Quantum biology revisited

Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of a Single Molecule

Single-molecule fluorescence spectroscopy is a powerful method that avoids ensemble averaging, but its temporal resolution is limited by the fluorescence lifetime to nanoseconds at most. At the ensemble level, two-dimensional spectroscopy provides insight into ultrafast femtosecond processes, such as energy transfer and line broadening, even beyond the Fourier limit, by correlating pump and probe spectra. Here, we combine these two techniques and demonstrate coherent 2D spectroscopy of individual dibenzoterrylene (DBT) molecules at room temperature. We excite the molecule in a confocal microscope with a phase-modulated train of femtosecond pulses and detect the emitted fluorescence with single-photon counting detectors. Using a phase-sensitive detection scheme, we were able to measure the nonlinear 2D spectra of most of the DBT molecules that we studied. Our method is applicable to a wide range of single emitters and opens new avenues for understanding energy transfer in single quantum objects on ultrafast time scales.

OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors

Non-Markovian dynamics arising from the strong coupling of a system to a structured environment is essential in many applications of quantum mechanics and emerging technologies. Deriving an accurate description of general quantum dynamics including memory effects is, however, a demanding task, prohibitive to standard analytical or direct numerical approaches. We present a major release of our open source software package, OQuPy (Open Quantum System in Python), which provides several recently developed numerical methods that address this challenging task. It utilizes the process tensor approach to open quantum systems (OQS) in which a single map, the process tensor, captures all possible effects of an environment on the system. The representation of the process tensor in a tensor network form allows for an exact yet highly efficient description of non-Markovian OQS (NM-OQS). The OQuPy package provides methods to (1) compute the dynamics and multi-time correlations of quantum systems coupled to single and multiple environments, (2) optimize control protocols for NM-OQS, (3) simulate interacting chains of NM-OQS, and (4) compute the mean-field dynamics of an ensemble of NM-OQS coupled to a common central system. Our aim is to provide an easily accessible and extensible tool for researchers of OQS in fields such as quantum chemistry, quantum sensing, and quantum information.

Pushing the limits of ultrafast diffraction: Imaging quantum coherences in isolated molecules

Quantum coherence governs the outcome and efficiency of photochemical reactions and ultrafast molecular dynamics. Recent ultrafast gas-phase X-ray scattering and electron diffraction have enabled the observation of femtosecond nuclear dynamics driven by vibrational coherence. However, probing attosecond electron dynamics and coupled electron-nuclear dynamics remains challenging. This article discusses advances in ultrafast X-ray scattering and electron diffraction, highlighting their potential to resolve attosecond charge migration and vibronic coupling at conical intersections. Novel techniques, such as X-ray scattering with orbital angular momentum beams and combined X-ray and electron diffraction, promise to selectively probe coherence contributions and visualize charge migration in real-space. These emerging methods could further our understanding of coherence effects in chemical reactions.

Semiclassical dynamics in Wigner phase space II: Nonadiabatic hybrid Wigner dynamics

We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman-Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects.

Photoelectrochemical Two-Dimensional Electronic Spectroscopy (PEC2DES) of Photosystem I: Charge Separation Dynamics Hidden in a Multichromophoric Landscape

We present a nonlinear spectroelectrochemical technique to investigate photosynthetic protein complexes. The PEC2DES setup combines photoelectrochemical detection (PEC) that selectively probes the protein photogenerated charges output with two-dimensional electronic spectroscopy (2DES) excitation that spreads the nonlinear optical response of the system in an excitation-detection map. PEC allows us to distinguish the contribution of charge separation (CS) from other de-excitation pathways, whereas 2DES allows us to disentangle congested spectral bands and evaluate the exciton dynamics (decays and coherences) of the photosystem complex. We have developed in operando phase-modulated 2DES by measuring the photoelectrochemical reaction rate in a biohybrid electrode functionalized with a plant photosystem complex I-light harvesting complex I (PSI-LHCI) layer. Optimizing the photoelectrochemical current signal yields reliable linear spectra unequivocally associated with PSI-LHCI. The 2DES signal is validated by nonlinear features like the characteristic vibrational coherence at 750 cm-1. However, no energy transfer dynamics is observed within the 450 fs experimental window. These intriguing results are discussed in the context of incoherent mixing resulting in reduced nonlinear contrast for multichromophoric complexes, such as the 160 chlorophyll PSI. The presented PEC2DES method identifies generated charges unlike purely optical 2DES and opens the way to probe the CS channel in multichromophoric complexes.

