Low- and high-frequency vibrations synergistically enhance singlet exciton fission through robust vibronic resonances.

Singlet exciton fission (SEF) is initiated by ultrafast internal conversion of a singlet exciton into a correlated triplet pair [Formula: see text]. The "reaction coordinates" for ultrafast SEF even in archetypal systems such as pentacene thin film remain unclear. Couplings between fast electrons and slow nuclei are ubiquitous across a range of phenomena in chemistry. Accordingly, spectroscopic detection of vibrational coherences in the [Formula: see text] photoproduct motivated investigations into a possible role of vibronic coupling, akin to that reported in several photosynthetic proteins. However, acenes are very different from chlorophylls with 10× larger vibrational displacements upon photoexcitation and low-frequency vibrations modulating intermolecular orbital overlaps. Whether (and if so how) these unique features carry any mechanistic significance for SEF remains a poorly understood question. Accordingly, synthetic design of new molecules aiming to mimic this process across the solar spectrum has broadly relied on tuning electronic couplings. We address this gap and identify previously unrecognized synergistic interplay of vibrations, which in striking contrast to photosynthesis, vitally enhances SEF across a broad, nonselective and, therefore, unavoidable range of vibrational frequencies. We argue that attaching mechanistic significance to spectroscopically observed prominent quantum beats is misleading. Instead, we show that vibronic mixing leads to anisotropic quantum beats and propose readily implementable polarization-based two-dimensional electronic spectroscopy experiments which uniquely distinguish vibrations which drive vibronic mixing and promote SEF, against spectator vibrations simply accompanying ultrafast internal conversion. Our findings introduce crucial ingredients in synthetic design of SEF materials and spectroscopy experiments aiming to decipher mechanistic details from quantum beats.

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.

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

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

Calculating Multidimensional Optical Spectra from Classical Trajectories.

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Atomic fluctuations in electronic materials revealed by dephasing.

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

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.

Dephasing Processes in the Molecular Dye Lumogen-F Orange Characterized by Two-Dimensional Electronic Spectroscopy.

Molecular dyes are finding more and more applications in photonics and quantum technologies, such as polaritonic optical microcavities, organic quantum batteries and single-photon emitters for quantum sensing and metrology. For all these applications, it is of crucial importance to characterize the dephasing mechanisms. In this work we use two-dimensional electronic spectroscopy (2DES) to study the temperature dependent dephasing processes in the prototypical organic dye Lumogen-F orange. We model the 2DES maps using the Bloch equations for a two-level system and obtain a dephasing time T2 = 53 fs at room temperature, which increases to T2 = 94 fs at 86 K. Furthermore, spectral diffusion processes are observed and modeled by a combination of underdamped and overdamped Brownian oscillators. Our results provide useful design parameters for advanced optoelectronic and photonic devices incorporating dye molecules.

Resolving Electron-Electron Scattering in Plasmonic Nanorod Ensembles Using Two-Dimensional Electronic Spectroscopy.

The use of two-dimensional electronic spectroscopy (2DES) to study electron-electron scattering dynamics in plasmonic gold nanorods is described. The 2DES resolved the time-dependent plasmon homogeneous line width Γh(t), which was sensitive to changes in Fermi-level carrier densities. This approach was effective because electronic excitation accelerated plasmon dephasing, which broadened Γh. Analysis of Γh(t) indicated plasmon coherence times were decreased by 20-50%, depending on excitation conditions. Electron-electron scattering rates of approximately 0.01 fs-1 were obtained by fitting the time-dependent Γh broadening; rates increased quadratically with both excitation pulse energy and frequency. This rate dependence agreed with Fermi-liquid theory-based predictions. Hot electron thermalization through electron-phonon scattering resulted in Γh narrowing. To our knowledge, this is the first use of the plasmon Γh(t) to isolate electron-electron scattering dynamics in colloidal metal nanoparticles. These results illustrate the effectiveness of 2DES for studying hot electron dynamics of solution-phase plasmonic ensembles.

