Global analysis of coherence and population dynamics in 2D electronic spectroscopy

Coherence in Chemistry: Foundations and Frontiers

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

UltraStat: Ultrafast Spectroscopy beyond the Fourier Limit Using Bayesian Inference

The discrete Fourier transform (dFT) plays a central role in many ultrafast experiments, allowing the recovery of spectroscopic observables from time-domain measurements. In resonant experiments when population relaxation and coherence components of the signal coexist, the dFT is usually preceded by multiexponential fitting to remove the large population term. However, this procedure results in errors in both the recovered decay rates and the line shapes of the coherence spectral components. While other methods such as linear prediction singular value decomposition fit both terms simultaneously, they are limited to specific models that may not represent the true signal. These methods do not allow for systematic noise analysis or error estimation and require a priori knowledge of the signal rank. Here, we describe a general approach to parameter estimation in ultrafast spectroscopy─UltraStat─grounded in Bayesian analysis without the limitations set by Fourier theory. Using simulated, but realistic data, we demonstrate in a statistical sense how UltraStat provides accurate parameter estimation in the presence of many experimental constraints: noise, signal truncation, limited photon budget, and nonuniform sampling. UltraStat provides superior resolution compared to the dFT, up to an order of magnitude in cases where the line shapes are well-approximated. In these cases, we establish that primarily noise, not sampling, limits spectral resolution. Moreover, we show that subsampling may reduce the number of acquired points by 90% compared to the Nyquist-Shannon criteria. UltraStat greatly improves parameter estimation by providing statistically bound spectral and dynamics analysis, pushing the limits of ultrafast science.

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.

Conical Intersections at Interfaces Revealed by Phase-Cycling Interface-Specific Two-Dimensional Electronic Spectroscopy (i2D-ES)

Conical intersections (CIs) hold significant stake in manipulating and controlling photochemical reaction pathways of molecules at interfaces and surfaces by affecting molecular dynamics therein. Currently, there is no tool for characterizing CIs at interfaces and surfaces. To this end, we have developed phase-cycling interface-specific two-dimensional electronic spectroscopy (i2D-ES) and combined it with advanced computational modeling to explore nonadiabatic CI dynamics of molecules at the air/water interface. Specifically, we integrated the phase locked pump pulse pair with an interface-specific electronic probe to obtain the two-dimensional interface-specific responses. We demonstrate that the nonadiabatic transitions of an interface-active azo dye molecule that occur through the CIs at the interface have different kinetic pathways from those in the bulk water. Upon photoexcitation, two CIs are present: one from an intersection of an optically active S2 state with a dark S1 state and the other from the intersection of the progressed S1 with the ground state S0. We find that the molecular conformations in the ground state are different for interfacial molecules. The interfacial molecules are intimately correlated with the locally populated excited state S2 being farther away from the CI region. This leads to slower nonadiabatic dynamics at the interface than in bulk water. Moreover, we show that the nonadiabatic transition from the S1 dark state to the ground state is significantly longer at the interface than that in the bulk, which is likely due to the orientationally restricted configuration of the excited state at the interface. Our findings suggest that orientational configurations of molecules manipulate reaction pathways at interfaces and surfaces.

Coherent Vibrations Promote Charge-Transfer across a Graphene-Based Interface

Discerning the impact of the coherent motion of the nuclei on the timing and efficiency of charge transfer at the donor-acceptor interface is essential for designing performance-enhanced optoelectronic devices. Here, we employ an experimental approach using photocurrent detection in coherent multidimensional spectroscopy to excite a donor aromatic macrocycle and collect the charge transferred to a 2D acceptor layer. For this purpose, we prepared a cobalt phthalocyanine-graphene (CoPc-Gr) interface. Unlike blends, the well-ordered architecture achieved through the physical separation of the two layers allows us to unambiguously collect the electrical signal from graphene alone and associate it with a microscopic understanding of the whole process. The CoPc-Gr interface exhibits an ultrafast electron-transfer signal, stemming from an interlayer mechanism. Remarkably, the signal presents an oscillating time evolution modulated by coherent vibrations originating from the laser-excited CoPc states. By performing Fourier analysis on the beatings and correlating it with the Raman features, along with a comprehensive first-principles characterization of the vibrational coupling in the CoPc excited states, we successfully identify both the orbitals and molecular vibrations that promote the charge transfer at the interface.