Distinct vibrational motions promote disparate excited-state decay pathways in cofacial perylenediimide dimers

A complex interplay of structural, electronic, and vibrational degrees of freedom underpins the fate of molecular excited states. Organic assemblies exhibit a myriad of excited-state decay processes, such as symmetry-breaking charge separation (SB-CS), excimer (EX) formation, singlet fission, and energy transfer. Recent studies of cofacial and slip-stacked perylene-3,4:9,10-bis(dicarboximide) (PDI) multimers demonstrate that slight variations in core substituents and H- or J-type aggregation can determine whether the system follows an SB-CS pathway or an EX one. However, questions regarding the relative importance of structural properties and molecular vibrations in driving the excited-state dynamics remain. Here, we use a combination of two-dimensional electronic spectroscopy, femtosecond stimulated Raman spectroscopy, and quantum chemistry computations to compare the photophysics of two PDI dimers. The dimer with 1,7-bis(pyrrolidin-1'-yl) substituents (5PDI2) undergoes ultrafast SB-CS from a photoexcited mixed state, while the dimer with bis-1,7-(3',5'-di-t-butylphenoxy) substituents (PPDI2) rapidly forms an EX state. Examination of their quantum beating features reveals that SB-CS in 5PDI2 is driven by the collective vibronic coupling of two or more excited-state vibrations. In contrast, we observe signatures of low-frequency vibrational coherence transfer during EX formation by PPDI2, which aligns with several previous studies. We conclude that key electronic and structural differences between 5PDI2 and PPDI2 determine their markedly different photophysics.

TD-DMRG Study of Exciton Dynamics with both Thermal and Static Disorders for Fenna-Matthews-Olson Complex

Photosynthesis is a fundamental process that converts solar energy into chemical energy. Understanding the microscopic mechanisms of energy transfer in photosynthetic systems is crucial for the development of novel optoelectronic materials. Simulating these processes poses significant challenges due to the intricate interactions between electrons and phonons, compounded by static disorder. In this work, we present a numerically nearly exact study using the time-dependent density matrix renormalization group (TD-DMRG) method to simulate the quantum dynamics of the Fenna-Matthews-Olson (FMO) complex considering an eight-site model with both thermal and static disorders. We employ the thermo-field dynamics formalism for temperature effects. We merge all electronic interactions into one large matrix product state (MPS) site, boosting accuracy efficiently without increasing complexity. Previous combined experimental and computational studies indicated that the static disorders range from 30 to 90 cm-1 for different FMO sites. We employ a Gaussian distribution and the auxiliary bosonic operator approach to consider the static disorder in our TD-DMRG algorithm. We investigate the impact of different initial excitation sites, temperatures, and degrees of static disorder on the exciton dynamics and temporal coherence. It is found that under the influence of the experimentally determined static disorder strength, the exciton population evolution shows a non-negligible difference at zero temperature, while it is hardly affected at room temperature.

Frequency-Dependent Vibronic Effects in Steady State Energy Transport

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

Persistence of Correlations in Neurotransmitter Transport through the Synaptic Cleft

The "quantum brain" proposal can revolutionize our understanding of cognition if proven valid. The core of the most common "quantum brain" mechanism is the appearance of correlated neuron triggering induced by quantum correlations between ions. In this work, we examine the preservation of the correlations created in the pre-synaptic neurons through the transfer of neurotransmitters across the synaptic cleft, a critical ingredient for the validity of the "quantum brain" hypothesis. We simulated the transport of two neurotransmitters at two different clefts, with the only assumption that they start simultaneously, and determined the difference in their first passage times. We show that in physiological conditions, the correlations are persistent even if the parameters of the two neurons are different.

Non-adiabatic molecular dynamics simulations provide new insights into the exciton transfer in the Fenna-Matthews-Olson complex

A trajectory surface hopping approach, which uses machine learning to speed up the most time-consuming steps, has been adopted to investigate the exciton transfer in light-harvesting systems. The present neural networks achieve high accuracy in predicting both Coulomb couplings and excitation energies. The latter are predicted taking into account the environment of the pigments. Direct simulation of exciton dynamics through light-harvesting complexes on significant time scales is usually challenging due to the coupled motion of nuclear and electronic degrees of freedom in these rather large systems containing several relatively large pigments. In the present approach, however, we are able to evaluate a statistically significant number of non-adiabatic molecular dynamics trajectories with respect to exciton delocalization and exciton paths. The formalism is applied to the Fenna-Matthews-Olson complex of green sulfur bacteria, which transfers energy from the light-harvesting chlorosome to the reaction center with astonishing efficiency. The system has been studied experimentally and theoretically for decades. In total, we were able to simulate non-adiabatically more than 30 ns, sampling also the relevant space of parameters within their uncertainty. Our simulations show that the driving force supplied by the energy landscape resulting from electrostatic tuning is sufficient to funnel the energy towards site 3, from where it can be transferred to the reaction center. However, the high efficiency of transfer within a picosecond timescale can be attributed to the rather unusual properties of the BChl a molecules, resulting in very low inner and outer-sphere reorganization energies, not matched by any other organic molecule, e.g., used in organic electronics. A comparison with electron and exciton transfer in organic materials is particularly illuminating, suggesting a mechanism to explain the comparably high transfer efficiency.

