Two-dimensional spectroscopy of electronic couplings in photosynthesis

Quantum phase synchronization revealing few-hundred femtosecond coherence in cryptophyte phycoerythrin 545 antenna from exciton-vibrational coupling

Quantum beats lasting a few hundred femtoseconds have been regarded as signatures of quantum energy transfer in photosynthetic antennae. The fragile coherence at room temperature casts doubt on its long-lived feature arising from the electronic coherence. Recently, the long-lived exciton-vibrational coherences of several hundred femtoseconds via quantum phase synchronization of the resonant higher frequency collective vibrational modes have been observed in core antenna allophycocyanin from algae. The long-lived coherence has an inherent property of protecting the coherence against the noisy environment. This is achieved by dissipation of the resonant anti-symmetric collective vibrational modes coupled to the excitonic levels, which have fast dephasing, leaving only the non-dissipative correlated symmetric modes [R. Zhu et al., Nat. Commun. 15, 3171 (2024)], which is different from that induced by the environmental low frequency modes. Coherence with a lifetime constant of 200 fs at room temperature has been observed in the cryptophyte phycoerythrin 545 (PE545) antenna before, while its origin, i.e., pure electronic or exciton-vibrational, remains to be explored. Here, we investigated coherent energy transfer dynamics in PE545 via two-dimensional electronic spectroscopy. A long-lasting coherence with a lifetime constant of 270 fs in the dynamical Stokes shift dynamics was observed. Especially, the high frequency vibrational mode at 1150 cm-1 is absent in the electronic energy dissipation process reflected in the dynamical Stokes' shifts spectrum, which is near resonant with the electronic gap of 1080 cm-1. Therefore, the facts strongly suggest that the long-lived coherence in PE545 is realized by the resonant exciton-vibrational coupling via quantum phase synchronization.

Overcoming experimental obstacles in two-dimensional spectroscopy of a single molecule

Two-dimensional electronic spectroscopy provides information on coupling and energy transfer between excited states on ultrafast timescales. Only recently, incoherent fluorescence detection has made it possible to combine this method with single-molecule optical spectroscopy to reach the ultimate limit of sensitivity. The main obstacle has been the low number of photons detected due to limited photostability. Here, we discuss the key experimental choices that allowed us to overcome these obstacles: broadband acousto-optic modulation, accurate phase-locked loops, photon-counting lock-in detection, delay stage linearization, and detector dead-time compensation. We demonstrate how the acquired photon stream data can be used to post-select detection events according to specific criteria.

Double-quantum two-dimensional electronic-vibrational spectroscopy: Theory. Vibronic coherences in nonadiabatic phenomena

Nonadiabatic phenomena are ubiquitous in polyatomic molecular systems and are responsible for many ultrafast dynamics occurring outside of the Born-Oppenheimer approximation. In particular, electronic curve crossings offer ultrafast, sub-100 fs pathways for efficient electronic relaxation between potential energy surfaces, where the electronic and vibrational degrees of freedom become strongly coupled. Due to the unique mixture of temporal and spectral resolution required to detect electronic curve crossings, experimental observation has remained a considerable challenge. Here, double-quantum coherence two-dimensional electronic-vibrational (2Q 2D EV) spectroscopy is introduced for the first time and proposed as an experimental approach to monitor vibronic dynamics near and at electronic curve crossings directly through vibronic coherences using a mixture of broadband visible and infrared pulses. A semi-classical vibronic Hamiltonian is used that characterizes the parametrically defined coupling between high-frequency vibrations and low-frequency vibrational modes involved in tuning electronic potential energy surfaces. This work displays how unique multidimensional pulse sequences can uncover dynamics that are hidden in conventional techniques.

Distinguishing packing configurations of molecular dimers using excited-state absorption peaks in two-dimensional electronic spectra

Packing conformations of molecular aggregates are known to strongly influence the locations and intensities of spectral peaks. Here, we develop the third-order nonlinear spectroscopy signals for a purely electronic model of a molecular dimer, which is a prototype aggregate system. The model-which focuses on excited-state absorption (ESA) pathways in two-dimensional electronic spectra-reveals that orientational averaging leads to diagnostic ESA peak locations for H- and J-dimers. We constructed DNA-templated dimers of cyanine molecules as representative systems and used ultrabroadband two-dimensional electronic spectroscopy measurements to support the predicted signatures arising from the theoretical model. Fitting of steady-state spectra supports the assigned packing conformations. The results elucidate how ESA peaks can be diagnostic spectral signatures of packing conformation. This work lays the foundation for future studies that can include the complicating effects of vibronic states and additional electronic levels.

