Slow Intramolecular Vibrational Relaxation Leads to Long-Lived Excited-State Wavepackets

Incoherent ultrafast energy transfer in phycocyanin 620 from Thermosynechococcus vulcanus revealed by polarization-controlled two dimensional electronic spectroscopy

Phycocyanin 620 (PC620) is the outermost light-harvesting complex in phycobilisome of cyanobacteria, engaged in light collection and energy transfer to the core antenna, allophycocyanin. Recently, long-lived exciton-vibrational coherences have been observed in allophycocyanin, accounting for the coherent energy transfer [Zhu et al., Nat. Commun. 15, 3171 (2024)]. PC620 has a nearly identical spatial location of three α84-β84 phycocyanobilin pigment pairs to those in allophycocyanin, inferring an existence of possible coherent energy transfer pathways. However, whether PC620 undergoes coherent or incoherent energy transfer remains debated. Furthermore, accurate determination of energy transfer rates in PC620 is still necessary owing to the spectral overlap and broadening in conventional time-resolved spectroscopic measurements. In this work, the energy transfer process within PC620 was directly resolved by polarization-controlled two dimensional electronic spectroscopy (2DES) and global analysis. The results show that the energy transfer from α84 to the adjacent β84 has a lifetime constant of 400 fs, from β155 to β84 of 6-8 ps, and from β155 to α84 of 66 ps, fully conforming to the Förster resonance energy transfer mechanism. The circular dichroism spectrum also reveals that the α84-β84 pigment pair does not form excitonic dimer, and the observed oscillatory signals are confirmed to be vibrational coherence, excluding the exciton-vibrational coupling. Nodal line slope analysis of 2DES further reveals that all the vibrational modes participate in the energy dissipation of the excited states. Our results consolidate that the ultrafast energy transfer process in PC620 is incoherent, where the twisted conformation of α84 is suggested as the main cause for preventing the formation of α84-β84 excitonic dimer in contrast to allophycocyanin.

Real-time capture of nuclear motions influencing photoinduced electron transfer

Although vibronic coupling phenomena have been recognized in the excite state dynamics of transition metal complexes, its impact on photoinduced electron transfer (PET) remains largely unexplored. This study investigates coherent wavepacket (CWP) dynamics during PET processes in a covalently linked electron donor-acceptor complex featuring a cyclometalated Pt(ii) dimer as the donor and naphthalene diimide (NDI) as the acceptors. Upon photoexciting the Pt(ii) dimer electron donor, ultrafast broadband transient absorption spectroscopy revealed direct modulation of NDI radical anion formation through certain CWP motions and correlated temporal evolutions of the amplitudes for these CWPs with the NDI radical anion formation. These results provide clear evidence that the CWP motions are the vibronic coherences coupled to the PET reaction coordinates. Normal mode analysis identified that the CWP motions originate from vibrational modes associated with the dihedral angles and bond lengths between the planes of the cyclometalating ligand and the NDI, the key modes altering their π-interaction, consequently influencing PET dynamics. The findings highlight the pivotal role of vibrations in shaping the favorable trajectories for the efficient PET processes.

Orchestrating Nuclear Dynamics in a Permanganate Doped Crystal with Chirped Pump-Probe Spectroscopy

Pump-probe spectroscopy is a powerful tool to investigate light-induced dynamical processes in molecules and solids. Targeting vibrational excitations occurring on the time scales of nuclear motions is challenging, as pulse durations shorter than a vibrational period are needed to initiate the dynamics, and complex experimental schemes are required to isolate weak signatures arising from wavepacket motion in different electronic states. Here, we demonstrate how introducing a temporal delay between the spectral components of femtosecond beams, namely a chirp resulting in the increase of their duration, can counterintuitively boost the desired signals by 2 orders of magnitude. Measuring the time-domain vibrational response of permanganate ions embedded in a KClO4 matrix, we identify an intricate dependence of the vibrational response on pulse chirps and probed wavelength that can be exploited to unveil weak signatures of the doping ions─otherwise dominated by the nonresonant matrix─or to obtain vibrational excitations pertaining only to the excited state, suppressing ground-state contributions.