Memory effects in the efficiency control of energy transfer under incoherent light excitation in noisy environments

Fluctuations in energy gap and coupling constants between chromophores can play an important role in absorption and energy transfer across a collection of two-level systems. In photosynthesis, light-induced quantum coherence can affect the efficiency of energy transfer to the designated "trap" state. Theoretically, the interplay between fluctuations and coherence has been studied often, employing either a Markovian or a perturbative approximation. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation. We introduce the effects of decay of the created excitation (to the ground state) on the desired propagation and trapping that provides a direction of flow of the excitation. In the presence of light-induced pumping, we establish a relation between the efficiency, the mean survival time, and the correlation decay time of the bath-induced fluctuations. A decrease in the steady-state coherence during the transition from the non-Markovian regime to the Markovian limit results in a decrease in efficiency. As in the well-known Haken-Strobl model, the ratio of the square of fluctuation strength to the rate plays a critical role in determining the mechanism of energy transfer and in shaping the characteristics of the efficiency profile. We recover a connection between the transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and uncorrelated bath models. We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.

Transient Chiral Dynamics in the Fenna-Matthews-Olson Complex Revealed by Two-Dimensional Circular Dichroism Spectroscopy

Chirality plays a pivotal role across scientific disciplines with profound implications spanning light-matter interactions, molecular recognition, and natural evolutionary processes. This study delves into the active influence of molecular chirality on exciton energy transfer within photosynthetic protein complexes, focusing on the Fenna-Matthews-Olson (FMO) complex. Employing two-dimensional circular dichroism (2DCD) spectroscopy, we investigate the transient chiral dynamics of excitons during energy transfer processes within the FMO complex. Our approach, incorporating pulse information into population dynamics based on the third-order response function, facilitates the calculation of 2DCD spectra and dynamics. This enables the extraction of chiral contributions to excitonic energy transfer and the examination of electronic wave functions. We demonstrate that 2DCD spectra offer excitation energies that are better resolved than those from conventional two-dimensional electronic spectroscopy. These findings deepen our understanding of exciton energy transfer mechanisms in natural photosynthesis, emphasizing the potential of 2DCD spectroscopy as a powerful tool for unraveling the chiral contribution to exciton dynamics.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7-2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8-14 ps, with a significantly inhibited ground state recovery.

Exciton annihilation and diffusion length in disordered multichromophoric nanoparticles

Efficient exciton transport is the essential property of natural and synthetic light-harvesting (LH) devices. Here we investigate exciton transport properties in LH organic polymer nanoparticles (ONPs) of 40 nm diameter. The ONPs are loaded with a rhodamine B dye derivative and bulky counterion, enabling dye loadings as high as 0.3 M, while preserving fluorescence quantum yields larger than 30%. We use time-resolved fluorescence spectroscopy to monitor exciton-exciton annihilation (EEA) kinetics within the ONPs dispersed in water. We demonstrate that unlike the common practice for photoluminescence investigations of EEA, the non-uniform intensity profile of the excitation light pulse must be taken into account to analyse reliably intensity-dependent population dynamics. Alternatively, a simple confocal detection scheme is demonstrated, which enables (i) retrieving the correct value for the bimolecular EEA rate which would otherwise be underestimated by a typical factor of three, and (ii) revealing minor EEA by-products otherwise unnoticed. Considering the ONPs as homogeneous rigid solutions of weakly interacting dyes, we postulate an incoherent exciton hoping mechanism to infer a diffusion constant exceeding 0.003 cm2 s-1 and a diffusion length as large as 70 nm. This work demonstrates the success of the present ONP design strategy at engineering efficient exciton transport in disordered multichromophoric systems.

Probing the design principles of photosynthetic systems through fluorescence noise measurement

Elucidating the energetic processes which govern photosynthesis, the engine of life on earth, are an essential goal both for fundamental research and for cutting-edge biotechnological applications. Fluorescent signal of photosynthetic markers has long been utilised in this endeavour. In this research we demonstrate the use of fluorescent noise analysis to reveal further layers of intricacy in photosynthetic energy transfer. While noise is a common tool analysing dynamics in physics and engineering, its application in biology has thus far been limited. Here, a distinct behaviour in photosynthetic pigments across various chemical and biological environments is measured. These changes seem to elucidate quantum effects governing the generation of oxidative radicals. Although our method offers insights, it is important to note that the interpretation should be further validated expertly to support as conclusive theory. This innovative method is simple, non-invasive, and immediate, making it a promising tool to uncover further, more complex energetic events in photosynthesis, with potential uses in environmental monitoring, agriculture, and food-tech.

