Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy

The phonon-modulated Jahn-Teller distortion of the nitrogen vacancy center in diamond

The negatively charged nitrogen vacancy (NV) center in diamond is an optically accessible material defect with a unique combination of spin and optical properties that has attracted interest in quantum-information sciences and as a design candidate for nanoscale quantum sensors. Here, we present time-resolved nonlinear optical spectroscopy measurements, conducted with ultrabroadband laser pulses, that reveal strong modulation of the excited-state by the longitudinal optical (LO) phonon of the diamond lattice. The LO phonon and its overtones geometrically distort neighboring NV centers, driving long lived (3.5 ps) excited state relaxation of coupled NV centers after the initial excitation and ultrafast (<150 fs) decay of the Jahn-Teller distortion. These observations elevate the LO phonon to an important tuning mode of the Jahn-Teller conical intersection and help resolve previous spectroscopy experiments that noted longer-lived excited-state dynamics.

Parameter estimation in ultrafast spectroscopy using probability theory

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data.

Probing DNA structural heterogeneity by identifying conformational subensembles of a bicovalently bound cyanine dye

DNA is a re-configurable, biological information-storage unit, and much remains to be learned about its heterogeneous structural dynamics. For example, while it is known that molecular dyes templated onto DNA exhibit increased photostability, the mechanism by which the structural dynamics of DNA affect the dye photophysics remains unknown. Here, we use femtosecond, two-dimensional electronic spectroscopy measurements of a cyanine dye, Cy5, to probe local conformations in samples of single-stranded DNA (ssDNA-Cy5), double-stranded DNA (dsDNA-Cy5), and Holliday junction DNA (HJ-DNA-Cy5). A line shape analysis of the 2D spectra reveals a strong excitation-emission correlation present in only the dsDNA-Cy5 complex, which is a signature of inhomogeneous broadening. Molecular dynamics simulations support the conclusion that this inhomogeneous broadening arises from a nearly degenerate conformer found only in the dsDNA-Cy5 complex. These insights will support future studies on DNA's structural heterogeneity.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

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.

Broadband visible two-dimensional spectroscopy of molecular dyes

Two-dimensional Fourier transform spectroscopy is a promising technique to study ultrafast molecular dynamics. Similar to transient absorption spectroscopy, a more complete picture of the dynamics requires broadband laser pulses to observe transient changes over a large enough bandwidth, exceeding the inhomogeneous width of electronic transitions, as well as the separation between the electronic or vibronic transitions of interest. Here, we present visible broadband 2D spectra of a series of dye molecules and report vibrational coherences with frequencies up to ∼1400 cm^-1 that were obtained after improvements to our existing two-dimensional Fourier transform setup [Al Haddad et al., Opt. Lett. 40, 312-315 (2015)]. The experiment uses white light from a hollow core fiber, allowing us to acquire 2D spectra with a bandwidth of 200 nm, in a range between 500 and 800 nm, and with a temporal resolution of 10-15 fs. 2D spectra of nile blue, rhodamine 800, terylene diimide, and pinacyanol iodide show vibronic spectral features with at least one vibrational mode and reveal information about structural motion via coherent oscillations of the 2D signals during the population time. For the case of pinacyanol iodide, these observations are complemented by its Raman spectrum, as well as the calculated Raman activity at the ground- and excited-state geometry.

Signatures of Vibrational and Electronic Quantum Beats in Femtosecond Coherence Spectra

Femtosecond laser pulses can produce oscillatory signals in transient-absorption spectroscopy measurements. The quantum beats are often studied using femtosecond coherence spectra (FCS), the Fourier domain amplitude, and phase profiles at individual oscillation frequencies. In principle, one can identify the mechanism that gives rise to each quantum-beat signal by comparing its measured FCS to those arising from microscopic models. To date, however, most measured FCS deviate from the ubiquitous harmonic oscillator model. Here, we expand the inventory of models to which the measured spectra can be compared. We develop quantum-mechanical models of the fundamental, overtone, and combination-band FCS arising from harmonic potentials, the FCS of anharmonic potentials, and the FCS of a purely electronic dimer. This work solidifies the use of FCS for identifying electronic coherences that can arise in measurements of molecular aggregates including photosynthetic proteins. Furthermore, future studies can use the derived expressions to fit the measured FCS and thereby extract microscopic parameters of molecular potential-energy surfaces.