Vibrational coherences in half-broadband 2D electronic spectroscopy: Spectral filtering to identify excited state displacements

Vibrational coherences in ultrafast pump-probe (PP) and 2D electronic spectroscopy (2DES) provide insights into the excited state dynamics of molecules. Femtosecond coherence spectra and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, the interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. A careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. This paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra.

Axial H-Bonding Solvent Controls Inhomogeneous Spectral Broadening, While Peripheral H-Bonding Solvent Controls Vibronic Broadening: Cresyl Violet in Methanol

The dynamics of the nuclei of both a chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both chromophore and its condensed-phase environment control many spectral features, including the vibronic and inhomogeneous broadening present in spectral line shapes. For the cresyl violet chromophore in methanol, we here analyze and isolate the effect of specific chromophore-solvent interactions on simulated spectral densities, reorganization energies, and linear absorption spectra. Employing both force field and ab initio molecular dynamics trajectories along with the inclusion of only certain solvent molecules in the excited-state calculations, we determine that the methanol molecules axial to the chromophore are responsible for the majority of inhomogeneous broadening, with a single methanol molecule that forms an axial hydrogen bond dominating the response. The strong peripheral hydrogen bonds do not contribute to spectral broadening, as they are very stable throughout the dynamics and do not lead to increased energy-gap fluctuations. We also find that treating the strong peripheral hydrogen bonds as molecular mechanical point charges during the molecular dynamics simulation underestimates the vibronic coupling. Including these peripheral hydrogen bonding methanol molecules in the quantum-mechanical region in a geometry optimization increases the vibronic coupling, suggesting that a more advanced treatment of these strongly interacting solvent molecules during the molecular dynamics trajectory may be necessary to capture the full vibronic spectral broadening.

Robust vibrational coherence protected by a core-shell structure in silver nanoclusters

Vibrational coherence has attracted considerable research interests because of its potential functions in light harvesting systems. Although positive signs of vibrational coherence in metal nanoclusters have been observed, the underlying mechanism remains to be verified. Here, we demonstrate that robust vibrational coherence with a lifetime of 1 ps can be clearly identified in Ag44(SR)30 core-shell nanoclusters, in which an icosahedral Ag12 core is well protected by a dodecahedral Ag20 cage. Ultrafast spectroscopy reveals that two vibrational modes at around 2.4 THz and 1.6 THz, corresponding to the breathing mode and quadrupolar-like mode of the icosahedral Ag12 core, respectively, are responsible for the generation of vibrational coherence. In addition, the vibrational coherence of Ag44 has an additional high frequency mode (2.4 THz) when compared with that of Ag29, in which there is only one low frequency vibration mode (1.6 THz), and the relatively faster dephasing in two-layer Ag29 relative to that in Ag44 further supports the fact that the robust vibrational coherence in Ag44 is ascribed to its unique matryoshka-like core-shell structure. Our findings not only present unambiguous experimental evidence for a multi-layer core-shell structure protected vibrational coherence under ambient conditions but also offers a practical strategy for the design of highly efficient quantum optoelectronic devices.

Two-Dimensional Electronic Spectroscopy Resolves Relative Excited-State Displacements

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

Spin-vibronic coherence drives singlet-triplet conversion

Design-specific control over the transitions between excited electronic states with different spin multiplicities is of the utmost importance in molecular and materials chemistry1-3. Previous studies have indicated that the combination of spin-orbit and vibronic effects, collectively termed the spin-vibronic effect, can accelerate quantum-mechanically forbidden transitions at non-adiabatic crossings4,5. However, it has been difficult to identify precise experimental manifestations of the spin-vibronic mechanism. Here we present coherence spectroscopy experiments that reveal the interplay between the spin, electronic and vibrational degrees of freedom that drive efficient singlet-triplet conversion in four structurally related dinuclear Pt(II) metal-metal-to-ligand charge-transfer (MMLCT) complexes. Photoexcitation activates the formation of a Pt-Pt bond, launching a stretching vibrational wavepacket. The molecular-structure-dependent decoherence and recoherence dynamics of this wavepacket resolve the spin-vibronic mechanism. We find that vectorial motion along the Pt-Pt stretching coordinates tunes the singlet and intermediate-state energy gap irreversibly towards the conical intersection and subsequently drives formation of the lowest stable triplet state in a ratcheting fashion. This work demonstrates the viability of using vibronic coherences as probes6-9 to clarify the interplay among spin, electronic and nuclear dynamics in spin-conversion processes, and this could inspire new modular designs to tailor the properties of excited states.