Ultrafast excitonic dynamics in DNA: Bridging correlated quantum dynamics and sequence dependence

After photoexcitation of DNA, the excited electron (in the LUMO) and the remaining hole (in the HOMO) localized on the same DNA base form a bound pair, called the Frenkel exciton, due to their mutual Coulomb interaction. In this study, we demonstrate that a tight-binding (TB) approach, using TB parameters for electrons and holes available in the literature, allows us to correlate relaxation properties, average charge separation, and dipole moments to a large ensemble of double-stranded DNA sequences (all 16384 possible sequences with 14 nucleobases). This way, we are able to identify a relatively small subensemble of sequences responsible for long-lived excited states, high average charge separation, and high dipole moment. Further analysis shows that these sequences are particularly T rich. By systematically screening the impact of electron-hole interaction (Coulomb forces), we verify that these correlations are relatively robust against finite-size variations of the interaction parameter, not directly accessible experimentally. This methodology combines simulation methods from quantum physics and physical chemistry with statistical analysis known from genetics and epigenetics, thus representing a powerful bridge to combine information from both fields.

Protein Effects on the Excitation Energies and Exciton Dynamics of the CP24 Antenna Complex

In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales.

Bexcitonics: Quasiparticle approach to open quantum dynamics

We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths of arbitrary complexity based on the Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM dynamics and mapping it into that of the system in interaction with a few bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from a decomposition of the bath correlation function into discrete features. Specifically, bexciton creation and annihilation couple the auxiliary density matrices in the HEOM. The approach provides a systematic strategy to construct exact quantum master equations that include the system-bath coupling to all orders even for non-Markovian environments. Specifically, by introducing different metrics and representations for the bexcitons it is possible to straightforwardly generate different variants of the HEOM, demonstrating that all these variants share a common underlying quasiparticle picture. Bexcitonic properties, while unphysical, offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence. For instance, we use it to analyze the instability of the HEOM when the bath is composed of underdamped oscillators and show that it leads to the creation of highly excited bexcitons. The bexcitonic picture can also be used to develop more efficient approaches to propagate the HEOM. As an example, we use the particle-like nature of the bexcitons to introduce mode-combination of bexcitons in both number and coordinate representation that uses the multi-configuration time-dependent Hartree to efficiently propagate the HEOM dynamics.

Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

Near-atomic-resolution structure of J-aggregated helical light-harvesting nanotubes

Cryo-electron microscopy has delivered a resolution revolution for biological self-assemblies, yet only a handful of structures have been solved for synthetic supramolecular materials. Particularly for chromophore supramolecular aggregates, high-resolution structures are necessary for understanding and modulating the long-range excitonic coupling. Here, we present a 3.3 Å structure of prototypical biomimetic light-harvesting nanotubes derived from an amphiphilic cyanine dye (C8S3-Cl). Helical 3D reconstruction directly visualizes the chromophore packing that controls the excitonic properties. Our structure clearly shows a brick layer arrangement, revising the previously hypothesized herringbone arrangement. Furthermore, we identify a new non-biological supramolecular motif-interlocking sulfonates-that may be responsible for the slip-stacked packing and J-aggregate nature of the light-harvesting nanotubes. This work shows how independently obtained native-state structures complement photophysical measurements and will enable accurate understanding of (excitonic) structure-function properties, informing materials design for light-harvesting chromophore aggregates.

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

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

Theoretical model of femtosecond coherence spectroscopy of vibronic excitons in molecular aggregates

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment-protein complexes.

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

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

A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters

Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.

Quantum information scrambling and chemical reactions

The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Out-of-time-order correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a double-well reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the early-time OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the low-temperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

Two-Dimensional Electronic Spectroscopy Resolves Relative Excited-State Displacements

Knowledge of relative displacements between potential energy surfaces (PES) is critical in spectroscopy and photochemistry. Information on displacements is encoded in vibrational coherences. Here we apply ultrafast two-dimensional electronic spectroscopy in a pump-probe half-broadband (HB2DES) geometry to probe the ground- and excited-state potential landscapes of cresyl violet. 2D coherence maps reveal that while the coherence amplitude of the dominant 585 cm-1 Raman-active mode is mainly localized in the ground-state bleach and stimulated emission regions, a 338 cm-1 mode is enhanced in excited-state absorption. Modeling these data with a three-level displaced harmonic oscillator model using the hierarchical equation of motion-phase matching approach (HEOM-PMA) shows that the S1 ← S0 PES displacement is greater along the 585 cm-1 coordinate than the 338 cm-1 coordinate, while Sn ← S1 displacements are similar along both coordinates. HB2DES is thus a powerful tool for exploiting nuclear wavepackets to extract quantitative multidimensional, vibrational coordinate information across multiple PESs.