Finite-Temperature, Anharmonicity, and Duschinsky Effects on the Two-Dimensional Electronic Spectra from Ab Initio Thermo-Field Gaussian Wavepacket Dynamics

Accurate description of finite-temperature vibrational dynamics is indispensable in the computation of two-dimensional electronic spectra. Such simulations are often based on the density matrix evolution, statistical averaging of initial vibrational states, or approximate classical or semiclassical limits. While many practical approaches exist, they are often of limited accuracy and difficult to interpret. Here, we use the concept of thermo-field dynamics to derive an exact finite-temperature expression that lends itself to an intuitive wavepacket-based interpretation. Furthermore, an efficient method for computing finite-temperature two-dimensional spectra is obtained by combining the exact thermo-field dynamics approach with the thawed Gaussian approximation for the wavepacket dynamics, which is exact for any displaced, distorted, and Duschinsky-rotated harmonic potential but also accounts partially for anharmonicity effects in general potentials. Using this new method, we directly relate a symmetry breaking of the two-dimensional signal to the deviation from the conventional Brownian oscillator picture.

Frenkel excitons in heat-stressed supramolecular nanocomposites enabled by tunable cage-like scaffolding

Delocalized Frenkel excitons-coherently shared excitations among chromophores-are responsible for the remarkable efficiency of supramolecular light-harvesting assemblies within photosynthetic organisms. The translation of nature's design principles to applications in optoelectronic devices has been limited by the fragility of the supramolecular structures used and the delicate nature of Frenkel excitons, particularly under mildly changing solvent conditions and elevated temperatures and upon deposition onto solid substrates. Here, we overcome those functionalization barriers through composition of stable supramolecular light-harvesting nanotubes enabled by tunable (~4.3-4.9 nm), uniform (±0.3 nm) cage-like scaffolds. High-resolution cryogenic electron microscopy, combined with scanning electron microscopy, broadband femtosecond transient absorption spectroscopy and near-field scanning optical microscopy revealed that excitons within the cage-like scaffolds are robust, even under extreme heat stress, and control over nanocomposite dimensions is maintained on solid substrates. Our bio-inspired nanocomposites provide a general framework for the development of next-generation organic devices made from stable supramolecular materials.

Molecular versus Excitonic Disorder in Individual Artificial Light-Harvesting Systems

Natural light-harvesting antennae employ a dense array of chromophores to optimize energy transport via the formation of delocalized excited states (excitons), which are critically sensitive to spatio-energetic variations of the molecular structure. Identifying the origin and impact of such variations is highly desirable for understanding and predicting functional properties yet hard to achieve due to averaging of many overlapping responses from individual systems. Here, we overcome this problem by measuring the heterogeneity of synthetic analogues of natural antennae-self-assembled molecular nanotubes-by two complementary approaches: single-nanotube photoluminescence spectroscopy and ultrafast 2D correlation. We demonstrate remarkable homogeneity of the nanotube ensemble and reveal that ultrafast (∼50 fs) modulation of the exciton frequencies governs spectral broadening. Using multiscale exciton modeling, we show that the dominance of homogeneous broadening at the exciton level results from exchange narrowing of strong static disorder found for individual molecules within the nanotube. The detailed characterization of static and dynamic disorder at the exciton as well as the molecular level presented here opens new avenues in analyzing and predicting dynamic exciton properties, such as excitation energy transport.

Interplay between coherence-time undersampling and scattered light in two-dimensional electronic spectroscopy

Scanning pulse delays in multi-pulse non-linear optical spectroscopy experiments is a major contributor to lengthy data acquisition. Using large steps for the scan can significantly speed up the experiment. However, an improper choice of step length can cause distortions to the resulting spectra, especially if the light scattered on the sample is mixed into the signal. In this work, we identify potential sources of such distortions and suggest appropriate countermeasures to avoid them while maintaining a faster data collection.

Rapid acquisition of broadband two-dimensional electronic spectra by continuous scanning with conventional delay lines

A passively phase-stable, broadband (∼7fs, >2000cm^-1) two-dimensional (2D) electronic spectroscopy apparatus that achieves rapid acquisition rates by continuously-rather than step-wise-scanning the Fourier-transform dimension is demonstrated for the first time, to the best of our knowledge. This is made possible through use of a partially common path interferometer design in which the coherence time τ is sampled in a "rotating frame." Rapid, continuous scanning of τ increases the duty cycle of signal collection, rejects the majority of excitation pulse scatter, and enables the measurement of a complete 2D spectrum in 92 ms, which minimizes the influence of pulse intensity and delay fluctuations on the 2D spectrum. In practice, these improvements make possible the acquisition of hundreds of 2D spectra in tens of minutes, which opens the door to dense sampling of ultrafast relaxation dynamics and to generating extremely broadband 3D Fourier-transform spectra.