Coherent Vibrational Dynamics of Au144(SC8H9)60 Nanoclusters

The coherent vibrational dynamics of Au₁₄₄(SC₈H₉)₆₀, obtained from femtosecond time-resolved transient absorption spectroscopy, are described. Two acoustic modes were identified and assigned, including 2.0 THz breathing and 0.7 THz quadrupolar vibrations. These assignments are consistent with predictions using classical mechanics models, indicating that bulk models accurately describe the vibrational properties of Au₁₄₄(SC₈H₉)₆₀. Coherent phonon signals were persistent for up to 3 ps, indicating energy dissipation by the nanocluster was the primary dephasing channel. The initial excitation phases of the breathing and quadrupolar modes were π-phase-shifted, reflecting differences in the displacive nuclear motion of the vibrations. The combined agreement of the vibrational frequencies, relative phases, and decoherence times supported predictions based on classical models. The vibrational frequencies were insensitive to silver substitution for gold but did show increased inhomogeneous damping of the coherent phonons. The ability to predict the vibrational properties of metal nanoclusters can have an impact on nanoresonator and mass sensing technologies.

Absolute excited state molecular geometries revealed by resonance Raman signals

Ultrafast reactions activated by light absorption are governed by multidimensional excited-state (ES) potential energy surfaces (PESs), which describe how the molecular potential varies with the nuclear coordinates. ES PESs ad-hoc displaced with respect to the ground state can drive subtle structural rearrangements, accompanying molecular biological activity and regulating physical/chemical properties. Such displacements are encoded in the Franck-Condon overlap integrals, which in turn determine the resonant Raman response. Conventional spectroscopic approaches only access their absolute value, and hence cannot determine the sense of ES displacements. Here, we introduce a two-color broadband impulsive Raman experimental scheme, to directly measure complex Raman excitation profiles along desired normal modes. The key to achieve this task is in the signal linear dependence on the Frank-Condon overlaps, brought about by non-degenerate resonant probe and off-resonant pump pulses, which ultimately enables time-domain sensitivity to the phase of the stimulated vibrational coherences. Our results provide the tool to determine the magnitude and the sensed direction of ES displacements, unambiguously relating them to the ground state eigenvectors reference frame.

Singlet Fission in Colloidal Nanoparticles of Amphipathic Diketopyrrolopyrrole Derivatives: Probing the Role of the Charge Transfer State

To evaluate the role of the charge transfer (CT) state in the singlet fission (SF) process, we prepared three 3,6-bis(thiophen-2-yl)diketopyrrolopyrrole (TDPP) derivatives with zero (Ph₂TDPP), one (Ph₂TDPP-COOH), and two (Ph₂TDPP-(COOH)₂) carboxylic groups, respectively. Their colloidal nanoparticles were also prepared by a simple precipitation method. The SF dynamics and mechanism in these colloid nanoparticles were investigated by using steady-state/transient absorption and fluorescence spectroscopy. Steady-state absorption spectra reveal that the strength of the CT resonance interactions between the adjacent DPP units is increased gradually from Ph₂TDPP to Ph₂TDPP-COOH and then to Ph₂TDPP-(COOH)₂. Fluorescence and transient absorption spectra demonstrate that SF is proceeded via a CT-assisted superexchange mechanism in these three nanoparticles. Furthermore, SF rate and yield are enhanced gradually with the increase of the number of the carboxylic group, which may be attributed to the enhancement of the CT coupling strength. The result of this work not only provides a better understanding of the SF mechanism especially for the role of the CT state but also gives some new insights for the design of efficient SF materials based on DPP derivatives.