2D-THz spectroscopy: exploring the nonlinear dynamics in quantum materials

Unraveling the nonlinear regime of light-matter interaction in quantum materials at ultrafast timescales has remained elusive over the past few decades. The primary obstacle entailed finding a resonant pump as well as a suitable, resonant probe that could effectively excite and capture the interaction pathways of the collective modes within their inherent timescales. Intriguingly, the characteristic energyscales of the said interactions and the timescales of ensuing dynamics lie in the THz range, making THz radiation not only an apt probe but also an ideal resonant tool for driving the collective modes out of equilibrium. In the said direction, 2D-THz spectroscopy serves as a state-of-the-art technique for unveiling the correlation dynamics of quantum materials through table-top experiments. On a microscopic level, this offers valuable insights into the competing interactions among the charge, spin, lattice, and orbital degrees of freedom. Though the field of 2D-THz spectroscopy is relatively new and yet to be explored in its full potential, this review highlights the progress made in investigating various coupling channels of collective modes, namely magnons, phonons, polaritons, etc in different insulating and semiconducting systems. We also provide pedagogical introduction to the 2D-THz spectroscopy and foresee its emergence alongside cutting-edge experimental tools, reshaping our understanding of quantum materials with new perspectives.

Two-Dimensional Electronic Spectroscopy of Rhodamine 700 Using an 8 fs Ultrabroadband Laser Source and Full-Wavelength Reference Detection

Two-dimensional electronic spectroscopy (2DES) is one of the premier tools for investigating photoinduced condensed phase dynamics, combining high temporal and spectral resolution to probe ultrafast phenomena. We have coupled an ultrabroadband laser source generated with a hollow-core fiber, compressing pulses to have a pulse duration of 8 fs, with a boxcars 2DES interferometer constructed from only conventional optics. The resulting ultrabroad bandwidth and high temporal resolution allow for superior spectral coverage of the typically broad molecular line shapes in the near-IR/visible region in room temperature solutions, and the exploration of the excited state dynamics at the earliest time epoch in complex systems. The new spectrometer is characterized by examining the dynamics of the dye molecule Rhodamine 700 in methanol solution. These data exhibit rich vibrational wavepacket dynamics, with 2DES data unraveling key molecular vibronic couplings between multiple vibrational modes. For the first time in a degenerate broadband 2DES experiment, we demonstrate the implementation of full-wavelength reference detection to correct wavelength-dependent laser intensity fluctuations. The net result is a 4-5× increased signal-to-noise (S/N) ratio compared to data acquired without reference detection, yielding a typical S/N ratio = 28. The increased S/N ratio facilitates more rapid data acquisition and examination of samples at lower optical densities, and thus concentrations, than typically used in 2DES experiments. These advances will help to alleviate the typical high demands on precious samples in 2DES measurements.

Ultrafast spectroscopy of liquids using extreme-ultraviolet to soft-X-ray pulses

Ultrafast X-ray spectroscopy provides access to molecular dynamics with unprecedented time resolution, element specificity and site selectivity. These unique properties are optimally suited for investigating intramolecular and intermolecular interactions of molecular species in the liquid phase. This Review summarizes experimental breakthroughs, such as water photolysis and proton transfer on femtosecond and attosecond time scales, dynamics of solvated electrons, charge-transfer processes in metal complexes, multiscale dynamics in haem proteins, proton-transfer dynamics in prebiotic systems and liquid-phase extreme-ultraviolet high-harmonic spectroscopy. An important novelty for ultrafast liquid-phase spectroscopy is the availability of high-brightness ultrafast short-wavelength sources that allowed access to the water window (from 200 eV to 550 eV) and thus to the K-edges of the key elements of organic and biological chemistry: C, N and O. Not only does this Review present experimental examples that demonstrate the unique capabilities of ultrafast short-wavelength spectroscopy in liquids, but it also highlights the broad range of spectroscopic methodologies already applied in this field.

Polariton spectra under the collective coupling regime. II. 2D non-linear spectra

In our previous work [Mondal et al., J. Chem. Phys. 162, 014114 (2025)], we developed several efficient computational approaches to simulate exciton-polariton dynamics described by the Holstein-Tavis-Cummings (HTC) Hamiltonian under the collective coupling regime. Here, we incorporated these strategies into the previously developed Lindblad-partially linearized density matrix (L-PLDM) approach for simulating 2D electronic spectroscopy (2DES) of exciton-polariton under the collective coupling regime. In particular, we apply the efficient quantum dynamics propagation scheme developed in Paper I to both the forward and the backward propagations in the PLDM and develop an efficient importance sampling scheme and graphics processing unit vectorization scheme that allow us to reduce the computational costs from O(K2)O(T3) to O(K)O(T0) for the 2DES simulation, where K is the number of states and T is the number of time steps of propagation. We further simulated the 2DES for an HTC Hamiltonian under the collective coupling regime and analyzed the signal from both rephasing and non-rephasing contributions of the ground state bleaching, excited state emission, and stimulated emission pathways.