Two-Dimensional Electronic Spectroscopy Characterization of Fucoxanthin-Chlorophyll Protein Reveals Excitonic Carotenoid-Chlorophyll Interactions

Fucoxanthin Chlorophyll Protein (FCP) is a Light Harvesting Complex found in diatoms and brown algae. It is particularly interesting for its efficiency in capturing the blue-green part of the light spectrum due to the presence of specific chromophores (fucoxanthin, chlorophyll a, and chlorophyll c). Recently, the crystallographic structure of FCP was solved, revealing the 3D arrangement of the pigments in the protein scaffold. While this information is helpful for interpreting the spectroscopic features of FCP, it has also raised new questions about the potential interactions between fucoxanthin and chlorophyll c. These interactions were suggested by their spatial closeness but have never been experimentally observed. To investigate this possible interaction mechanism, in this work, two-dimensional electronic spectroscopy (2DES) has been applied to study the ultrafast relaxation dynamics of FCP. The experiments captured an instantaneous delocalization of the excitation among fucoxanthin and chlorophyll c, suggesting the presence of a non-negligible coupling between the chromophores.

Photocarrier Recombination Dynamics in Highly Scattering Cu2O Nanocatalyst Clusters

Inversion analysis of transient absorption data to capture the photoexcited charge carrier population rate dynamics is a powerful technique for extracting realistic lifetimes and identifying recombination pathways. However, for highly scattering samples such as Cu2O nanoparticles (NPs) with associated dielectric Mie scattering, the scattering leads to an inaccurate measure of the excited photocarrier. This work studies methods to correct for the scattering to generalize the use of inversion analysis and provide secondary information about the nature of the scattering NPs. Scattering profiles of semitransparent disks containing Cu2O NPs with different shapes and sizes are measured to demonstrate that the inclusion of scattering in analysis reduces the photoexcited carrier density by 1 order of magnitude. It is found that the photocarrier density response is affected by shape rather than size. A Fourier transform of the scattering profiles produces a distribution of length scales within the sample characteristic of the mean separation of scatterers. This analysis reveals that NPs are forming clusters. Links are made between the scattering and carrier dynamics.

Electronic Structure of Isolated Graphene Nanoribbons in Solution Revealed by Two-Dimensional Electronic Spectroscopy

Structurally well-defined graphene nanoribbons (GNRs) are nanostructures with unique optoelectronic properties. In the liquid phase, strong aggregation typically hampers the assessment of their intrinsic properties. Recently we reported a novel type of GNRs, decorated with aliphatic side chains, yielding dispersions consisting mostly of isolated GNRs. Here we employ two-dimensional electronic spectroscopy to unravel the optical properties of isolated GNRs and disentangle the transitions underlying their broad and rather featureless absorption band. We observe that vibronic coupling, typically neglected in modeling, plays a dominant role in the optical properties of GNRs. Moreover, a strong environmental effect is revealed by a large inhomogeneous broadening of the electronic transitions. Finally, we also show that the photoexcited bright state decays, on the 150 fs time scale, to a dark state which is in thermal equilibrium with the bright state, that remains responsible for the emission on nanosecond time scales.

Coherent and Incoherent Ultrafast Dynamics in Colloidal Gold Nanorods

The study of the mechanisms that control the ultrafast dynamics in gold nanoparticles is gaining more attention, as these nanomaterials can be used to create nanoarchitectures with outstanding optical properties. Here pump-probe and two-dimensional electronic spectroscopy have been synergistically employed to investigate the early ultrafast femtosecond processes following photoexcitation in colloidal gold nanorods with low aspect ratio. Complementary insights into the coherent plasmonic dynamics at the femtosecond time scale and incoherent hot electron dynamics over picosecond time scales have been obtained, including important information on the different sensitivity to the pump fluence of the longitudinal and transverse plasmons and their different contributions to the photoinduced broadening and shift.