Coherent vibrational dynamics of Au144(SR)60 nanoclusters

The coherent vibrational dynamics of gold nanoclusters (NCs) provides important information on the coupling between vibrations and electrons as well as their mechanical properties, which is critical for understanding the evolution from a metallic state to a molecular state with diminishing size. Coherent vibrations have been widely explored in small-sized atomically precise gold NCs, while it remains a challenge to observe them in large-sized gold NCs. In this work, we report the coherent vibrational dynamics of atomically precise Au144(SR)60 NCs via temperature-dependent femtosecond transient absorption (TA) spectroscopy. The population dynamics of Au144(SR)60 consists of three relaxation processes: internal conversion, core-shell charge transfer and relaxation to the ground state. After removing the population dynamics from the TA kinetics, fast Fourier transform analysis on the residual oscillation reveals distinct vibrational modes at 1.5 THz (50 cm-1) and 2 THz (67 cm-1), which arise from the wavepacket motions along the ground-state and excited-state potential energy surfaces (PES), respectively. These results are helpful for understanding the physical properties of gold nanostructures with a threshold size that lies in between those of molecular-like NCs and metallic-state nanoparticles.

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.

On the use of vibronic coherence to identify reaction coordinates for ultrafast excited-state dynamics of transition metal-based chromophores

The question of whether one can use information from quantum coherence as a means of identifying vibrational degrees of freedom that are active along an excited-state reaction coordinate is discussed. Specifically, we are exploring the notion of whether quantum oscillations observed in single-wavelength kinetics data exhibiting coherence dephasing times that are intermediate between that expected for either pure electronic or pure vibrational dephasing are vibronic in nature and therefore may be coupled to electronic state-to-state evolution. In the case of a previously published Fe(II) polypyridyl complex, coherences observed subsequent to ¹A₁ → ¹MLCT excitation were linked to large-amplitude motion of a portion of the ligand framework; dephasing times on the order of 200-300 fs suggested that these degrees of freedom could be associated with ultrafast (∼100 fs) conversion from the initially formed MLCT excited state to lower-energy, metal-centered ligand-field excited state(s) of the compound. Incorporation of an electronically benign but sterically restrictive Cu(I) ion into the superstructure designed to interfere with this motion yielded a compound exhibiting a ∼25-fold increase in the compound's MLCT lifetime, a result that was interpreted as confirmation of the initial hypothesis. However, new data acquired on a different chemical system - Cr(acac')₃ (where acac' represents various derivatives of acetylacetonate) - yielded results that call into question this same hypothesis. Coherences observed subsequent to ⁴A₂ → ⁴T₂ ligand-field excitation on a series of molecules implicated similar vibrational degrees of freedom across the series, but exhibited dephasing times ranging from 340 fs to 2.5 ps without any clear correlation to the dynamics of excited-state evolution in the system. Taken together, the results obtained on both of these chemical platforms suggest that while identification of coherences can indeed point to degrees of freedom that should be considered as candidate modes for defining reaction trajectories, our understanding of the factors that determine the interplay across coherences, dephasing times, and electronic and geometric structure is insufficient at the present time to view this parameter as a robust metric for differentiating active versus spectator modes for ultrafast dynamics.

Ultrafast branching in intersystem crossing dynamics revealed by coherent vibrational wavepacket motions in a bimetallic Pt(II) complex

Ultrafast excited state processes of transition metal complexes (TMCs) are governed by complicated interplays between electronic and nuclear dynamics, which demand a detailed understanding to achieve optimal functionalities of photoactive TMC-based materials for many applications. In this work, we investigated a cyclometalated platinum(II) dimer known to undergo a Pt-Pt bond contraction in the metal-metal-to-ligand-charge-transfer (MMLCT) excited state using femtosecond broadband transient absorption (fs-BBTA) spectroscopy in combination with geometry optimization and normal mode calculations. Using a sub-20 fs pump and broadband probe pulses in fs-BBTA spectroscopy, we were able to correlate the coherent vibrational wavepacket (CVWP) evolution with the stimulated emission (SE) dynamics of the ¹MMLCT state. The results demonstrated that the 145 cm^-1 CVWP motions with the damping times of ∼0.9 ps and ∼2 ps originate from coherent Pt-Pt stretching vibrations in the singlet and triplet MMLCT states, respectively. On the basis of excited state potential energy surface calculations in our previous work, we rationalized that the CVWP transfer from the Franck-Condon (FC) state to the ³MMLCT state was mediated by a triplet ligand-centered (³LC) intermediate state through two step intersystem crossing (ISC) on a time scale shorter than a period of the Pt-Pt stretching wavepacket motions. Moreover, it was found that the CVWP motion had 110 cm^-1 frequency decays with the damping time of ∼0.2 ps, matching the time constant of 0.253 ps, corresponding to a redshift in the SE feature at early times. This observation indicates that the Pt-Pt bond contraction changes the stretching frequency from 110 to 145 cm^-1 and stabilizes the ¹MMLCT state relative to the ³LC state with a ∼0.2 ps time scale. Thus, the ultrafast ISC from the ¹MMLCT to the ³LC states occurs before the Pt-Pt bond shortening. The findings herein provide insight into understanding the impact of Pt-Pt bond contraction on the ultrafast branching of the ¹MMLCT population into the direct (¹MMLCT → ³MMLCT) and indirect ISC pathways (¹MMLCT → ³LC → ³MMLCT) in the Pt(II) dimer. These results revealed intricate excited state electronic and nuclear motions that could steer the reaction pathways with a level of detail that has not been achieved before.