Empirical asymmetric phonon sideband due to phonons in the protein matrix present in photosynthetic complexes: Time-domain response theory

The phonon spectral density plays a key role in probing the dynamical and spectral behavior of molecular aggregates. One may utilize the intimate connection between the one-phonon profile and the phonon spectral density to extract a plausible form of the spectral density of media with rich structure using advanced optical spectroscopy. The excitonic transition is normally accompanied by a broad, asymmetric phonon-side band due to the coupling to the phonons in the surrounding protein matrix present in photosynthetic complexes. The asymmetry in the one-phonon profile of a homogeneous absorption spectrum and other experiments performed on photosynthetic bacterial reaction centers (BRCs) led the Small group to employ a half-Gaussian distribution function on the red side and half-Lorentzian distribution function on the blue side of the absorption lineshape to account for the one-phonon profile asymmetrical shape and relaxation effects contributing to spectroscopy and dynamics of BRCs at hand. Different research groups successfully employed the theory of Small to simulate their photosynthetic spectral data so they could calculate the homogeneous absorption and hole-burned spectra of photosynthetic complexes. Although this report does not directly use the formulae of homogeneous absorption, hole-burning, and fluorescence line-narrowed spectra of BRCs, and photosynthetic complexes, developed by Hayes-Small, it builds on their idea of the phonon sideband asymmetric shape in deriving an accurate and computationally efficient linear electronic transition dipole moment time correlation function. Besides the compelling tractability and efficiency of this correlation function, it accounts for excitonic coupling and eliminates all the inconsistencies arising in the Hayes-Small theory.

Unraveling quantum coherences mediating primary charge transfer processes in photosystem II reaction center

Photosystem II (PSII) reaction center (RC) is a unique complex that is capable of efficiently separating electronic charges across the membrane. The primary energy- and charge-transfer (CT) processes occur on comparable ultrafast timescales, which makes it extremely challenging to understand the fundamental mechanism responsible for the near-unity quantum efficiency of the transfer. Here, we elucidate the role of quantum coherences in the ultrafast energy and CT in the PSII RC by performing two-dimensional (2D) electronic spectroscopy at the cryogenic temperature of 20 kelvin, which captures the distinct underlying quantum coherences. Specifically, we uncover the electronic and vibrational coherences along with their lifetimes during the primary ultrafast processes of energy and CT. We construct an excitonic model that provides evidence for coherent energy and CT at low temperature in the 2D electronic spectra. The principles could provide valuable guidelines for creating artificial photosystems with exploitation of system-bath coupling and control of coherences to optimize the photon conversion efficiency to specific functions.

Artificial-Intelligence-Enhanced On-the-Fly Simulation of Nonlinear Time-Resolved Spectra

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes in molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be interpreted, but it is a challenging task for which theoretical simulations are often indispensable. Accurate simulations of transient absorption or two-dimensional electronic spectra are, however, computationally very expensive, prohibiting the wider adoption of existing first-principles methods. Here, we report an artificial-intelligence-enhanced protocol to drastically reduce the computational cost of simulating nonlinear time-resolved electronic spectra, which makes such simulations affordable for polyatomic molecules of increasing size. The protocol is based on the doorway-window approach for the on-the-fly surface-hopping simulations. We show its applicability for the prototypical molecule of pyrazine for which it produces spectra with high precision with respect to ab initio reference while cutting the computational cost by at least 95% compared to pure first-principles simulations.

Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators

The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.

Exciton dynamics from the mapping approach to surface hopping: comparison with Förster and Redfield theories

We compare the recently introduced multi-state mapping approach to surface hopping (MASH) with the Förster and Redfield theories of excitation energy transfer. Whereas Förster theory relies on weak coupling between chromophores, and Redfield theory assumes the electronic excitations to be weakly coupled to fast chromophore vibrations, MASH is free from any perturbative or Markovian approximations. We illustrate this with an example application to the rate of energy transfer in a Frenkel-exciton dimer, showing that MASH interpolates correctly between the opposing regimes in which the Förster and Redfield results are reliable. We then compare the three methods for a realistic model of the Fenna-Matthews-Olson complex with a structured vibrational spectral density and static disorder in the excitation energies. In this case there are no exact results for comparison so we use MASH to assess the validity of Förster and Redfield theories. We find that Förster theory is the more accurate of the two on the picosecond timescale, as has been shown previously for a simpler model of this particular light-harvesting complex. We also explore various ways to sample the initial electronic state in MASH and find that they all give very similar results for exciton dynamics.