Linear Dichroism Microscopy Resolves Competing Structural Models of a Synthetic Light-Harvesting Complex

The initial stages of photosynthesis in light-harvesting antennae, driven by excitonic energy transport, have inspired the design of artificial light-harvesting complexes. Double-walled nanotubes (DWNTs) formed from the cyanine dye C8S3 provide a robust, self-assembled system that mimics natural chlorosomes in both structure and optical properties. Two competing molecular packing models─bricklayer (BL) and herringbone (HB)─have been proposed to explain the structural and optical characteristics of these DWNTs. This study resolves the debate by combining theoretical analysis with advanced polarization-resolved wide-field photoluminescence microscopy. Quantum-classical simulations reveal reduced linear dichroism (LDr) as a decisive parameter for distinguishing between the models. Experimental measurements of single DWNTs yielded LDr values as high as 0.93, strongly favoring the BL model. The BL model's unique excitonic patterns, dominated by negative couplings among individual chromophores, generate superradiant exciton states with transition dipoles preferentially aligned along the nanotube axis. In contrast, the HB model's mixed positive and negative couplings produce destructive interference, leading to a weaker alignment of transition dipoles. Our approach deepens the understanding of the structure-property relationships in self-assembled systems and demonstrates the potential of slip-stacking engineering to fine-tune excitonic properties for artificial light-harvesting applications.

What Two-Dimensional Electronic Spectroscopy Can Tell Us about Energy Transfer in Dendrimers: Ab Initio Simulations

Two-dimensional (2D) electronic spectra of the phenylene ethynylene dendrimer with 2-ring and 3-ring branches were evaluated by combining the on-the-fly trajectory surface hopping nonadiabatic dynamics and the doorway-window simulation protocol. The ground state bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA) contributions to the 2D signal were obtained and carefully analyzed. The results demonstrate that the ultrafast intramolecular nonadiabatic excited-state energy transfer (EET) from the 2-ring to the 3-ring units is comprehensively characterized by the SE and ESA signals. It is proven that the monitoring of the 2D ESA signal is especially convenient, because it is spectrally well separated from the SE and GSB signals. Hence, 2D electronic spectroscopy provides a detailed and multifaceted view of the intramolecular EET process in dendrimers.

Application of the Time-Domain Multichromophoric Fluorescence Resonant Energy Transfer Method in the NISE Programme

We present the implementation of the time-domain multichromophoric fluorescence resonant energy transfer (TC-MCFRET) approach in the numerical integration of the Schrödinger equation (NISE) program. This method enables the efficient simulation of incoherent energy transfer between distinct segments within large and complex molecular systems, such as photosynthetic complexes. Our approach incorporates a segmentation protocol to divide these systems into manageable components and a modified thermal correction to ensure detailed balance. The implementation allows us to calculate the energy transfer rate in the NISE program systematically and easily. To validate our method, we applied it to a range of test cases, including parallel linear aggregates and biologically relevant systems like the B850 rings from LH2 and the Fenna-Matthews-Olson complex. Our results show excellent agreement with previous studies, demonstrating the accuracy and efficiency of our TD-MCFRET method. We anticipate that this approach will be widely applicable to the calculation of energy transfer rates in other large molecular systems and will pave the way for future simulations of multidimensional electronic spectra.

Spectroscopy and Excited-State Dynamics of Methyl Ferulate in Molecular Beams

The spectroscopic and dynamic properties of methyl ferulate─a naturally occurring ultraviolet-protecting filter─and microsolvated methyl ferulate have been studied under molecular beam conditions using resonance-enhanced multiphoton ionization spectroscopy in combination with quantum chemical calculations. We demonstrate and rationalize how the phenyl substitution pattern affects the state ordering of the lower excited singlet state manifold and what the underlying reason is for the conformation-dependent Franck-Condon (FC) activity in the UV-excitation spectra. Studies on microsolvated methyl ferulate reveal potential coordination sites and the influence of such coordination on the spectroscopic properties. Our quantum chemical studies also enable us to obtain a quantitative understanding of the dominant excited-state decay routes of the photoexcited ππ* state involving a ∼3 ns intersystem crossing pathway to the triplet manifold─which is much slower than found for coumarates─and a relatively fast intersystem crossing back to the ground state (∼30 ns). We show that a common T1/S0 crossing can very well explain the observation that T1 lifetimes are quasi-independent of the phenyl substitution pattern.

Cross Peaks on Two-Dimensional Optical Spectra Arising from Quantum Cross-Correlation Functions

Cross peaks on 2D optical spectra are indicative of interactions between molecular excitonic states. Currently, the two conventional assignments of cross peaks are direct coupling and population transfer between excitonic states. Here, we show that there is another possible source of cross peaks. We theoretically demonstrate that for a model comprising two nondirectly interacting excitons or two-level systems (TLSs), cross peaks can arise if there is a complex-valued or quantum frequency-gap cross-correlation function between the two TLSs. Considering only real-valued or classical cross-correlation functions will result in no cross peaks. We derive and validate the mathematical expressions describing such cross peaks. We then simulate the 2D electronic spectra of an example model system comprising nondirectly interacting TLSs whose quantum cross-correlation functions arise from coupling to a common overdamped Brownian oscillator mode. We show that there are clear observational differences between such quantum correlation cross peaks with conventional direct coupling and population transfer cross peaks.