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules.

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

Seeing Multiexcitons through Sample Inhomogeneity: Band-Edge Biexciton Structure in CdSe Nanocrystals Revealed by Two-Dimensional Electronic Spectroscopy.

The electronic structure of multiexcitons significantly impacts the performance of nanostructures in lasing and light-emitting applications. However, these multiexcitons remain poorly understood due to their complexity arising from many-body physics. Standard transient-absorption and photoluminescence spectroscopies are unable to unambiguously distinguish effects of sample inhomogeneity from exciton-biexciton interactions. Here, we exploit the energy and time resolution of two-dimensional electronic spectroscopy to access the electronic structure of the band-edge biexciton in colloidal CdSe quantum dots. By removing effects of inhomogeneities, we show that the band-edge biexciton structure must consist of a discrete manifold of electronic states. Furthermore, the biexciton states within the manifold feature distinctive binding energies. Our findings have direct implications for optical gain thresholds and efficiency droop in light-emitting devices and provide experimental measures of many-body physics in nanostructures.

Probing Homogeneous Line Broadening in CdSe Nanocrystals Using Multidimensional Electronic Spectroscopy.

The finite spectral line width of an ensemble of CdSe nanocrystals arises from size and shape inhomogeneity and the single-nanocrystal spectrum itself. This line width directly limits the performance of nanocrystal-based devices, yet most optical measurements cannot resolve the underlying contributions. We use two-dimensional electronic spectroscopy (2D ES) to measure the line width of the band-edge exciton of CdSe nanocrystals as a function of radii and surface chemistry. We find that the homogeneous width decreases for increasing nanocrystal radius and that surface chemistry plays a critical role in controlling this line width. To explore the hypothesis that unpassivated trap states serve to broaden the homogeneous line width and to explain its size-dependence, we use 3D ES to identify the spectral signatures of exciton-phonon coupling to optical and acoustic phonons. We find enhanced coupling to optical phonon modes for nanocrystals that lack electron-passivating ligands, suggesting that localized surface charges enhance exciton-phonon coupling via the Fröhlich interaction. Lastly, the data reveal that spectral diffusion contributes negligibly to the homogeneous line width on subnanosecond time scales.

Coherence in energy transfer and photosynthesis.

Ultrafast energy transfer is used to transmit electronic excitation among the many molecules in photosynthetic antenna complexes. Recent experiments and theories have highlighted the role of coherent transfer in femtosecond studies of these proteins, suggesting the need for accurate dynamical models to capture the subtle characteristics of energy transfer mechanisms. Here we discuss how to think about coherence in light harvesting and electronic energy transfer. We review the various fundamental concepts of coherence, spanning from classical phenomena to the quantum superposition, and define coherence in electronic energy transfer. We describe the current status of experimental studies on light-harvesting complexes. Insights into the microscopic process are presented to highlight how and why this is a challenging problem to elucidate. We present an overview of the applicable dynamical theories to model energy transfer in the intermediate coupling regime.

The Role of Resonant Vibrations in Electronic Energy Transfer.

Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.

Measuring the Ultrafast Spectral Diffusion and Vibronic Coupling Dynamics in CdSe Colloidal Quantum Wells using Two-Dimensional Electronic Spectroscopy.

We measure the ultrafast spectral diffusion, vibronic dynamics, and energy relaxation of a CdSe colloidal quantum wells (CQWs) system at room temperature using two-dimensional electronic spectroscopy (2DES). The energy relaxation of light-hole (LH) excitons and hot carriers to heavy-hole (HH) excitons is resolved with a time scale of ∼210 fs. We observe the equilibration dynamics between the spectroscopically accessible HH excitonic state and a dark state with a time scale of ∼160 fs. We use the center line slope analysis to quantify the spectral diffusion dynamics in HH excitons, which contains an apparent sub-200 fs decay together with oscillatory features resolved at 4 and 25 meV. These observations can be explained by the coupling to various lattice phonon modes. We further perform quantum calculations that can replicate and explain the observed dynamics. The 4 meV mode is observed to be in the near-critically damped regime and may be mediating the transition between the bright and dark HH excitons. These findings show that 2DES can provide a comprehensive and detailed characterization of the ultrafast spectral properties in CQWs and similar nanomaterials.