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.

Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest

Nonadiabatic transition dynamics lies at the core of many electron/hole transfer, photoactivated, and vacuum field-coupled processes. About a century after Ehrenfest proposed "Phasenraum" and the Ehrenfest theorem, we report a conceptually novel trajectory-based nonadiabatic dynamics approach, nonadiabatic field (NAF), based on a generalized exact coordinate-momentum phase space formulation of quantum mechanics. It does not employ the conventional Born-Oppenheimer or Ehrenfest trajectory in the nonadiabatic coupling region. Instead, in NAF the equations of motion of the independent trajectory involve a nonadiabatic nuclear force term in addition to an adiabatic nuclear force term of a single electronic state. A few benchmark tests for gas phase and condensed phase systems indicate that NAF offers a practical tool to capture the correct correlation of electronic and nuclear dynamics for processes where the states remain coupled all the time as well as for the asymptotic region where the coupling of electronic states vanishes.

Homogeneous Dephasing in Photosynthetic Bacterial Reaction Centers: Time Correlation Function Approach

A new tractable linear electronic transition dipole moment time correlation function (ETDMTCF) that accurately accounts for electronic dephasing, asymmetry, and width of 1-phonon profile, which the zero-phonon line (ZPL) contributes to it, in Rhodopseudomonas viridis bacterial reaction center is derived. This time correlation function proves to be superior to other frequency-domain expressions in case of strong electron-phonon coupling (which is often the case in bacterial RCs and pigment-protein complexes), many vibrational modes involved, and high temperature, whereby more vibronic and electronic (sequence) transitions would arise. The Fourier transform of this ETDMTCF leads to asymmetric multiphonon profiles composed of Lorentzian distribution and Gaussian distribution on the high- and low-energy sides, respectively, whereby the overtone widths fold themselves with that of the one-phonon profile. This ETDMTCF also features expedient computation in large systems using asymmetric phonon profiles to account correctly for dephasing and pigment-protein interaction (electron-phonon coupling). The derived ETDMTCF allows computing all nonlinear optical signals in both time and frequency domains, through the nonlinear dipole moment time correlation functions (as guided by nonlinear optical response theory) in line with the eight Liouville space pathways. The linear transition dipole moment time correlation function is of a central value as the nonlinear transition dipole moment time correlation function is expressed in terms of the linear transition dipole moment time correlation function, derived herein. One of the great advantages of presenting this ETDMTCF is its applicability to nonlinear transition dipole moment time correlation functions in line with the eight Liouville space pathways needed in computing nonlinear signals. As such, there is more to the utility and applicability of the presented ETDMTCF besides computational expediency and efficiency. Results show good agreement with the reported literature. The intimate connection between a one-phonon profile and the corresponding bath spectral density in photosynthetic complexes is discussed.

Accelerating an integrative view of quantum biology

Quantum biology studies span multiple disciplines including physics, engineering, and biology with the goal of understanding the quantum underpinnings of living systems. Recent findings have brought wide attention to the role of quantum mechanisms in the function and regulation of biological processes. Moreover, a number of activities have been integral in building a vibrant quantum biology community. Due to the inherent interdisciplinary nature of the field, it is a challenge for quantum biology researchers to integrate and advance findings across the physical and biological disciplines. Here we outline achievable approaches to developing a shared platform-including the establishment of standardized manipulation tools and sensors, and a common scientific lexicon. Building a shared community framework is also crucial for fostering robust interdisciplinary collaborations, enhancing knowledge sharing, and diversifying participation in quantum biology. A unified approach promises not only to deepen our understanding of biological systems at a quantum level but also to accelerate the frontiers of medical and technological innovations.

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

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

Optimal conditions for environment-assisted quantum transport on the fully connected network

We present a theoretical analysis of the efficiency and rate of excitation transport on a network described by a complete graph in which every site is connected to every other. The long-time transport properties are analytically calculated for networks of arbitrary size that are symmetric except for the trapping site, start with a range of initial states, and are subject to dephasing and excitation decay. Conditions for which dephasing increases transport are identified, and optimal conditions are found for various physical parameters. The optimal conditions demonstrate robustness and a convergence of timescales previously observed in the context of light-harvesting complexes.