Fine-Tuning the Microstructure and Photophysical Characteristics of Fluorescent Conjugated Copolymers Using Photoalignment and Liquid-Crystal Ordering

Replicating the microstructural basis and the near 100% excitation energy transfer efficiency in naturally occurring light-harvesting complexes (LHCs) remains challenging in synthetic energy-harvesting devices. Biological photosynthesis regulates active ensembles of light-absorbing and funneling chlorophylls in proteins in response to fluctuating sunlight. Here, use of long-range liquid crystal (LC) ordering to tailor chain orientation and packing structure in liquid crystalline conjugated polymer (LCCP) layers for bio-mimicry of certain structural basis and light-harvesting properties of LHCs is reported. It is found that long-range orientational ordering in an LC phase of poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) copolymer stabilizes a small fraction of randomly-oriented F8BT nanocrystals dispersed in an amorphous matrix of F8BT chains, resembling a self-doped host-guest system whereby excitation energy funneling and photoluminescence quantum efficiencies are enhanced significantly by triggering 3D donor-to-acceptor Förster resonance energy transfer (FRET) and dominant intrachain emission in the nano-crystal acceptor. Further, photoalignment of nematic F8BT layers is combined with LC orientational ordering to fabricate large-area-extended monodomains exhibiting >60% crystallinity and ≈20 nm-long interchain packing order. Remarkably, these monodomains demonstrate strong linearly polarized emission, whilst also promoting a new band-edge absorption species and an extra emissive interchain excited state as compared to the non-aligned films.

The development and applications of multidimensional biomolecular spectroscopy illustrated by photosynthetic light harvesting

The parallel and synergistic developments of atomic resolution structural information, new spectroscopic methods, their underpinning formalism, and the application of sophisticated theoretical methods have led to a step function change in our understanding of photosynthetic light harvesting, the process by which photosynthetic organisms collect solar energy and supply it to their reaction centers to initiate the chemistry of photosynthesis. The new spectroscopic methods, in particular multidimensional spectroscopies, have enabled a transition from recording rates of processes to focusing on mechanism. We discuss two ultrafast spectroscopies - two-dimensional electronic spectroscopy and two-dimensional electronic-vibrational spectroscopy - and illustrate their development through the lens of photosynthetic light harvesting. Both spectroscopies provide enhanced spectral resolution and, in different ways, reveal pathways of energy flow and coherent oscillations which relate to the quantum mechanical mixing of, for example, electronic excitations (excitons) and nuclear motions. The new types of information present in these spectra provoked the application of sophisticated quantum dynamical theories to describe the temporal evolution of the spectra and provide new questions for experimental investigation. While multidimensional spectroscopies have applications in many other areas of science, we feel that the investigation of photosynthetic light harvesting has had the largest influence on the development of spectroscopic and theoretical methods for the study of quantum dynamics in biology, hence the focus of this review. We conclude with key questions for the next decade of this review.

Development of phase-cycling interface-specific two-dimensional electronic sum frequency generation (2D-ESFG) spectroscopy

Two-dimensional electronic spectroscopy (2D-ES) has become an important technique for studying energy transfer, electronic coupling, and electronic-vibrational coherence in the past ten years. However, since 2D-ES is not interface specific, the electronic information at surfaces and interfaces could not be demonstrated clearly. Two-dimensional electronic sum-frequency generation (2D-ESFG) is an emerging spectroscopic technique that explores the correlations between different interfacial electronic transitions and is the extension of 2D-ES to surface and interfacial specificity. In this work, we present the detailed development and implementation of phase-cycling 2D-ESFG spectroscopy using an acousto-optic pulse shaper in a pump-probe geometry. With the pulse pair generated by a pulse shaper rather than optical devices based on birefringence or interference, this 2D-ESFG setup enables rapid scanning, phase cycling, and the separation of rephasing and nonrephasing signals. In addition, by collecting data in a rotating frame, we greatly improve experimental efficiency. We demonstrate the method for azo-derivative molecules at the air/water interface. This method could be readily extended to different interfaces and surfaces. The unique phase-cycling 2D-ESFG technique enables one to quantify the energy transfer, charge transfer, electronic coupling, and many other electronic properties and dynamics at surfaces and interfaces with precision and relative ease of use. Our goal in this article is to present the fine details of the fourth-order nonlinear optical technique in a manner that is comprehensive, succinct, and approachable such that other researchers can implement, improve, and adapt it to probe unique and innovative problems to advance the field.