Observation of parallel intersystem crossing and charge transfer-state dynamics in [Fe(bpy)3]2+ from ultrafast 2D electronic spectroscopy

Transition metal-based charge-transfer complexes represent a broad class of inorganic compounds with diverse photochemical applications. Charge-transfer complexes based on earth-abundant elements have been of increasing interest, particularly the canonical [Fe(bpy)3]2+. Photoexcitation into the singlet metal-ligand charge transfer (1MLCT) state is followed by relaxation first to the ligand-field manifold and then to the ground state. While these dynamics have been well-studied, processes within the MLCT manifold that facilitate and/or compete with relaxation have been more elusive. We applied ultrafast two-dimensional electronic spectroscopy (2DES) to disentangle the dynamics immediately following MLCT excitation of this compound. First, dynamics ascribed to relaxation out of the initially formed 1MLCT state was found to correlate with the inertial response time of the solvent. Second, the additional dimension of the 2D spectra revealed a peak consistent with a ∼20 fs 1MLCT → 3MLCT intersystem crossing process. These two observations indicate that the complex simultaneously undergoes intersystem crossing and direct conversion to ligand-field state(s). Resolution of these parallel pathways in this prototypical earth-abundant complex highlights the ability of 2DES to deconvolve the otherwise obscured excited-state dynamics of charge-transfer complexes.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

The Role of H-Bonds in the Excited-State Properties of Multichromophoric Systems: Static and Dynamic Aspects

Given their importance, hydrogen bonds (H-bonds) have been the subject of intense investigation since their discovery. Indeed, H-bonds play a fundamental role in determining the structure, the electronic properties, and the dynamics of complex systems, including biologically relevant materials such as DNA and proteins. While H-bonds have been largely investigated for systems in their electronic ground state, fewer studies have focused on how the presence of H-bonds could affect the static and dynamic properties of electronic excited states. This review presents an overview of the more relevant progress in studying the role of H-bond interactions in modulating excited-state features in multichromophoric biomimetic complex systems. The most promising spectroscopic techniques that can be used for investigating the H-bond effects in excited states and for characterizing the ultrafast processes associated with their dynamics are briefly summarized. Then, experimental insights into the modulation of the electronic properties resulting from the presence of H-bond interactions are provided, and the role of the H-bond in tuning the excited-state dynamics and the related photophysical processes is discussed.

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.

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

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

Leveraging Dynamical Symmetries in Two-Dimensional Electronic Spectra to Extract Population Transfer Pathways

We present a method to deterministically isolate population transfer kinetics from two-dimensional electronic spectroscopic signals. Central to this analysis is the characterization of how all possible subensembles of excited state systems evolve through the population time. When these dynamics are diagrammatically mapped by using double-sided Feynman pathways where population time dynamics are included, a useful symmetry emerges between excited state absorption and ground state bleach recovery dynamics of diagonal and below diagonal cross-peak signals. This symmetry allows removal of pathways from the spectra to isolate signals that evolve according to energy transfer kinetics. We describe a regression procedure to fit to energy transfer time constants and characterize the accuracy of the method in a variety of complex excited state systems using simulated two-dimensional spectra. Our results show that the method is robust for extracting ultrafast energy transfer in multistate excitonic systems, systems containing dark states that affect the signal kinetics, and systems with interfering vibrational relaxation pathways. This procedure can be used to accurately extract energy transfer kinetics from a wide variety of condensed phase systems.

The Energy Transfer Yield between Carotenoids and Chlorophylls in Peridinin Chlorophyll a Protein Is Robust against Mutations

The energy transfer (ET) from carotenoids (Cars) to chlorophylls (Chls) in photosynthetic complexes occurs with almost unitary efficiency thanks to the synergistic action of multiple finely tuned channels whose photophysics and dynamics are not fully elucidated yet. We investigated the energy flow from the Car peridinin (Per) to Chl a in the peridinin chlorophyll a protein (PCP) from marine algae Amphidinium carterae by using two-dimensional electronic spectroscopy (2DES) with a 10 fs temporal resolution. Recently debated hypotheses regarding the S2-to-S1 relaxation of the Car via a conical intersection and the involvement of possible intermediate states in the ET were examined. The comparison with an N89L mutant carrying the Per donor in a lower-polarity environment helped us unveil relevant details on the mechanisms through which excitation was transferred: the ET yield was conserved even when a mutation perturbed the optimization of the system thanks to the coexistence of multiple channels exploited during the process.