Vibronic mixing enables ultrafast energy flow in light-harvesting complex II

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps.

Interference among Multiple Vibronic Modes in Two-Dimensional Electronic Spectroscopy

Vibronic coupling between electronic and vibrational states in molecules plays a critical role in most photo-induced phenomena. Many key details about a molecule’s vibronic coupling are hidden in linear spectroscopic measurements, and therefore nonlinear optical spectroscopy methods such as two-dimensional electronic spectroscopy (2D ES) have become more broadly adopted. A single vibrational mode of a molecule leads to a Franck–Condon progression of peaks in a 2D spectrum. Each peak oscillates as a function of the waiting time, and Fourier transformation can produce a spectral slice known as a ‘beating map’ at the oscillation frequency. The single vibrational mode produces a characteristic peak structure in the beating map. Studies of single modes have limited utility, however, because most molecules have numerous vibrational modes that couple to the electronic transition. Interactions or interference among the modes may lead to complicated peak patterns in each beating map. Here, we use lineshape-function theory to simulate 2D ES arising from a system having multiple vibrational modes. The simulations reveal that the peaks in each beating map are affected by all of the vibrational modes and therefore do not isolate a single mode, which was anticipated.

Optimized noise reduction scheme for heterodyne spectroscopy using array detectors

In this work, we optimize and further advance a noise reduction scheme for heterodyne spectroscopy. This scheme linearly combines data from reference detectors to predict the noise statistics in the signal detector through an optimized coefficient matrix. We validate this scheme for visible white-light-continuum and 800-nm light sources using un-matched CMOS arrays and show that the signal-to-noise ratio can approach the noise floor of the signal detector while using only ~5% of the energy for reference detection. We also optimize the strategy for estimating the coefficient matrix in practical applications. When combined with elaborate algorithms to perform pixel data compression and expansion, our scheme is applicable in difficult situations, including when the sample position is rapidly scanned, when detectors exhibit nonlinear response, and/or when laser fluctuations are large. The scheme is generalized to scenarios with complex chopping or phase cycling patterns, and a simple approach is provided for the chopping case. Finally, a robust and computationally efficient method is devised to remove multiplicative noise.

Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy

During the past two decades, two-dimensional electronic spectroscopy (2DES) and related techniques have emerged as a potent experimental toolset to study the ultrafast elementary steps of photosynthesis. Apart from the highly engaging albeit controversial analysis of the role of quantum coherences in the photosynthetic processes, 2DES has been applied to resolve the dynamics and pathways of energy and electron transport in various light-harvesting antenna systems and reaction centres, providing unsurpassed level of detail. In this paper we discuss the main technical approaches and their applicability for solving specific problems in photosynthesis. We then recount applications of 2DES to study the exciton dynamics in plant and photosynthetic light-harvesting complexes, especially light-harvesting complex II (LHCII) and the fucoxanthin-chlorophyll proteins of diatoms, with emphasis on the types of unique information about such systems that 2DES is capable to deliver. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.

E to Z Photoisomerization of Phytochrome Cph1Δ Exceeds the Born-Oppenheimer Adiabatic Limit

The Born-Oppenheimer adiabatic limit applies broadly in chemistry because most reactions occur on the ground electronic state. Photochemical reactions involve two or more electronic states and need not be subject to this adiabatic limit. The spectroscopic signatures of nonadiabatic processes are subtle, and therefore, experimental investigations have been limited to the few systems dominated by single photochemical outcomes. Systems with branched excited-state pathways have been neglected, despite their potential to reveal insights into photochemical reactivity. Here we present experimental evidence from coherent three-dimensional electronic spectroscopy that the E to Z photoisomerization of phytochrome Cph1 is strongly nonadiabatic, and the simulations reproduce the measured features only when the photoisomerization proceeds nonadiabatically near, but not through, a conical intersection. The results broaden the general understanding of photoisomerization mechanisms and motivate future studies of nonadiabatic processes with multiple outcomes arising from branching on excited-state potential energy surfaces.