On-the-Fly Simulation of Two-Dimensional Fluorescence-Excitation Spectra

Two-dimensional (2D) fluorescence-excitation (2D-FLEX) spectroscopy is a recently proposed nonlinear femtosecond technique for the detection of photoinduced dynamics. The method records a time-resolved fluorescence signal in its excitation- and detection-frequency dependence and hence combines the exclusive detection of excited state dynamics (fluorescence) with signals resolved in both excitation and emission frequencies (2D electronic spectroscopy). In this work, we develop an on-the-fly protocol for the simulation of 2D-FLEX spectra of molecular systems, which is based on interfacing the classical doorway-window representation of spectroscopic responses with trajectory surface hopping simulations. Applying this methodology to gas-phase pyrazine, we show that femtosecond 2D-FLEX spectra can deliver detailed information that is otherwise obtainable via attosecond spectroscopy.

Coarse-Grained Approach to Simulate Signatures of Excitation Energy Transfer in Two-Dimensional Electronic Spectroscopy of Large Molecular Systems

Two-dimensional electronic spectroscopy (2DES) has proven to be a highly effective technique in studying the properties of excited states and the process of excitation energy transfer in complex molecular assemblies, particularly in biological light-harvesting systems. However, the accurate simulation of 2DES for large systems still poses a challenge because of the heavy computational demands it entails. In an effort to overcome this limitation, we devised a coarse-grained 2DES method. This method encompasses the treatment of the entire system by dividing it into distinct weakly coupled segments, which are assumed to communicate predominantly through incoherent exciton transfer. We first demonstrate the efficiency of this method through simulation on a model dimer system, which demonstrates a marked improvement in calculation efficiency, with results that exhibit good concordance with reference spectra calculated with less approximate methods. Additionally, the application of this method to the light-harvesting antenna 2 (LH2) complex of purple bacteria showcases its advantages, accuracy, and limitations. Furthermore, simulating the anisotropy decay in LH2 induced by energy transfer and its comparison with experiments confirm that the method is capable of accurately describing dynamical processes in a biologically relevant system. This method presented lends itself to an extension that accounts for the effect of intrasegment relaxation processes on the 2DES spectra, which for computational efficiency are ignored in the implementation reported here. It is envisioned that the method will be employed in the future to accurately and efficiently calculate 2D spectra of more extensive systems, such as photosynthetic supercomplexes.

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.

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.

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

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

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.

PigmentHunter: A point-and-click application for automated chlorophyll-protein simulations

Chlorophyll proteins (CPs) are the workhorses of biological photosynthesis, working together to absorb solar energy, transfer it to chemically active reaction centers, and control the charge-separation process that drives its storage as chemical energy. Yet predicting CP optical and electronic properties remains a serious challenge, driven by the computational difficulty of treating large, electronically coupled molecular pigments embedded in a dynamically structured protein environment. To address this challenge, we introduce here an analysis tool called PigmentHunter, which automates the process of preparing CP structures for molecular dynamics (MD), running short MD simulations on the nanoHUB.org science gateway, and then using electrostatic and steric analysis routines to predict optical absorption, fluorescence, and circular dichroism spectra within a Frenkel exciton model. Inter-pigment couplings are evaluated using point-dipole or transition-charge coupling models, while site energies can be estimated using both electrostatic and ring-deformation approaches. The package is built in a Jupyter Notebook environment, with a point-and-click interface that can be used either to manually prepare individual structures or to batch-process many structures at once. We illustrate PigmentHunter's capabilities with example simulations on spectral line shapes in the light harvesting 2 complex, site energies in the Fenna-Matthews-Olson protein, and ring deformation in photosystems I and II.

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.

Energy Transfer and Exciton Relaxation in B880-B800-RC Complex through Two-Dimensional Electronic Spectroscopy

The light-harvesting (LH) and reaction center (RC) core complex of purple bacterium Roseiflexus castenholzii, B880-B800-RC, are different from those of the typical photosynthetic unit, (B850-B800)x-B880-RC. To investigate the excitation flowing dynamics in this unique complex, two-dimensional electronic spectroscopy is employed. The obtained time constants for the exciton relaxation in B880, exciton relaxation in B800, B800 → B880 energy transfer (EET), and B880 → closed RC EET are 43 fs, 177 fs, 1.9 ps, and 205 ps, respectively. These time constants result in an overall EET efficiency similar to that of the typical photosynthetic unit. Analysis of the oscillatory signals reveals that while several vibronic coherences are involved in the exciton relaxation process, only one prominent vibronic coherence, with a frequency of 27 cm-1 and coupled to the B880 electronic transition, may contribute to the B800 → B880 EET process.

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

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

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.

