We consider a microscopic model of qubit networks coupled to external vibrations by Holstein and Peierls couplings. By treating the positions of the network sites and the site-dependent phonon frequencies as independent variables, we determine the Hamiltonian parameters corresponding to minimum transfer time by Bayesian optimization. The results show that Holstein couplings may accelerate transfer through suboptimal network configurations but cannot accelerate quantum dynamics beyond the limit of the transfer time in an optimal phonon-free configuration. By contrast, Peierls couplings distort the optimal networks to accelerate quantum transfer through configurations with less than six sites. However, the speed-up offered by Peierls couplings decreases with the network size and disappears for networks with more than seven sites. For networks with seven sites or more, Peierls couplings distort the optimal network configurations and change the mechanism of quantum transfer but do not affect the lower limit of the transfer time. The machine-learning approach demonstrated here can be applied to determine quantum speed limits in other applications.

Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network

The recurrent neural network with the long short-term memory cell (LSTM-NN) is employed to simulate the long-time dynamics of open quantum systems. The bootstrap method is applied in the LSTM-NN construction and prediction, which provides a Monte Carlo estimation of a forecasting confidence interval. Within this approach, a large number of LSTM-NNs are constructed by resampling time-series sequences that were obtained from the early stage quantum evolution given by numerically exact multilayer multiconfigurational time-dependent Hartree method. The built LSTM-NN ensemble is used for the reliable propagation of the long-time quantum dynamics, and the simulated result is highly consistent with the exact evolution. The forecasting uncertainty that partially reflects the reliability of the LSTM-NN prediction is also given. This demonstrates the bootstrap-based LSTM-NN approach is a practical and powerful tool to propagate the long-time quantum dynamics of open systems with high accuracy and low computational cost.

A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

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.

Structural Investigation of Photochemical Intermediates in Solution by Cold UV Spectroscopy in the Gas Phase: Photosubstitution of Dicyanobenzenes by Allylsilanes

Electrospray ion sources with an in-line quartz cell were constructed to produce photochemical intermediates in solution. These ion sources can detect photochemical intermediates having lifetimes longer than a few seconds. Intermediates formed by photosubstitution of 1,4-dicyanobenzene (DCB) by allyltrimethylsilane (AMS) in acetonitrile using a Xe lamp were injected into the mass spectrometer. The cationic intermediate (C₁₁H₁₀N₂·H⁺) was observed at m/z = 171, but no anionic intermediate was found, although C₁₁H₉N₂^- was expected based on prior studies. Theoretical studies suggested that C₁₁H₉N₂^- was simultaneously converted to neutral C₁₁H₁₀N₂ and cationic C₁₁H₁₀N₂·H⁺ species, which can be stable intermediates in the photosubstitution reaction. The UV photodissociation (UVPD) spectrum of C₁₁H₁₀N₂·H⁺ under cold (∼10 K) gas-phase conditions determined the conformation of the C₁₁H₁₀N₂ unit of the C₁₁H₁₀N₂·H⁺ cation. This report demonstrates that cold gas-phase UV spectroscopy is a prospectively powerful tool for investigation of the electronic and geometric structures of photochemical intermediates produced in solution.

Fully Quantum Modeling of Exciton Diffusion in Mesoscale Light Harvesting Systems