Ultrafast excited state dynamics in the monomeric and trimeric photosystem I core complex of Spirulina platensis probed by two-dimensional electronic spectroscopy

Photosystem I (PSI), a naturally occurring supercomplex composed of a core part and a light-harvesting antenna, plays an essential role in the photosynthetic electron transfer chain. Evolutionary adaptation dictates a large variability in the type, number, arrangement, and absorption of the Chlorophylls (Chls) responsible for the early steps of light-harvesting and charge separation. For example, the specific location of long-wavelength Chls (referred to as red forms) in the cyanobacterial core has been intensively investigated, but the assignment of the chromophores involved is still controversial. The most red-shifted Chl a form has been observed in the trimer of the PSI core of the cyanobacterium Spirulina platensis, with an absorption centered at ∼740 nm. Here, we apply two-dimensional electronic spectroscopy to study photoexcitation dynamics in isolated trimers and monomers of the PSI core of S. platensis. By means of global analysis, we resolve and compare direct downhill and uphill excitation energy transfer (EET) processes between the bulk Chls and the red forms, observing significant differences between the monomer (lacking the most far red Chl form at 740 nm) and the trimer, with the ultrafast EET component accelerated by five times, from 500 to 100 fs, in the latter. Our findings highlight the complexity of EET dynamics occurring over a broad range of time constants and their sensitivity to energy distribution and arrangement of the cofactors involved. The comparison of monomeric and trimeric forms, differing both in the antenna dimension and in the extent of red forms, enables us to extract significant information regarding PSI functionality.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

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

Vibronic dynamics resolved by global and target analysis of ultrafast transient absorption spectra

We present a methodology that provides a complete parametric description of the time evolution of the electronically and vibrationally excited states as detected by ultrafast transient absorption (TA). Differently from previous approaches, which started fitting the data after ≈100 fs, no data are left out in our methodology, and the "coherent artifact" and the instrument response function are fully taken into account. In case studies, the method is applied to solvents, the dye Nile blue, and all-trans β-carotene in cyclohexane solution. The estimated Damped Oscillation Associated Spectra (DOAS) and phases express the most important vibrational frequencies present in the molecular system. By global fit alone of the experimental data, it is difficult to interpret in detail the underlying dynamics. Since it is unfeasible to directly fit the data by a theoretical simulation, our enhanced DOAS methodology thus provides a useful "middle ground" where the theoretical description and the fit of the experimental data can meet. β-carotene in cyclohexane was complementarily studied with femtosecond stimulated Raman spectroscopy (FSRS). The fs-ps dynamics of β-carotene in cyclohexane in TA and FSRS experiments can be described by a sequential scheme S2 → hot S1 → S1' → S1 → S0 with lifetimes of 167 fs (fixed), 0.35, 1.1, and 9.6 ps. The correspondence of DOAS decaying concomitantly with hot S1 and the Species Associated Difference Spectra of hot S1 in TA and FSRS suggest that we observe here features of the vibrational relaxation and nuclear reorganization responsible for the hot S1 to S1 transition.

2D Electronic Spectroscopic Techniques for Quantum Technology Applications

2D electronic spectroscopy (2DES) techniques have gained particular interest given their capability of following ultrafast coherent and noncoherent processes in real-time. Although the fame of 2DES is still majorly linked to the investigation of energy and charge transport in biological light-harvesting complexes, 2DES is now starting to be recognized as a particularly valuable tool for studying transport processes in artificial nanomaterials and nanodevices. Particularly meaningful is the possibility of assessing coherent mechanisms active in the transport of excitation energy in these materials toward possible quantum technology applications. The diverse nature of these new target samples poses significant challenges and calls for a critical rethinking of the technique and its different realizations. With the confluence of promising new applications and rapidly developing technical capabilities, the enormous potential of 2DES techniques to impact the field of nanosystems, quantum technologies, and quantum devices is here delineated.

Solvent-Dependent Characterization of Fucoxanthin through 2D Electronic Spectroscopy Reveals New Details on the Intramolecular Charge-Transfer State Dynamics

The electronic state manifolds of carotenoids and their relaxation dynamics are the object of intense investigation because most of the subtle details regulating their photophysics are still unknown. In order to contribute to this quest, here, we present a solvent-dependent 2D Electronic Spectroscopy (2DES) characterization of fucoxanthin, a carbonyl carotenoid involved in the light-harvesting process of brown algae. The 2DES technique allows probing its ultrafast relaxation dynamics in the first 1000 fs after photoexcitation with a 10 fs time resolution. The obtained results help shed light on the dynamics of the first electronic state manifold and, in particular, on an intramolecular charge-transfer state (ICT), whose photophysical properties are particularly elusive given its (almost) dark nature.