T. Characterizing divergent spin-orbit coupling effects on ultrafast nonradiative decay in transition-metal compounds

Two-dimensional electronic spectroscopy reveals divergent, spin-orbit coupling mediated, electronic relaxation dynamics in iridium(IV) hexa-bromide ([IrB6]2-) and the ruthenium(II)-based DSSC dye N719.

Addition of a Carbonyl End Group Increases the Rate of Excited-State Decay in a Carotenoid via Conjugation Extension and Symmetry Breaking

Steady-state absorption, transient absorption, and transient grating spectroscopies were employed to elucidate the role of a conjugated carbonyl group in the photophysics of carotenoids. Spheroidenone and spheroidene have similar molecular structures and differ only in an additional carbonyl group in spheroidenone. Comparison of the optical responses of these two molecules under similar experimental conditions was used to understand the role of this carbonyl group in the structure. It was found that the carbonyl group has two main effects: first, it dramatically increases the depopulation rate of the excited states of the molecule. The lifetimes of all the excited states of spheroidenone were found to be almost half of the ones for spheroidene. Second, the presence of the carbonyl group in the chain alters the decay mechanism to the symmetry-forbidden S₁ state of the molecule, so that the higher vibrational levels of the S₁ state are populated much more effectively. It was also revealed that for both molecules, the S₂/S _x → S₁(hot) → S₁ decay process is not purely sequential and follows a branched model.

Femtosecond pulse compression using a neural-network algorithm

A key requirement for femtosecond spectroscopy measurements is to compress the laser pulse to its transform-limited duration. In particular, for few-cycle laser pulses, the compression process is time-consuming using conventional algorithms that converge statistically. Here we show that machine learning can accelerate the process of pulse compression: we have developed an adaptive neural-network algorithm to control a deformable-mirror-based pulse shaper that converges 100× faster than a standard evolutionary algorithm.

Signatures of Herzberg-Teller coupling in three-dimensional electronic spectroscopy

The coupling between electronic and nuclear variables is a key consideration in molecular dynamics and spectroscopy. However, simulations that include detailed vibronic coupling terms are challenging to perform, and thus a variety of approximations can be used to model and interpret experimental results. Recent work shows that these simplified models can be inadequate. It is therefore important to understand spectroscopic signals that can identify failures of those approximations. Here we use an extended response-function method to simulate coherent three-dimensional electronic spectroscopy (3D ES) and study the sensitivity of this method to the breakdown of the Franck-Condon approximation. The simulations include a coordinate-dependent transition dipole operator that produces nodes, phase shifts, and peak patterns in 3D ES that can be used to identify Herzberg-Teller coupling. Guided by the simulation results, we interpret measurements on a molecular aggregate.

Fluorescence-Detected Two-Quantum and One-Quantum-Two-Quantum 2D Electronic Spectroscopy

We demonstrate two-quantum (2Q) coherent two-dimensional (2D) electronic spectroscopy using a shot-to-shot-modulated pulse shaper and fluorescence detection. Broadband collinear excitation is realized with the supercontinuum output of an argon-filled hollow-core fiber, enabling us to excite multiple transitions simultaneously in the visible range. The 2Q contribution is extracted via a three-pulse sequence with 16-fold phase cycling and simulated employing cresyl violet as a model system. Furthermore, we report the first experimental realization of one-quantum-two-quantum (1Q-2Q) 2D spectroscopy, offering less congested spectra as compared with the 2Q implementation. We avoid scattering artifacts and nonresonant solvent contributions by using fluorescence as the observable. This allows us to extract quantitative information about doubly excited states that agree with literature expectations. The high sensitivity and background-free nature of fluorescence detection allow for a general applicability of this method to many other systems.

Coherent Two-Quantum Two-Dimensional Electronic Spectroscopy Using Incoherent Light

Two-quantum two-dimensional electronic spectroscopy (2Q 2D ES) may provide a measure of electron-correlation energies in molecules. Attempts to obtain this profound but elusive signal have relied on experimental implementations using femtosecond laser pulses, which induce an overwhelming background signal of nonresonant response. Here we explore theoretically the signatures of electron correlation in coherent 2Q 2D ES measurements that use spectrally incoherent light, I⁽⁴⁾ 2Q 2D ES. One can use such fields to suppress nonresonant response, and therefore this method may better isolate the desired signature of electron correlation. Using an appropriate treatment of the multilevel Bloch electronic system, we find that I⁽⁴⁾ 2Q 2D ES presents an opportunity to measure electron-correlation energies in molecules.