Engineering Transport via Collisional Noise: A Toolbox for Biology Systems

The study of noise assisted-transport in quantum systems is essential in a wide range of applications, from near-term NISQ devices to models for quantum biology. Here, we study a generalized XXZ model in the presence of stochastic collision noise, which allows describing environments beyond the standard Markovian formulation. Our analysis through the study of the local magnetization, the inverse participation ratio (IPR) or its generalization, and the inverse ergodicity ratio (IER) showed clear regimes, where the transport rate and coherence time could be controlled by the dissipation in a consistent manner. In addition, when considering various excitations, we characterized the interplay between collisions and system interactions, identifying regimes in which transport was counterintuitively enhanced when increasing the collision rate, even in the case of initially separated excitations. These results constitute an example of an essential building block for the understanding of quantum transport in structured noisy and warm-disordered environments.

Quantum Biology and the Potential Role of Entanglement and Tunneling in Non-Targeted Effects of Ionizing Radiation: A Review and Proposed Model

It is well established that cells, tissues, and organisms exposed to low doses of ionizing radiation can induce effects in non-irradiated neighbors (non-targeted effects or NTE), but the mechanisms remain unclear. This is especially true of the initial steps leading to the release of signaling molecules contained in exosomes. Voltage-gated ion channels, photon emissions, and calcium fluxes are all involved but the precise sequence of events is not yet known. We identified what may be a quantum entanglement type of effect and this prompted us to consider whether aspects of quantum biology such as tunneling and entanglement may underlie the initial events leading to NTE. We review the field where it may be relevant to ionizing radiation processes. These include NTE, low-dose hyper-radiosensitivity, hormesis, and the adaptive response. Finally, we present a possible quantum biological-based model for NTE.

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

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

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.

A quantum trajectory picture of single photon absorption and energy transport in photosystem II

We use quantum trajectory theory to study the dynamics of the first step in photosynthesis for a single photon interacting with photosystem II (PSII). By considering individual trajectories we are able to look beyond the ensemble average dynamics to compute the PSII system evolution conditioned upon individual photon counting measurements. Measurements of the transmitted photon beam strongly affects the system state, since detection of an outgoing photon confirms that the PSII must be in the electronic ground state, while a null measurement implies it is in an excited electronic state. We show that under ideal conditions, observing the null result transforms a state with a low excited state population to a state with nearly all population contained in the excited states. We study the PSII dynamics conditioned on such photon counting for both a pure excitonic model of PSII and a more realistic model with exciton-phonon coupling to a dissipative phononic environment. In the absence of such coupling, we show that the measured fluorescence rates show oscillations constituting a photon-counting witness of excitonic coherence. Excitonic coupling to the phonon environment has a strong effect on the observed rates of fluorescence, damping the oscillations. Addition of non-radiative decay and incoherent transitions to radical pair states in the reaction center to the phononic model allows extraction of a quantum efficiency of 92.5% from the long-time evolution, consistent with bulk experimental measurements.

Visioning synthetic futures for yeast research within the context of current global techno-political trends

Yeast research is entering into a new period of scholarship, with new scientific tools, new questions to ask and new issues to consider. The politics of emerging and critical technology can no longer be separated from the pursuit of basic science in fields, such as synthetic biology and engineering biology. Given the intensifying race for technological leadership, yeast research is likely to attract significant investment from government, and that it offers huge opportunities to the curious minded from a basic research standpoint. This article provides an overview of new directions in yeast research with a focus on Saccharomyces cerevisiae, and places these trends in their geopolitical context. At the highest level, yeast research is situated within the ongoing convergence of the life sciences with the information sciences. This convergent effect is most strongly pronounced in areas of AI-enabled tools for the life sciences, and the creation of synthetic genomes, minimal genomes, pan-genomes, neochromosomes and metagenomes using computer-assisted design tools and methodologies. Synthetic yeast futures encompass basic and applied science questions that will be of intense interest to government and nongovernment funding sources. It is essential for the yeast research community to map and understand the context of their research to ensure their collaborations turn global challenges into research opportunities.

Incoherent Energy Transfer between the Baseplate and FMO Protein Explored at Ideal Geometries

The Förster resonance energy transfer (FRET) between the Fenna-Matthews-Olson (FMO) protein complex and the chlorosomal baseplate (CBP) is investigated by using an idealized model. This simplified model is based on crystal structure and molecular dynamics conformations. Some of the further input, such as the transition dipole moments, was extracted from earlier molecular-level simulations. The resulting model mimics the effects of the relative position between the CBP and the FMO complex on the corresponding FRET efficiency under ideal conditions, involving about 1.3 billion FRET calculations per investigated model. In this idealized model and employing some approximations, it is found that FRET efficiency is almost completely independent of the FMO trimer orientation (displacement, distance, and rotation), despite FMO and CBP being highly structured complexes. Even removing individual FMO BChl triples will only reduce the FRET efficiency by up to 8.6%. An FMO containing only the least efficient BChl triple will retain about 25% of the FRET efficiency of a full FMO complex. In addition to its proposed function as an energetic funnel, FMO is thus identified to act as a highly robust spatial funnel for CBP excitation harvesting, independent of the mutual CBP-FMO orientation.