Ultrafast proton transfer of the aqueous phenol radical cation

Proton transfer (PT) reactions are fundamental to numerous chemical and biological processes. While sub-picosecond PT involving electronically excited states has been extensively studied, little is known about ultrafast PT triggered by photoionization. Here, we employ femtosecond optical pump-probe spectroscopy and quantum dynamics calculations to investigate the ultrafast proton transfer dynamics of the aqueous phenol radical cation (PhOH˙⁺). Analysis of the vibrational wave packet dynamics reveals unusually short dephasing times of 0.18 ± 0.02 ps and 0.16 ± 0.02 ps for the PhOH˙⁺ O-H wag and bend frequencies, respectively, suggestive of ultrafast PT occurring on the ∼0.1 ps timescale. The reduced potential energy surface obtained from ab initio calculations shows that PT is barrierless when it is coupled to the intermolecular hindered translation between PhOH˙⁺ and the proton-acceptor water molecule. Quantum dynamics calculations yield a lifetime of 193 fs for PhOH˙⁺, in good agreement with the experimental results and consistent with the PT reaction being mediated by the intermolecular O⋯O stretch. These results suggest that photoionization can be harnessed to produce photoacids that undergo ultrafast PT. In addition, they also show that PT can serve as an ultrafast deactivation channel for limiting the oxidative damage potential of radical cations.

Observing Intramolecular Vibrational Energy Redistribution via the Short-Time Fourier Transform

Intramolecular vibrational energy relaxation (IVR) is important in many problems in chemical physics. Here, we apply the short-time Fourier transform method for analyzing IVR with classical dynamics. Calculating time-dependent Fourier transforms to perform such an analysis requires extending the usual Fourier transform method, and we do that here. The guiding concept behind the generalization is that if there is a shift of vibrational energy from one frequency range to another, we see a difference between the spectrum before the shift and the spectrum after the shift. We use time-window functions to transform the power spectrum of a trajectory into a time-dependent density spectrum of the average kinetic energy. The time-dependent average kinetic energy for each interval of the spectrum becomes an indicator to monitor the extent and nature of the energy transfer into and out of the corresponding modes. We illustrate this method for the H₂O molecule. By analyzing cases with different initial conditions, we show that the short-time Fourier transform method can distinguish trends in IVR that depend on the initial distribution of energy and not just on the total energy.

Real-time Observation of Structural Dynamics Triggering Excimer Formation in a Perylene Bisimide Folda-dimer by Ultrafast Time-Domain Raman Spectroscopy

In π-conjugated organic photovoltaic materials, an excimer state has been generally regarded as a trap state which hinders efficient excitation energy transport. But despite wide investigations of the excimer for overcoming the undesirable energy loss, the understanding of the relationship between the structure of the excimer in stacked organic compounds and its properties remains elusive. Here, we present the landscape of structural dynamics from the excimer formation to its relaxation in a co-facially stacked archetypical perylene bisimide folda-dimer using ultrafast time-domain Raman spectroscopy. We directly captured vibrational snapshots illustrating the ultrafast structural evolution triggering the excimer formation along the interchromophore coordinate on the complex excited-state potential surfaces and following evolution into a relaxed excimer state. Not only does this work showcase the ultrafast structural dynamics necessary for the excimer formation and control of excimer characteristics but also provides important criteria for designing the π-conjugated organic molecules.