Extracting double-quantum coherence in two-dimensional electronic spectroscopy under pump-probe geometry

Two-dimensional electronic spectroscopy (2DES) can be implemented with different geometries, e.g., BOXCARS, collinear, and pump-probe geometries. The pump-probe geometry has the advantage of overlapping only two beams and reducing phase cycling steps. However, its applications are typically limited to observing the dynamics with single-quantum coherence and population, leaving the challenge to measure the dynamics of the double-quantum (2Q) coherence, which reflects the many-body interactions. We demonstrate an experimental technique in 2DES under pump-probe geometry with a designed pulse sequence and the signal processing method to extract 2Q coherence. In the designed pulse sequence, with the probe pulse arriving earlier than the pump pulses, our measured signal includes the 2Q signal as well as the zero-quantum signal. With phase cycling and data processing using causality enforcement, we extract the 2Q signal. The proposal is demonstrated with rubidium atoms. We observe the collective resonances of two-body dipole-dipole interactions in both the D1 and D2 lines.

Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Manipulation of photosynthetic energy transfer by vibrational strong coupling

Uncovering the mystery of efficient and directional energy transfer in photosynthetic organisms remains a critical challenge in quantum biology. Recent experimental evidence and quantum theory developments indicate the significance of quantum features of molecular vibrations in assisting photosynthetic energy transfer, which provides the possibility of manipulating the process by controlling molecular vibrations. Here, we propose and theoretically demonstrate efficient manipulation of photosynthetic energy transfer by using vibrational strong coupling between the vibrational state of a Fenna-Matthews-Olson (FMO) complex and the vacuum state of an optical cavity. Specifically, based on a full-quantum analytical model to describe the strong coupling effect between the optical cavity and molecular vibration, we realize efficient manipulation of energy transfer efficiency (from 58% to 92%) and energy transfer time (from 20 to 500 ps) in one branch of FMO complex by actively controlling the coupling strength and the quality factor of the optical cavity under both near-resonant and off-resonant conditions, respectively. Our work provides a practical scenario to manipulate photosynthetic energy transfer by externally interfering molecular vibrations via an optical cavity and a comprehensible conceptual framework for researching other similar systems.

Full visible range two-dimensional electronic spectroscopy with high time resolution

Two-dimensional electronic spectroscopy (2DES) is a powerful method to study coherent and incoherent interactions and dynamics in complex quantum systems by correlating excitation and detection energies in a nonlinear spectroscopy experiment. Such dynamics can be probed with a time resolution limited only by the duration of the employed laser pulses and in a spectral range defined by the pulse spectrum. In the blue spectral range (<500 nm), the generation of sufficiently broadband ultrashort pulses with pulse durations of 10 fs or less has been challenging so far. Here, we present a 2DES setup based on a hollow-core fiber supercontinuum covering the full visible range (400-700 nm). Pulse compression via custom-made chirped mirrors yields a time resolution of <10 fs. The broad spectral coverage, in particular the extension of the pulse spectra into the blue spectral range, unlocks new possibilities for coherent investigations of blue-light absorbing and multichromophoric compounds, as demonstrated by a 2DES measurement of chlorophyll a.

Plasmon mediated coherent population oscillations in molecular aggregates

The strong coherent coupling of quantum emitters to vacuum fluctuations of the light field offers opportunities for manipulating the optical and transport properties of nanomaterials, with potential applications ranging from ultrasensitive all-optical switching to creating polariton condensates. Often, ubiquitous decoherence processes at ambient conditions limit these couplings to such short time scales that the quantum dynamics of the interacting system remains elusive. Prominent examples are strongly coupled exciton-plasmon systems, which, so far, have mostly been investigated by linear optical spectroscopy. Here, we use ultrafast two-dimensional electronic spectroscopy to probe the quantum dynamics of J-aggregate excitons collectively coupled to the spatially structured plasmonic fields of a gold nanoslit array. We observe rich coherent Rabi oscillation dynamics reflecting a plasmon-driven coherent exciton population transfer over mesoscopic distances at room temperature. This opens up new opportunities to manipulate the coherent transport of matter excitations by coupling to vacuum fields.

Coupling and Slips in Photosynthetic Reactions-From Femtoseconds to Eons

Photosynthesis stands as a unique biological phenomenon that can be comprehensively explored across a wide spectrum, from femtoseconds to eons. Across each timespan, a delicate interplay exists between coupling and inherent deviations that are essential for sustaining the overall efficiency of the system. Both quantum mechanics and thermodynamics act as guiding principles for the diverse processes occurring from femtoseconds to eons. Processes such as excitation energy transfer and the accumulation of oxygen in the atmosphere, along with the proliferation of organic matter on the Earth's surface, are all governed by the coupling-slip principle. This article will delve into select time points along this expansive scale. It will highlight the interconnections between photosynthesis, the global population, disorder, and the issue of global warming.