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

The dynamics of the excitation energy transfer (EET) in photosynthetic complexes is an interesting question both from the perspective of fundamental understanding and the research in artificial photosynthesis. Over the past decade, very accurate spectral densities have been developed to capture spatial inhomogeneities in the Fenna-Matthews-Olson (FMO) complex. However, challenges persist in numerically simulating these systems, both in terms of parameterizing them and following their dynamics over long periods of time because of long non-Markovian memories. We investigate the dynamics of FMO with the exact treatment of various theoretical spectral densities using the new tensor network path integral-based methods, which are uniquely capable of addressing the difficulty of long memory length and incoherent Förster theory. It is also important to be able to analyze the pathway of EET flow, which can be difficult to identify given the non-trivial structure of connections between bacteriochlorophyll molecules in FMO. We use the recently introduced ideas of relating coherence to population derivatives to analyze the transport process and reveal some new routes of transport. The combination of exact and approximate methods sheds light on the role of coherences in affecting the fine details of the transport and promises to be a powerful toolbox for future exploration of other open systems with quantum transport.

Impact of Structure, Coupling Scheme, and State of Interest on the Energy Transfer in CP29

The Qy and Bx excitation energy transfer (EET) in the minor light-harvesting complex CP29 (LHCII B4.1) antenna complex of Pisum sativum was characterized using a computational approach. We applied Förster resonance energy transfer (FRET) and the transition density cube (TDC) method to estimate the Coulombic coupling, based on a combination of classical molecular dynamics and quantum mechanics/molecular mechanics calculations. Employing TDC instead of FRET mostly affects the EET between chlorophylls (Chls) and carotenoids (Crts), as expected due to the Crts being spatially more challenging for FRET. Only between Chls, effects are found to be small (about only 0.1 EET efficiency change when introducing TDC instead of FRET). Effects of structural sampling were found to be small, illustrated by a small average standard deviation for the Qy state coupling elements (FRET/TDC: 0.97/0.94 cm-1). Due to the higher flexibility of the Bx state, the corresponding deviations are larger (FRET/TDC between Chl-Chl pairs: 17.58/22.67 cm-1, between Crt-Chl pairs: 62.58/31.63 cm-1). In summary, it was found for the Q band that the coupling between Chls varies only slightly depending on FRET or TDC, resulting in a minute effect on EET acceptor preference. In contrast, the coupling in the B band spectral region is found to be more affected. Here, the S2 (1Bu) states of the spatially challenging Crts may act as acceptors in addition to the B states of the Chls. Depending on FRET or TDC, several Chls show different Chl-to-Crt couplings. Interestingly, the EET between Chls or Crts in the B band is found to often outcompete the corresponding decay processes. The individual efficiencies for B band EET to Crts vary however strongly with the chosen coupling scheme (e.g., up to 0.29/0.99 FRET/TDC efficiency for the Chl a604/neoxanthin pair). Thus, the choice of the coupling scheme must involve a consideration of the state of interest.

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.

Two-dimensional fluorescence excitation spectroscopy: A novel technique for monitoring excited-state photophysics of molecular species with high time and frequency resolution

We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates.

Theory predicts UV/vis-to-IR photonic down conversion mediated by excited state vibrational polaritons

This work proposes a photophysical phenomenon whereby ultraviolet/visible (UV/vis) excitation of a molecule involving a Franck-Condon (FC) active vibration yields infrared (IR) emission by strong coupling to an optical cavity. The resulting UV/vis-to-IR photonic down conversion process is mediated by vibrational polaritons in the electronic excited state potential. It is shown that the formation of excited state vibrational polaritons (ESVP) via UV/vis excitation only involve vibrational modes with both a non-zero FC activity and IR activity in the excited state. Density functional theory calculations are used to identify 1-Pyreneacetic acid as a molecule with this property and the dynamics of ESVP are modeled. Overall, this work introduces an avenue of polariton chemistry where excited state dynamics are influenced by the formation of vibrational polaritons. Along with this, the UV/vis-to-IR photonic down conversion is potentially useful in both sensing excited state vibrations and quantum transduction schemes.