Deciphering Photoinduced Charge Transfer Dynamics in a Cross-Linked Graphene-Dye Nanohybrid

The search for synthetic materials that mimic natural photosynthesis by converting solar energy into other more useful forms of energy is an ever-growing research endeavor. Graphene-based materials, with their exceptional electronic and optical properties, are exemplary candidates for high-efficiency solar energy harvesting devices. High photoactivity can be conveniently achieved by functionalizing graphene with small molecule organic semiconductors whose band-gaps can be tuned by structural modification, leading to interactions between the π-conjugated electronic systems in both the semiconductor and graphene. Here we investigate the ultrafast transient optical properties of a cross-linked graphene-dye (diphenyl-dithiophenediketopyrrolopyrrole) nanohybrid material, in which oligomers of the organic semiconductor dye are covalently bound to a random network of few-layer graphene flakes, and compare the results to those obtained for the reference dye monomer. Using a combination of ultrafast transient absorption and two-dimensional electronic spectroscopy, we provide substantial evidence for photoinduced charge transfer that occurs within 18 ps in the nanohybrid system. Notably, subpicosecond photoinduced torsional relaxation observed in the constituent dye monomer is absent in the cross-linked nanohybrid system. Through density functional theory calculations, we compare the competing effects of covalent bonding, increasing conjugation length, and the presence of multiple graphene flakes. We find evidence that the observed ultrafast charge transfer process occurs through a superexchange mechanism in which the oligomeric dye bridge provides virtual states enabling charge transfer between graphene-dye covalent bond sites.

A Revisit on Impulsive Stimulated Raman Spectroscopy: Importance of Spectral Dispersion of Chirped Broadband Probe

The usefulness of a chirped broadband probe and spectral dispersion to obtain Raman spectra under nonresonant/resonant impulsive excitation is revisited. A general methodology is presented that inherently takes care of phasing the time-domain low-frequency oscillations without probe pulse compression and retrieves the absolute phase of the oscillations. As test beds, neat solvents (CCl₄, CHCl₃, and CH₂Cl₂) are used. Observation of periodic intensity modulation along detection wavelengths for particular modes is explained using a simple electric field interaction picture. This method is extended to diatomic molecule (iodine) and polyatomic molecules (Nile blue and methylene blue) to assign vibrational frequencies in ground/excited electronic state that are supported by density functional theory calculations. A comparison between frequency-domain and time-domain counterparts, i.e., stimulated Raman scattering and impulsive stimulated Raman scattering using degenerate pump-probe pairs is presented, and most importantly, it is shown how impulsive stimulated Raman scattering using chirped broadband probe retains unique advantages offered by both.

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.

Excited-State Energy Surfaces in Molecules Revealed by Impulsive Stimulated Raman Excitation Profiles

Photophysical and photochemical processes are ruled by the interplay between transient vibrational and electronic degrees of freedom, which are ultimately determined by the multidimensional potential energy surfaces (PESs). Differences between ground and excited PESs are encoded in the relative intensities of resonant Raman bands, but they are experimentally challenging to access, requiring measurements at multiple wavelengths under identical conditions. Herein, we perform a two-color impulsive vibrational scattering experiment to launch nuclear wavepacket motions by an impulsive pump and record their coupling with a targeted excited-state potential by resonant Raman processes with a delayed probe, generating in a single measurement background-free vibrational spectra across the entire sample absorption. Building on the interference between the multiple pathways resonant with the excited-state manifold that generate the Raman signal, we show how to experimentally tune their relative phase by varying the probe chirp, decoding nuclear displacements along different normal modes and revealing the multidimensional PESs. Our results are validated against time-dependent density functional theory.