Photocurrent-Detected 2D Electronic Spectroscopy Reveals Ultrafast Hole Transfer in Operating PM6/Y6 Organic Solar Cells

The performance of nonfullerene-acceptor-(NFA)-based organic solar cells is rapidly approaching the efficiency of inorganic cells. The chemical versatility of NFAs extends the light-harvesting range to the infrared, while preserving a considerably high open-circuit-voltage, crucial to achieve power-conversion efficiencies >17%. Such low voltage losses in the charge separation process have been attributed to a low-driving-force and efficient exciton dissociation. Here, we address the nature of the subpicosecond dynamics of electron/hole transfer in PM6/Y6 solar cells. While previous reports focused on active layers only, we developed a photocurrent-detected two-dimensional spectroscopy to follow the charge transfer in fully operating devices. Our measurements reveal an efficient hole-transfer from the Y6-acceptor to the PM6-donor on the subpicosecond time scale. On the contrary, at the same time scale, no electron-transfer is seen from the donor to the acceptor. These findings, putting ultrafast spectroscopy in action on operating optoelectronic devices, provide insight for further enhancing NFA solar cell performance.

Direct Evidence for Excitation Energy Transfer Limitations Imposed by Low-Energy Chlorophylls in Photosystem I-Light Harvesting Complex I of Land Plants

The overall efficiency of photosynthetic energy conversion depends both on photochemical and excitation energy transfer processes from extended light-harvesting antenna networks. Understanding the trade-offs between increase in the antenna cross section and bandwidth and photochemical conversion efficiency is of central importance both from a biological perspective and for the design of biomimetic artificial photosynthetic complexes. Here, we employ two-dimensional electronic spectroscopy to spectrally resolve the excitation energy transfer dynamics and directly correlate them with the initial site of excitation in photosystem I–light harvesting complex I (PSI-LHCI) supercomplex of land plants, which has both a large antenna dimension and a wide optical bandwidth extending to energies lower than the peak of the reaction center chlorophylls. Upon preferential excitation of the low-energy chlorophylls (red forms), the average relaxation time in the bulk supercomplex increases by a factor of 2–3 with respect to unselective excitation at higher photon energies. This slowdown is interpreted in terms of an excitation energy transfer limitation from low-energy chlorophyll forms in the PSI-LHCI. These results aid in defining the optimum balance between the extension of the antenna bandwidth to the near-infrared region, which increases light-harvesting capacity, and high photoconversion quantum efficiency.

The effect of hydrogen bonds on the ultrafast relaxation dynamics of a BODIPY dimer

The influence of hydrogen bonds (H-bonds) in the structure, dynamics, and functionality of biological and artificial complex systems is the subject of intense investigation. In this broad context, particular attention has recently been focused on the ultrafast H-bond dependent dynamical properties in the electronic excited state because of their potentially dramatic consequences on the mechanism, dynamics, and efficiency of photochemical reactions and photophysical processes of crucial importance for life and technology. Excited-state H-bond dynamics generally occur on ultrafast time scales of hundreds of femtoseconds or less, making the characterization of associated mechanisms particularly challenging with conventional time-resolved techniques. Here, 2D electronic spectroscopy is exploited to shed light on this still largely unexplored dynamic mechanism. An H-bonded molecular dimer prepared by self-assembly of two boron-dipyrromethene dyes has been specifically designed and synthesized for this aim. The obtained results confirm that upon formation of H-bonds and the dimer, a new ultrafast relaxation channel is activated in the ultrafast dynamics, mediated by the vibrational motions of the hydrogen donor and acceptor groups. This relaxation channel also involves, beyond intra-molecular relaxations, an inter-molecular transfer process. This is particularly significant considering the long distance between the centers of mass of the two molecules. These findings suggest that the design of H-bonded structures is a particularly powerful tool to drive the ultrafast dynamics in complex materials.