Exciton delocalization in a fully synthetic DNA-templated bacteriochlorin dimer

A bacteriochlorophyll a (Bchla) dimer is a basic functional unit in the LH1 and LH2 photosynthetic pigment-protein antenna complexes of purple bacteria, where an ordered, close arrangement of Bchla pigments-secured by noncovalent bonding to a protein template-enables exciton delocalization at room temperature. Stable and tunable synthetic analogs of this key photosynthetic subunit could lead to facile engineering of exciton-based systems such as in artificial photosynthesis, organic optoelectronics, and molecular quantum computing. Here, using a combination of synthesis and theory, we demonstrate that exciton delocalization can be achieved in a dimer of a synthetic bacteriochlorin (BC) featuring stability, high structural modularity, and spectral properties advantageous for exciton-based devices. The BC dimer was covalently templated by DNA, a stable and highly programmable scaffold. To achieve exciton delocalization in the absence of pigment-protein interactions critical for the Bchla dimer, we relied on the strong transition dipole moment in BC enabled by two auxochromes along the Qy transition, and omitting the central metal and isocyclic ring. The spectral properties of the synthetic "free" BC closely resembled those of Bchla in an organic solvent. Applying spectroscopic modeling, the exciton delocalization in the DNA-templated BC dimer was evaluated by extracting the excitonic hopping parameter, J to be 214 cm-1 (26.6 meV). For comparison, the same method applied to the natural protein-templated Bchla dimer yielded J of 286 cm-1 (35.5 meV). The smaller value of J in the BC dimer likely arose from the partial bacteriochlorin intercalation and the difference in medium effect between DNA and protein.

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.

Probing exciton dynamics with spectral selectivity through the use of quantum entangled photons

Quantum light is increasingly recognized as a promising resource for developing optical measurement techniques. Particular attention has been paid to enhancing the precision of the measurements beyond classical techniques by using nonclassical correlations between quantum entangled photons. Recent advances in the quantum optics technology have made it possible to manipulate spectral and temporal properties of entangled photons, and photon correlations can facilitate the extraction of matter information with relatively simple optical systems compared to conventional schemes. In these respects, the applications of entangled photons to time-resolved spectroscopy can open new avenues for unambiguously extracting information on dynamical processes in complex molecular and materials systems. Here, we propose time-resolved spectroscopy in which specific signal contributions are selectively enhanced by harnessing nonclassical correlations of entangled photons. The entanglement time characterizes the mutual delay between an entangled twin and determines the spectral distribution of photon correlations. The entanglement time plays a dual role as the knob for controlling the accessible time region of dynamical processes and the degrees of spectral selectivity. In this sense, the role of the entanglement time is substantially equivalent to the temporal width of the classical laser pulse. The results demonstrate that the application of quantum entangled photons to time-resolved spectroscopy leads to monitoring dynamical processes in complex molecular and materials systems by selectively extracting desired signal contributions from congested spectra. We anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

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.

Predicting Mutation-Induced Changes in the Electronic Properties of Photosynthetic Proteins from First Principles: The Fenna-Matthews-Olson Complex Example

Multiscale molecular modeling is utilized to predict optical absorption and circular dichroism spectra of two single-point mutants of the Fenna-Matthews-Olson photosynthetic pigment-protein complex. The modeling approach combines classical molecular dynamics simulations with structural refinement of photosynthetic pigments and calculations of their excited states in a polarizable protein environment. The only experimental input to the modeling protocol is the X-ray structure of the wild-type protein. The first-principles modeling reproduces changes in the experimental optical spectra of the considered mutants, Y16F and Q198V. Interestingly, the Q198V mutation has a negligible effect on the electronic properties of the targeted bacteriochlorophyll a pigment. Instead, the electronic properties of several other pigments respond to this mutation. The molecular modeling demonstrates that a single-point mutation can induce long-range effects on the protein structure, while extensive structural changes near a pigment do not necessarily lead to significant changes in the electronic properties of that pigment.

Single-photon absorption and emission from a natural photosynthetic complex

Photosynthesis is generally assumed to be initiated by a single photon1-3 from the Sun, which, as a weak light source, delivers at most a few tens of photons per nanometre squared per second within a chlorophyll absorption band1. Yet much experimental and theoretical work over the past 40 years has explored the events during photosynthesis subsequent to absorption of light from intense, ultrashort laser pulses2-15. Here, we use single photons to excite under ambient conditions the light-harvesting 2 (LH2) complex of the purple bacterium Rhodobacter sphaeroides, comprising B800 and B850 rings that contain 9 and 18 bacteriochlorophyll molecules, respectively. Excitation of the B800 ring leads to electronic energy transfer to the B850 ring in approximately 0.7 ps, followed by rapid B850-to-B850 energy transfer on an approximately 100-fs timescale and light emission at 850-875 nm (refs. 16-19). Using a heralded single-photon source20,21 along with coincidence counting, we establish time correlation functions for B800 excitation and B850 fluorescence emission and demonstrate that both events involve single photons. We also find that the probability distribution of the number of heralds per detected fluorescence photon supports the view that a single photon can upon absorption drive the subsequent energy transfer and fluorescence emission and hence, by extension, the primary charge separation of photosynthesis. An analytical stochastic model and a Monte Carlo numerical model capture the data, further confirming that absorption of single photons is correlated with emission of single photons in a natural light-harvesting complex.