The Critical Number of Gold Atoms for a Metallic State Nanocluster: Resolving a Decades-Long Question

Probing the transition from a metallic state to a molecular state in gold nanoparticles is fundamentally important for understanding the origin of surface plasmon resonance and the nature of the metallic bond. Atomically precise gold nanoclusters are desired for probing such a transition based upon a series of precise sizes with X-ray structures. While the definition of the metallic state in nanoclusters is simple, that is, when the HOMO-LUMO gap (E_g) becomes negligibly small (E_g < k_BT, where k_B is the Boltzmann constant and T the temperature), the experimental determination of ultrasmall E_g (e.g., of k_BT level) is difficult, and the thermal excitation of valence electrons apparently comes into play in ultrasmall E_g nanoclusters. Although a sharp transition from nonmetallic Au₂₄₆(SR)₈₀ to metallic Au₂₇₉(SR)₈₄ (SR: thiolate) has been observed, there is still uncertainty about the transition region. Here, we summarize several criteria on determining the metallic state versus the molecular (or nonmetallic) state in gold nanoclusters, including (1) E_g determined by optical and electrochemical methods, (2) steady-state absorption spectra, (3) cryogenic optical spectra, (4) transient absorption spectra, (5) excited-state lifetime and power dependence, and (6) coherent oscillations in ultrafast electron dynamics. We emphasize that multiple analyses should be performed and cross-checked in practice because no single criterion is definitive. We also review the photophysics of several gold nanoclusters with nascent surface plasmon resonance. These criteria are expected to deepen the understanding of the metallic to molecular state transition of gold and other metal nanoclusters and also promote the design of functional nanomaterials and their applications.

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.

Vibrational Dephasing along the Reaction Coordinate of an Electron Transfer Reaction

The role of molecular vibration in photoinduced electron transfer (ET) reactions has been extensively debated in recent years. In this study, we investigated vibrational wavepacket dynamics in a model ET system consisting of an organic dye molecule as an electron acceptor dissolved in various electron donating solvents. By using broad band pump-probe (BBPP) spectroscopy with visible laser pulses of sub-10 fs duration, coherent vibrational wavepackets of naphthacene dye with frequencies spanning 170-1600 cm-1 were observed in the time domain. The coherence properties of 11 vibrational modes were analyzed by an inverse Fourier filtering procedure, and we discovered that the dephasing times of some vibrational coherences are reduced with increasing ET rates. Density functional theory calculations indicated that the corresponding vibrational modes have a large Huang-Rhys factor between the reactant and the product states, supporting the hypothesis that the loss of phase coherence along certain vibrational modes elucidates that those vibrations are coupled to the reaction coordinate of an ET reaction.

Ultrafast vibrational wave packet dynamics of the aqueous tyrosyl radical anion induced by photodetachment

The ultrafast dynamics triggered by the photodetachment of the tyrosinate dianion in aqueous environment shed light on the elementary processes that accompany the interaction of ionizing radiation with biological matter. Photodetachment of the tryosinate dianion yields the tyrosyl radical anion, an important intermediate in biological redox reactions, although the study of its ultrafast dynamics is limited. Here, we utilize femtosecond optical pump-probe spectroscopy to investigate the ultrafast structural reorganization dynamics that follow the photodetachment of the tyrosinate dianion in aqueous solution. Photodetachment of the tyrosinate dianion leads to vibrational wave packet motion along seven vibrational modes that are coupled to the photodetachment process. The vibrational modes are assigned with the aid of density functional theory (DFT) calculations. Our results offer a glimpse of the elementary dynamics of ionized biomolecules and suggest the possibility of extending this approach to investigate the ionization-induced structural rearrangement of other aromatic amino acids and larger biomolecules.

Optical Properties and Excited-State Dynamics of Atomically Precise Gold Nanoclusters

Understanding the excited-state dynamics of nanomaterials is essential to their applications in photoenergy storage and conversion. This review summarizes recent progress in the excited-state dynamics of atomically precise gold (Au) nanoclusters (NCs). We first discuss the electronic structure and typical relaxation pathways of Au NCs from subpicoseconds to microseconds. Unlike plasmonic Au nanoparticles, in which collective electron excitation dominates, Au NCs show single-electron transitions and molecule-like exciton dynamics. The size-, shape-, structure-, and composition-dependent dynamics in Au NCs are further discussed in detail. For small-sized Au NCs, strong quantum confinement effects give rise to relaxation dynamics that is significantly dependent on atomic packing, shape, and heteroatom doping. For relatively larger-sized Au NCs, strong size dependence can be observed in exciton and electron dynamics. We also discuss the origin of coherent oscillations and their roles in excited-state relaxation. Finally, we provide our perspective on future directions in this area.