Visualizing Ultrafast Electron Transfer Processes in Semiconductor-Metal Hybrid Nanoparticles: Toward Excitonic-Plasmonic Light Harvesting

Recently, it was demonstrated that charge separation in hybrid metal-semiconductor nanoparticles (HNPs) can be obtained following photoexcitation of either the semiconductor or of the localized surface plasmon resonance (LSPR) of the metal. This suggests the intriguing possibility of photocatalytic systems benefiting from both plasmon and exciton excitation, the main challenge being to outcompete other ultrafast relaxation processes. Here we study CdSe-Au HNPs using ultrafast spectroscopy with high temporal resolution. We describe the complete pathways of electron transfer for both semiconductor and LSPR excitation. In the former, we distinguish hot and band gap electron transfer processes in the first few hundred fs. Excitation of the LSPR reveals an ultrafast (<30 fs) electron transfer to CdSe, followed by back-transfer from the semiconductor to the metal within 210 fs. This study establishes the requirements for utilization of the combined excitonic-plasmonic contribution in HNPs for diverse photocatalytic applications.

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

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

Signatures of exciton dynamics and interaction in coherently and fluorescence-detected four- and six-wave-mixing two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) can be realized in increasing nonlinear orders of interaction with the electric field, bringing new information about single- and multi-particle properties and dynamics. Furthermore, signals can be detected both coherently (C-2DES) and by fluorescence (F-2DES), with fundamental and practical differences. We directly compare the simultaneous measurements of four- and six-wave mixing C-2DES and F-2DES on an excitonic heterodimer of squaraine molecules. Spectral features are described in increasing orders of nonlinearity by an explicit excitonic model. We demonstrate that the four-wave-mixing spectra are sensitive to one-exciton energies, their delocalization and dynamics, while the six-wave-mixing spectra include information on bi-exciton and higher excited states including the state energies, electronic coupling, and exciton-exciton annihilation. We focus on the possibility to extract the dynamics arising from exciton-exciton interaction directly from the six-wave-mixing spectra. To this end, in analogy to previously demonstrated fifth-order coherently detected exciton-exciton-interaction 2DES (EEI2D spectroscopy), we introduce a sixth-order fluorescence-detected EEI2D spectroscopy variant.

Biomimetic Nanoarchitectures for Light Harvesting: Self-Assembly of Pyropheophorbide-Peptide Conjugates

The biological light-harvesting process offers an unlimited source of inspiration. The high level of control, adaptation capability, and efficiency challenge humankind to create artificial biomimicking nanoarchitectures with the same performances to respond to our energy needs. Here, in the extensive search for design principles at the base of efficient artificial light harvesters, an approach based on self-assembly of pigment-peptide conjugates is proposed. The solvent-driven and controlled aggregation of the peptide moieties promotes the formation of a dense network of interacting pigments, giving rise to an excitonic network characterized by intense and spectrally wide absorption bands. The ultrafast dynamics of the nanosystems studied through two-dimensional electronic spectroscopy reveals that the excitation energy is funneled in an ultrafast time range (hundreds of femtoseconds) to a manifold of long-living dark states, thus suggesting the considerable potentiality of the systems as efficient harvesters.

DNA scaffold supports long-lived vibronic coherence in an indodicarbocyanine (Cy5) dimer

Vibronic coupling between pigment molecules is believed to prolong coherences in photosynthetic pigment–protein complexes. Reproducing long-lived coherences using vibronically coupled chromophores in synthetic DNA constructs presents a biomimetic route to efficient artificial light harvesting. Here, we present two-dimensional (2D) electronic spectra of one monomeric Cy5 construct and two dimeric Cy5 constructs (0 bp and 1 bp between dyes) on a DNA scaffold and perform beating frequency analysis to interpret observed coherences. Power spectra of quantum beating signals of the dimers reveal high frequency oscillations that correspond to coherences between vibronic exciton states. Beating frequency maps confirm that these oscillations, 1270 cm⁻¹ and 1545 cm⁻¹ for the 0-bp dimer and 1100 cm⁻¹ for the 1-bp dimer, are coherences between vibronic exciton states and that these coherences persist for ∼300 fs. Our observations are well described by a vibronic exciton model, which predicts the excitonic coupling strength in the dimers and the resulting molecular exciton states. The energy spacing between those states closely corresponds to the observed beat frequencies. MD simulations indicate that the dyes in our constructs lie largely internal to the DNA base stacking region, similar to the native design of biological light harvesting complexes. Observed coherences persist on the timescale of photosynthetic energy transfer yielding further parallels to observed biological coherences, establishing DNA as an attractive scaffold for synthetic light harvesting applications.