Plasmon-Enhanced Exciton Delocalization in Squaraine-Type Molecular Aggregates.

Enlarging exciton coherence lengths in molecular aggregates is critical for enhancing the collective optical and transport properties of molecular thin film nanostructures or devices. We demonstrate that the exciton coherence length of squaraine aggregates can be increased from 10 to 24 molecular units at room temperature when preparing the aggregated thin film on a metallic rather than a dielectric substrate. Two-dimensional electronic spectroscopy measurements reveal a much lower degree of inhomogeneous line broadening for aggregates on a gold film, pointing to a reduced disorder. The result is corroborated by simulations based on a Frenkel exciton model including exciton-plasmon coupling effects. The simulation shows that localized, energetically nearly resonant excitons on spatially well separated segments can be radiatively coupled via delocalized surface plasmon polariton modes at a planar molecule-gold interface. Such plasmon-enhanced delocalization of the exciton wave function is of high importance for improving the coherent transport properties of molecular aggregates on the nanoscale. Additionally, it may help tailor the collective optical response of organic materials for quantum optical applications.

Observing Multiexciton Correlations in Colloidal Semiconductor Quantum Dots via Multiple-Quantum Two-Dimensional Fluorescence Spectroscopy.

Correlations between excitons, that is, electron-hole pairs, have a great impact on the optoelectronic properties of semiconductor quantum dots and thus are relevant for applications such as lasers and photovoltaics. Upon multiphoton excitation, these correlations lead to the formation of multiexciton states. It is challenging to observe these states spectroscopically, especially higher multiexciton states, because of their short lifetimes and nonradiative decay. Moreover, solvent contributions in experiments with coherent signal detection may complicate the analysis. Here we employ multiple-quantum two-dimensional (2D) fluorescence spectroscopy on colloidal CdSe1-xSx/ZnS alloyed core/shell quantum dots. We selectively map the electronic structure of multiexcitons and their correlations by using two- and three-quantum 2D spectroscopy, conducted in a simultaneous measurement. Our experiments reveal the characteristics of biexcitons and triexcitons such as transition dipole moments, binding energies, and correlated transition energy fluctuations. We determine the binding energies of the first six biexciton states by simulating the two-quantum 2D spectrum. By analyzing the line shape of the three-quantum 2D spectrum, we find strong correlations between biexciton and triexciton states. Our method contributes to a more comprehensive understanding of multiexcitonic species in quantum dots and other semiconductor nanostructures.

Zeaxanthin independence of photophysics in light-harvesting complex II in a membrane environment.

Green plants protect against photodamage by dissipating excess energy in a process called non-photochemical quenching (NPQ). In vivo, NPQ is activated by a drop in the luminal pH of the thylakoid membrane that triggers conformational changes of the antenna complexes, which activate quenching channels. The drop in pH also triggers de-epoxidation of violaxanthin, one of the carotenoids bound within the antenna complexes, into zeaxanthin, and so the amplitude of NPQ in vivo has been shown to increase in the presence of zeaxanthin. In vitro studies on light-harvesting complex II (LHCII), the major antenna complex in plants, compared different solubilization environments, which give rise to different levels of quenching and so partially mimic NPQ in vivo. However, in these studies both completely zeaxanthin-independent and zeaxanthin-dependent quenching have been reported, potentially due to the multiplicity of solubilization environments. Here, we characterize the zeaxanthin dependence of the photophysics in LHCII in a near-physiological membrane environment, which produces slightly enhanced quenching relative to detergent solubilization, the typical in vitro environment. The photophysical pathways of dark-adapted and in vitro de-epoxidized LHCIIs are compared, representative of the low-light and high-light conditions in vivo, respectively. The amplitude of quenching as well as the dissipative photophysics are unaffected by zeaxanthin at the level of individual LHCIIs, suggesting that zeaxanthin-dependent quenching is independent of the channels induced by the membrane. Furthermore, our results demonstrate that additional factors beyond zeaxanthin incorporation in LHCII are required for full development of NPQ.