General noise suppression scheme with reference detection in heterodyne nonlinear spectroscopy

We devised a novel two-step reference scheme that can greatly suppress the additive and convolutional noises in heterodyne nonlinear spectroscopy. To optimally remove additive noise, we fully utilized the spectral correlation in multi-channel reference data through a linear combination and regression algorithm. Using our pump-probe 2D IR spectrometer, we demonstrated that our scheme can improve the signal-to-noise ratio by 10-30 times and reach the noise floor of the signal detector. The new algorithm is guaranteed to reduce noise, enables the use of unmatched reference detectors, and does not introduce baseline shift or signal distortion. This scheme is applicable to many heterodyne spectroscopic techniques.

Triplet Separation Drives Singlet Fission after Femtosecond Correlated Triplet Pair Production in Rubrene

Singlet fission, a multistep molecular process in which one photon generates two triplet excitons, holds great technological promise. Here, by applying a combination of transient transmittance and two-dimensional electronic spectroscopy with 5 fs laser pulses, we resolve the full set of fission steps before the onset of spin dephasing. In addition to its role as a viable singlet fission material, single-crystalline rubrene is selected because its energetics and transition dipole alignment uniquely allow for the unambiguous identification of the various fission steps through their contributions to distinct spectroscopic features. The measurements reveal that the neighboring correlated triplet pair achieves its maximum population within 20 fs. Subsequent growth of the triplet signal on picosecond time scales is attributable to spatial separation of the triplets, proceeding nonadiabatically through weakly coupled but near-resonant states. As such, we provide evidence in crystalline rubrene for a singlet fission step that, until now, has not been convincingly observed.

Ultrabroadband 2D electronic spectroscopy with high-speed, shot-to-shot detection

Two-dimensional electronic spectroscopy (2DES) is an incisive tool for disentangling excited state energies and dynamics in the condensed phase by directly mapping out the correlation between excitation and emission frequencies as a function of time. Despite its enhanced frequency resolution, the spectral window of detection is limited to the laser bandwidth, which has often hindered the visualization of full electronic energy relaxation pathways spread over the entire visible region. Here, we describe a high-sensitivity, ultrabroadband 2DES apparatus. We report a new combination of a simple and robust setup for increased spectral bandwidth and shot-to-shot detection. We utilize 8-fs supercontinuum pulses generated by gas filamentation spanning the entire visible region (450 - 800 nm), which allows for a simultaneous interrogation of electronic transitions over a 200-nm bandwidth, and an all-reflective interferometric delay system with angled nanopositioner stages achieves interferometric precision in coherence time control without introducing wavelength-dependent dispersion to the ultrabroadband spectrum. To address deterioration of detection sensitivity due to the inherent instability of ultrabroadband sources, we introduce a 5-kHz shot-to-shot, dual chopping acquisition scheme by combining a high-speed line-scan camera and two optical choppers to remove scatter contributions from the signal. Comparison of 2D spectra acquired by shot-to-shot detection and averaged detection shows a 15-fold improvement in the signal-to-noise ratio. This is the first direct quantification of detection sensitivity on a filamentation-based ultrabroadband 2DES apparatus.

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.

The Primary Photochemistry of Vision Occurs at the Molecular Speed Limit

Ultrafast photochemical reactions are initiated by vibronic transitions from the reactant ground state to the excited potential energy surface, directly populating excited-state vibrational modes. The primary photochemical reaction of vision, the isomerization of retinal in the protein rhodopsin, is known to be a vibrationally coherent reaction, but the Franck-Condon factors responsible for initiating the process have been difficult to resolve with conventional time-resolved spectroscopies. Here we employ experimental and theoretical 2D photon echo spectroscopy to directly resolve for the first time the Franck-Condon factors that initiate isomerization on the excited potential energy surface and track the reaction dynamics. The spectral dynamics reveal vibrationally coherent isomerization occurring on the fastest possible time scale, that of a single period of the local torsional reaction coordinate. We successfully model this process as coherent wavepacket motion through a conical intersection on a ∼30 fs time scale, confirming the reaction coordinate as a local torsional coordinate with a frequency of ∼570 cm^-1. As a result of spectral features being spread out along two frequency coordinates, we unambiguously assign reactant and product states following passage through the conical intersection, which reveal the key vibronic transitions that initiate the vibrationally coherent photochemistry of vision.