Quantum Entanglement and State-Transference in Fenna-Matthews-Olson Complexes: A Post-Experimental Simulation Analysis in the Computational Biology Domain

Fenna-Mathews-Olson complexes participate in the photosynthetic process of Sulfur Green Bacteria. These biological subsystems exhibit quantum features which possibly are responsible for their high efficiency; the latter may comprise multipartite entanglement and the apparent tunnelling of the initial quantum state. At first, to study these aspects, a multidisciplinary approach including experimental biology, spectroscopy, physics, and math modelling is required. Then, a global computer modelling analysis is achieved in the computational biology domain. The current work implements the Hierarchical Equations of Motion to numerically solve the open quantum system problem regarding this complex. The time-evolved states obtained with this method are then analysed under several measures of entanglement, some of them already proposed in the literature. However, for the first time, the maximum overlap with respect to the closest separable state is employed. This authentic multipartite entanglement measure provides information on the correlations, not only based on the system bipartitions as in the usual analysis. Our study has led us to note a different view of FMO multipartite entanglement as tiny contributions to the global entanglement suggested by other more basic measurements. Additionally, in another related trend, the initial state, considered as a Förster Resonance Energy Transfer, is tracked using a novel approach, considering how it could be followed under the fidelity measure on all possible permutations of the FMO subsystems through its dynamical evolution by observing the tunnelling in the most probable locations. Both analyses demanded significant computational work, making for a clear example of the complexity required in computational biology.

High-order pump-probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers

Time-resolved spectroscopy is commonly used to study diverse phenomena in chemistry, biology, and physics. Pump-probe experiments and coherent two-dimensional (2D) spectroscopy have resolved site-to-site energy transfer, visualized electronic couplings, and much more. In both techniques, the lowest-order signal, in a perturbative expansion of the polarization, is of third order in the electric field, which we call a one-quantum (1Q) signal because in 2D spectroscopy it oscillates in the coherence time with the excitation frequency. There is also a two-quantum (2Q) signal that oscillates in the coherence time at twice the fundamental frequency and is fifth order in the electric field. We demonstrate that the appearance of the 2Q signal guarantees that the 1Q signal is contaminated by non-negligible fifth-order interactions. We derive an analytical connection between an nQ signal and (2n + 1)th-order contaminations of an rQ (with r < n) signal by studying Feynman diagrams of all contributions. We demonstrate that by performing partial integrations along the excitation axis in 2D spectra, we can obtain clean rQ signals free of higher-order artifacts. We exemplify the technique using optical 2D spectroscopy on squaraine oligomers, showing clean extraction of the third-order signal. We further demonstrate the analytical connection with higher-order pump-probe spectroscopy and compare both techniques experimentally. Our approach demonstrates the full power of higher-order pump-probe and 2D spectroscopy to investigate multi-particle interactions in coupled systems.

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

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

Filming enhanced ionization in an ultrafast triatomic slingshot

Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e., filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid "slingshot" motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules.

Formally Exact Simulations of Mesoscale Exciton Diffusion in a Light-Harvesting 2 Antenna Nanoarray

The photosynthetic apparatus of plants and bacteria combine atomically precise pigment-protein complexes with dynamic membrane architectures to control energy transfer on the 10-100 nm length scales. Recently, synthetic materials have integrated photosynthetic antenna proteins to enhance exciton transport, though the influence of artificial packing on the excited-state dynamics in these biohybrid materials is not fully understood. Here, we use the adaptive hierarchy of pure states (adHOPS) to perform a formally exact simulation of excitation energy transfer within artificial aggregates of light-harvesting complex 2 (LH2) with a range of packing densities. We find that LH2 aggregates support a remarkable exciton diffusion length ranging from 100 nm at a biological packing density to 300 nm at the densest packing previously suggested in an artificial aggregate. The unprecedented scale of these formally exact calculations also underscores the efficiency with which adHOPS simulates excited-state processes in molecular materials.

Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions

We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S₂ which exhibits a sub-100-fs nonadiabatic decay to a dark state S₁. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.

Ultrafast Coherent Delocalization Revealed in Multilayer QDs under a Chiral Potential

In recent years, it was found that current passing through chiral molecules exhibits spin preference, an effect known as Chiral Induced Spin Selectivity (CISS). The effect also enables the reduction of scattering and therefore enhances delocalization. As a result, the delocalization of an exciton generated in the dots is not symmetric and relates to the electronic and hole excited spins. In this work utilizing fast spectroscopy on hybrid multilayered QDs with a chiral polypeptide linker system, we probed the interdot chiral coupling on a short time scale. Surprisingly, we found strong coherent coupling and delocalization despite having long 4-nm chiral linkers. We ascribe the results to asymmetric delocalization that is controlled by the electron spin. The effect is not measured when using shorter nonchiral linkers. As the system mimics light-harvesting antennas, the results may shed light on a mechanism of fast and efficient energy transfer in these systems.

An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra

Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.

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

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

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.