Electronic Couplings in (Bio-) Chemical Processes.

During the last two decades, 2D optical techniques have been extended to the visible range, targeting electronic transitions. Since the report of the very first 2D electronic measurement (Hybl et al. in J Chem Phys 115:6606-6622, [2001]), two-dimensional electronic spectroscopy (2DES) has allowed fundamentally new insights into the structure and dynamics of condensed-phase systems (Ginsberg et al. in Acc Chem Res 42:1352-1363, 2009; Jonas in Annu Rev Phys Chem 54:425-463, 2003), producing experiments that measure correlations among electronic states of an absorbing species within complex systems. 2DES is used to investigate photo-physical phenomena involving electronic or vibrational couplings in multi-chromophoric systems [energy transfer in photosynthesis is one great example of how 2DES can disentangle various energy transfer pathways (Brixner et al. in Nature 625-628, 2005; Engel et al. in Nature 446:782-786, 2007; Collini et al. in Nature 463:644-647, 2010)], but also ultrafast photochemical processes in which the tracked molecules change permanently or are heterogeneous (Ruetzel et al. in Proc Natl Acad Sci 111:4764-4769, 2014; Consani et al. in Science 339:1586-1589, 2013). We divide this chapter according to some of the major areas that have been established thanks to 2DES in the following fields: heterogeneity of systems, excitation energy transfer mechanisms, photo-induced coherent oscillations associated with electronic and vibrational couplings, and complex chemical reactions (Fig. 1). Fig. 1 Main fields impacted by two-dimensional electronic spectroscopy (2DES) in condensed phase. The major discoveries of each field will be described in different paragraphs.

Two-Color Nonlinear Spectroscopy for the Rapid Acquisition of Coherent Dynamics.

There has been considerable recent interest in the observation of coherent dynamics in photosynthetic systems by 2D electronic spectroscopy (2DES). In particular, coherences that persist during the "waiting time" in a 2DES experiment have been attributed to electronic, vibrational, and vibronic origins in various systems. The typical method for characterizing these coherent dynamics requires the acquisition of 2DES spectra as a function of waiting time, essentially a 3DES measurement. Such experiments require lengthy data acquisition times that degrade the signal-to-noise of the recorded coherent dynamics. We present a rapid and high signal-to-noise pulse-shaping-based approach for the characterization of coherent dynamics. Using chlorophyll a, we demonstrate that this method retains much of the information content of a 3DES measurement and provides insight into the physical origin of the coherent dynamics, distinguishing between ground and excited state coherences. It also enables high resolution determination of ground and excited state frequencies.

Coherent Oscillations in Chlorosome Elucidated by Two-Dimensional Electronic Spectroscopy.

Chlorosomes are the most efficient photosynthetic light-harvesting complexes found in nature and consist of many bacteriochlorophyll (BChl) molecules self-assembled into supramolecular aggregates. Here we elucidate the presence and the origin of coherent oscillations in chlorosome at cryogenic temperature using 2D electronic spectroscopy. We observe coherent oscillations of multiple frequencies superimposed on the ultrafast amplitude decay of 2D spectra. Comparison of oscillatory features in the rephasing and nonrephasing 2D spectra suggests that an oscillation of 620 cm(-1) frequency arises from electronic coherence. However, this coherent oscillation can be enhanced by vibronic coupling with intermolecular vibrations of BChl aggregate, and thus it might originate from vibronic coherence rather than pure electronic coherence. Although the 620 cm(-1) oscillation dephases rapidly, the electronic (or vibronic) coherence may still take part in the initial step of energy transfer in chlorosome, which is comparably fast.