Dyes coupled to DNA display distance-dependent vibronic couplings that prolongs quantum coherences detected with 2D spectroscopy.

Global Analysis for Time and Spectrally Resolved Multidimensional Microscopy: Application to CH3NH3PbI3 Perovskite Thin Films

The advancement of improved photoactive materials, such as those proposed for next-generation solar cells, low-power lighting, and lasing applications, requires a deep understanding of their correlated spatial, spectral, and temporal properties. In principle, correlated time-resolved microscopy techniques are capable of capturing such information. However, the large data sets that encapsulate temporal, spectral, and spatial information create the prodigious challenge of analyzing gigabytes of correlated data, which typically takes enormous computational resources. These challenges motivate the development of robust and efficient data analysis tools to realize fast spatial and spectral decomposition and to gain physical insights that arise from statistical analysis. Herein, we propose a reliable and fast global analysis method based on variable projection and subsampling methods, which exhibits exceptionally high sensitivity to buried spatial and spectral information in large and multidimensional microscopy data sets as compared to traditional methods. The reliability and robustness of this new method is tested on transient absorption and impulsive vibrational microscopy data sets acquired on polycrystalline CH₃NH₃PbI₃ perovskite films.

Relaxation Dynamics of Chlorophyll b in the Sub-ps Ultrafast Timescale Measured by 2D Electronic Spectroscopy

A thorough characterization of the early time sub-100 fs relaxation dynamics of biologically relevant chromophores is of crucial importance for a complete understanding of the mechanisms regulating the ultrafast dynamics of the relaxation processes in more complex multichromophoric light-harvesting systems. While chlorophyll a has already been the object of several investigations, little has been reported on chlorophyll b, despite its pivotal role in many functionalities of photosynthetic proteins. Here the relaxation dynamics of chlorophyll b in the ultrafast regime have been characterized using 2D electronic spectroscopy. The comparison of experimental measurements performed at room temperature and 77 K allows the mechanisms and the dynamics of the sub-100 fs relaxation dynamics to be characterized, including spectral diffusion and fast internal conversion assisted by a specific set of vibrational modes.

How the Protein Environment Can Tune the Energy, the Coupling, and the Ultrafast Dynamics of Interacting Chlorophylls: The Example of the Water-Soluble Chlorophyll Protein

The interplay between active molecules and the protein environment in light-harvesting complexes tunes the photophysics and the dynamical properties of pigment-protein complexes in a subtle way, which is not fully understood. Here we characterized the photophysics and the ultrafast dynamics of four variants of the water-soluble chlorophyll protein (WSCP) as an ideal model system to study the behavior of strongly interacting chlorophylls. We found that when coordinated by the WSCP protein, the presence of the formyl group in chlorophyll b replacing the methyl group in chlorophyll a strongly affects the exciton energy and the dynamics of the system, opening up the possibility of tuning the photophysics and the transport properties of multichromophores by engineering specific interactions with the surroundings.

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

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

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

Coherent and dissipative quantum process tensor reconstructions in two-dimensional electronic spectroscopy

A major goal of time-resolved spectroscopy is to resolve the dynamical processes that follow photoexcitation. This amounts to identifying all the quantum states involved and the rates of population transfer between them. Unfortunately, such quantum state and kinetic reconstructions are ambiguous using one-dimensional methods such as transient absorption even when all the states of the system are fully resolved. Higher-dimensionality methods like two-dimensional spectroscopy lift some of the ambiguity, but unless the spectral features are well-separated, current inversion methods generally fail. Here, we show that, using both coherence and population signals of the nonlinear response, it is indeed possible to accurately extract both static and dynamic information from the 2D spectrum even when features are highly congested. Coherences report on the positions of the vibronic states of the system, providing a useful constraint for extracting the full kinetic scheme. We model time-resolved 2D photon echo spectra using a sum-over-states approach and show in which regimes the Hamiltonian and kinetic schemes may be recovered. Furthermore, we discuss how such algorithms may be applied to experimental data and where some of the underlying assumptions may fail. The ability to systematically extract the maximal information content of multidimensional spectroscopic data is an important step toward utilizing the full power of these techniques and elucidating the structure and dynamics of increasingly complex molecular systems.