It has long been a challenge to accurately and efficiently simulate exciton-phonon dynamics in mesoscale photosynthetic systems with a fully quantum mechanical treatment due to extensive computational resources required. In this work, we tackle this seemingly intractable problem by combining the Dirac-Frenkel time-dependent variational method with Davydov trial states and implementing the algorithm in graphic processing units. The phonons are treated on the same footing as the exciton. Tested with toy models, which are nanoarrays of the B850 pigments from the light harvesting 2 complexes of purple bacteria, the methodology is adopted to describe exciton diffusion in huge systems containing more than 1600 molecules. The superradiance enhancement factor extracted from the simulations indicates an exciton delocalization over two to three pigments, in agreement with measurements of fluorescence quantum yield and lifetime in B850 systems. With fractal analysis of the exciton dynamics, it is found that exciton transfer in B850 nanoarrays exhibits a superdiffusion component for about 500 fs. Treating the B850 ring as an aggregate and modeling the inter-ring exciton transfer as incoherent hopping, we also apply the method of classical master equations to estimate exciton diffusion properties in one-dimensional (1D) and two-dimensional (2D) B850 nanoarrays using derived analytical expressions of time-dependent excitation probabilities. For both coherent and incoherent propagation, faster energy transfer is uncovered in 2D nanoarrays than 1D chains, owing to availability of more numerous propagating channels in the 2D arrangement.

Role of Spatially Correlated Fluctuations in Photosynthetic Excitation Energy Transfer with an Equilibrium and a Nonequilibrium Initial Bath

The transfer of excitation energy in photosynthetic light-harvesting complexes has inspired growing interest for its scientific and engineering significance. Recent experimental findings have suggested that spatially correlated environmental fluctuations may account for the existence of long-lived quantum coherent energy transfer observed even at physiological temperature. In this paper, we investigate the effects of spatial correlations on the excitation energy transfer dynamics by including a nonequilibrium initial bath in a simulated donor-acceptor model. The initial bath state, which is assumed to be either equilibrium or nonequilibrium, is expanded in powers of coupling strength within the polaron formalism of a quantum master equation. The spatial correlations of bath fluctuations strongly influence the decay of coherence in the dynamics. The role of a nonequilibrium initial bath is also influenced by spatial correlations and becomes the most conspicuous for certain degrees of spatial correlations from which we propose a picture that the spatial correlations of bath fluctuations open up new energy transfer pathways, playing a role of protecting coherence. Besides, we apply the polaron master equation approach to study the dynamics in a two-site subsystem of the FMO complex and provide a practical example that shows the versatility of this approach.

Ultrafast Resonance Energy Transfer in Ethylene-Bridged BODIPY Heterooligomers: From Frenkel to Förster Coupling Limit

A series of distinct BODIPY heterooligomers (dyads, triads, and tetrads) comprising a variable number of typical green BODIPY monomers and a terminal red-emitting styryl-equipped species acting as an energy sink was prepared and subjected to computational and photophysical investigations in solvent media. An ethylene tether between the single monomeric units provides a unique foldameric system, setting the stage for a systematic study of excitation energy transfer processes (EET) on the basis of nonconjugated oscillators. The influence of stabilizing β-ethyl substituents on conformational space and the disorder of site energies and electronic couplings was addressed. In this way both the strong (Frenkel) and the weak (Förster) coupling limit could be accessed within a single system: the Frenkel limit within the strongly coupled homooligomeric green donor subunit and the Förster limit at the terminal heterosubstituted ethylene bridge. Femtosecond transient-absorption spectroscopy combined with mixed quantum-classical dynamic simulations demonstrate the limitations of the Förster resonance energy transfer (FRET) theory and provide a consistent framework to elucidate the trend of increasing relaxation lifetimes at higher homologues, revealing one of the fastest excitation energy transfer processes detected to date with a corresponding lifetime of 39 fs.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

Convolutional Neural Networks for Long Time Dissipative Quantum Dynamics

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network composed of convolutional layers is a powerful tool for predicting long-time dynamics of open quantum systems provided the preceding short-time evolution of a system is known. The neural network model developed in this work simulates long-time dynamics efficiently and accurately across different dynamical regimes from weakly damped coherent motion to incoherent relaxation. The model was trained on a data set relevant to photosynthetic excitation energy transfer and can be deployed to study long-lasting quantum coherence phenomena observed in light-harvesting complexes. Furthermore, our model performs well for the initial conditions different than those used in the training. Our approach reduces the required computational resources for long-time simulations and holds the promise for becoming a valuable tool in the study of open quantum systems.