Conformational Homogeneity in the Pr Isomer of Phytochrome Cph1

Numerous time-resolved studies of the P_r to P_fr photoisomerization in phytochrome Cph1 have revealed multiphasic excited-state decay kinetics. It remains unclear whether these kinetics arise from multiple ground-state conformational subpopulations or from a single ground-state conformation that undergoes an excited-state photoisomerization process-either branching on the excited state or relaxing through multiple sequential intermediates. Many studies have attempted to resolve this debate by fitting the measured dynamics to proposed kinetic models, arriving at different conclusions. Here we probe spectral signatures of ground-state heterogeneity of P_r. Two-dimensional electronic spectra display negligible inhomogeneous line broadening, and vibrational coherence spectra extracted from transient absorption measurements do not contain nodes and phase shifts at the fluorescence maximum. These spectroscopic results support the homogeneous model, in which the primary photochemical transformation of P_r to Lumi-R occurs adiabatically on the excited-state potential energy surface.

Spin-Orbit Coupling Drives Femtosecond Nonadiabatic Dynamics in a Transition Metal Compound

Transient absorption measurements conducted using broadband, 6 fs laser pulses reveal unexpected femtosecond dynamics in the [IrBr₆]^2- model system. Vibrational spectra and the X-ray crystal structure indicate that these dynamics are not induced by a Jahn-Teller distortion, a type of conical intersection typically associated with the spectral features of transition metal compounds. Two-dimensional electronic spectra of [IrBr₆]^2- contain 23 cross peaks, which necessarily arise from spin-orbit coupling. Real-valued 2D spectra support a spectroscopic basis where strong nonadiabatic coupling, ascribed to multiple conical intersections, mediates rapid energy relaxation to the lowest-energy excited state. Subsequent analysis gives rise to a more generalized description of a conical intersection as a degeneracy between two adiabatic states having the same total angular momentum.

Rapid-scan coherent 2D fluorescence spectroscopy

We developed pulse-shaper-assisted coherent two-dimensional (2D) electronic spectroscopy in liquids using fluorescence detection. A customized pulse shaper facilitates shot-to-shot modulation at 1 kHz and is employed for rapid scanning over all time delays. A full 2D spectrum with 15 × 15 pixels is obtained in approximately 6 s of measurement time (plus further averaging if needed). Coherent information is extracted from the incoherent fluorescence signal via 27-step phase cycling. We exemplify the technique on cresyl violet in ethanol and recover literature-known oscillations as a function of population time. Signal-to-noise behavior is analyzed as a function of the amount of averaging. Rapid scanning provides a 2D spectrum with a root-mean-square error of < 0.05 after 1 min of measurement time.

Broadband 7-fs diffractive-optic-based 2D electronic spectroscopy using hollow-core fiber compression

We demonstrate noncollinear coherent two-dimensional (2D) electronic spectroscopy for which broadband pulses are generated in an argon-filled hollow-core fiber pumped by a 1-kHz Ti:Sapphire laser. Compression is achieved to 7 fs duration (TG-FROG) using dispersive mirrors. The hollow fiber provides a clean spatial profile and smooth spectral shape in the 500-700 nm region. The diffractive-optic-based design of the 2D spectrometer avoids directional filtering distortions and temporal broadening from time smearing. For demonstration we record data of cresyl-violet perchlorate in ethanol and use phasing to obtain broadband absorptive 2D spectra. The resulting quantum beating as a function of population time is consistent with literature data.

Experimental Detection of Branching at a Conical Intersection in a Highly Fluorescent Molecule

Conical intersections are molecular configurations at which adiabatic potential-energy surfaces touch. They are predicted to be ubiquitous, yet condensed-phase experiments have focused on the few systems with clear spectroscopic signatures of negligible fluorescence, high photoactivity, or femtosecond electronic kinetics. Although rare, these signatures have become diagnostic for conical intersections. Here we detect a coherent surface-crossing event nearly two picoseconds after optical excitation in a highly fluorescent molecule that has no photoactivity and nanosecond electronic kinetics. Time-frequency analysis of high-sensitivity measurements acquired using sub-8 fs pulses reveals phase shifts of the signal due to branching of the wavepacket through a conical intersection. The time-frequency analysis methodology demonstrated here on a model compound will enable studies of conical intersections in molecules that do not exhibit their diagnostic signatures. Improving the ability to detect conical intersections will enrich the understanding of their mechanistic role in molecular photochemistry.