Optimization and selection of time-frequency transforms for wave-packet analysis in ultrafast spectroscopy

The analysis of quantum beats in time-resolved spectroscopic signals is becoming a task of primary importance because it is now clear that they bring crucial information about chemical reactivity, transport, and relaxation processes. Here we describe how to exploit the wide family of time-frequency transform methodologies to obtain information not only about the frequency but also about the dynamics of the oscillating components contributing to the overall beating signal. Several linear and bilinear transforms have been considered, and a general and easy procedure to judge in a non-arbitrary way the performances of different transforms has been outlined.

Diagonal slice four-wave mixing: natural separation of coherent broadening mechanisms

We present an ultrafast coherent spectroscopy data acquisition scheme that samples slices of the time domain used in multidimensional coherent spectroscopy to achieve faster data collection than full spectra. We derive analytical expressions for resonance lineshapes using this technique that completely separate homogeneous and inhomogeneous broadening contributions into separate projected lineshapes for arbitrary inhomogeneous broadening. These lineshape expressions are also valid for slices taken from full multidimensional spectra and allow direct measurement of the parameters contributing to the lineshapes in those spectra as well as our own.

Coherences of Bacteriochlorophyll a Uncovered Using 3D-Electronic Spectroscopy

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

Coherence in carotenoid-to-chlorophyll energy transfer

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

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

Deciphering hot- and multi-exciton dynamics in core-shell QDs by 2D electronic spectroscopies

2D electronic spectroscopy maps acquired in different configurations unveil intraband hot carrier cooling and interband multi-exciton recombination dynamics.

Although the harnessing of multiple and hot excitons is a prerequisite for many of the groundbreaking applications of semiconductor quantum dots (QDs), the characterization of their dynamics through conventional spectroscopic techniques is cumbersome. Here, we show how a careful analysis of 2DES maps acquired in different configurations (BOXCARS and pump–probe geometry) allows the tracking and visualization of intraband Auger relaxation mechanisms, driving the hot carrier cooling, and interband bi- and tri-exciton recombination dynamics. The results obtained on archetypal core–shell CdSe/ZnS QDs suggest that, given the global analysis of the resulting datasets, 2D electronic spectroscopy techniques can successfully and efficiently dispel the intertwined dynamics of fast and ultrafast recombination processes in nanomaterials. Hence, we propose this analysis scheme to be used in future research on novel quantum confined systems.

Two-Dimensional Electronic Spectroscopy Reveals Dynamics and Mechanisms of Solvent-Driven Inertial Relaxation in Polar BODIPY Dyes

In this work, we demonstrate the use of two-dimensional electronic spectroscopy (2DES) to study the mechanism and time scale of the femtosecond Stokes shift dynamics in molecules characterized by intramolecular charge transfer, such as distyryl-functionalized boron dipyrromethene (BODIPY) molecules. The obtained results demonstrate that 2DES allows clear and direct visualization of the phenomenon. The analysis of the 2D data in terms of 2D frequency-frequency decay associated maps provides indeed not only the time scale of the relaxation process but also the starting and the final point of the energy flow and the associated reorganization energy, identified by looking at the coordinates of a negative signature below the diagonal. The sensitivity of the 2DES technique to vibrational coherence dynamics also allowed the identification of a possible relaxation mechanism involving specific interaction between a vibrational mode of the dye and the solvent.

Mechanistic insight into internal conversion process within Q-bands of chlorophyll a

The non-radiative relaxation of the excitation energy from higher energy states to the lowest energy state in chlorophylls is a crucial preliminary step for the process of photosynthesis. Despite the continuous theoretical and experimental efforts to clarify the ultrafast dynamics of this process, it still represents the object of an intense investigation because the ultrafast timescale and the congestion of the involved states makes its characterization particularly challenging. Here we exploit 2D electronic spectroscopy and recently developed data analysis tools to provide more detailed insights into the mechanism of internal conversion within the Q-bands of chlorophyll a. The measurements confirmed the timescale of the overall internal conversion rate (170 fs) and captured the presence of a previously unidentified ultrafast (40 fs) intermediate step, involving vibronic levels of the lowest excited state.