Interplay of vibrational wavepackets during an ultrafast electron transfer reaction

Electron transfer reactions facilitate energy transduction and photoredox processes in biology and chemistry. Recent findings show that molecular vibrations can enable the dramatic acceleration of some electron transfer reactions, and control it by suppressing and enhancing reaction paths. Here, we report ultrafast spectroscopy experiments and quantum dynamics simulations that resolve how quantum vibrations participate in an electron transfer reaction. We observe ballistic electron transfer (~30 fs) along a reaction coordinate comprising high-frequency promoting vibrations. Along another vibrational coordinate, the system becomes impulsively out of equilibrium as a result of the electron transfer reaction. This leads to the generation (by the electron transfer reaction, not the laser pulse) of a new vibrational coherence along this second reaction coordinate in a mode associated with the reaction product. These results resolve a complex reaction trajectory composed of multiple vibrational coordinates that, like a sequence of ratchets, progressively diminish the recurrence of the reactant state.

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.

Accessing Excited State Molecular Vibrations by Femtosecond Stimulated Raman Spectroscopy

Excited state vibrations are crucial for determining the photophysical and photochemical properties of molecular compounds. Stimulated Raman scattering can coherently stimulate and probe molecular vibrations with optical pulses, but it is generally restricted to ground state properties. Working under resonance conditions enables cross-section enhancement and selective excitation to a targeted electronic level but is hampered by an increased signal complexity due to the presence of overlapping spectral contributions. Here, we show how detailed information about ground and excited state vibrations can be disentangled by exploiting the relative time delay between Raman and probe pulses to control the excited state population, combined with a diagrammatic formalism to dissect the pathways concurring with the signal generation. The proposed method is then exploited to elucidate the vibrational properties of the ground and excited electronic states in the paradigmatic case of cresyl violet. We anticipate that the presented approach holds the potential for selective mapping of the reaction coordinates pertaining to transient electronic stages implied in photoactive compounds.

Spectral Signatures of Ground- and Excited-State Wavepacket Interference after Impulsive Excitation

Impulsive transient absorption spectroscopy is used to track the formation and evolution of vibrational coherences in cresyl violet perchlorate under different excitation conditions. Resonant and off-resonant pump pulses result in the selective formation of excited (S₁)- and ground (S₀)-state wavepackets. Partially resonant and broadband excitation conditions lead to the simultaneous formation of wavepackets in the ground and excited states. The wavepackets are characterized by the phase-flips in the coherent signal associated with wavepacket motion across the absorption and emission maxima and by a red shift of 2-10 cm^-1 in the Raman features of the excited state compared to the ground-state wavepacket. We observe that, when wavepackets are simultaneously excited on the ground- and excited-state surfaces, interference on a picosecond timescale between coherent oscillations in the two wavepackets gives rise to features that cannot be attributed to the passage of a wavepacket through a conical intersection, such as shifting phase-flips and zero-amplitude nodes. Wavepacket filtering using windowed Fourier transforms highlights these interference effects and demonstrates that special care must be taken in order to properly interpret data that have been processed in this manner.

Heat trapping in a nano-layered microenvironment: estimation of temperature by thermal sensing molecules

We have previously found reversible photo-induced expansion and contraction of organic/inorganic clay hybrids, and even sliding of niobate nano-sheets at the macroscopic level of organic/inorganic niobate hybrids, induced by the molecular photo-isomerization of the polyfluoroalkylated azobenzene derivative (C3F-Azo-C6H) intercalated within the interlayer, which is viewed as an artificial muscle model unit. Based on systematic investigations of the steady state photo-isomerization and transient behavior of the reaction, we comprehended that the phenomena is caused by trapping of excess energy liberated during the isomerization, as well as the relaxation processes upon excitation of azobenzene chromophores in the interlayers of the hybrid. In this paper, quantitative estimation of transient 'heat' trapped in various microenvironments has been studied by each co-intercalation of temperature sensing dye molecules - rhodamine B (RhB) or tris(bipyridine)ruthenium(ii) chloride (Rubpy) with C3F-Azo-C6H within clay (SSA) nano-layers. The amount of dye molecules co-intercalated was kept to trace amounts that did not alter the bi-layered structure of the hybrid. The temperature of the microenvironment surrounding the probe molecules was estimated from the emission lifetime analysis. The evidently reduced emission lifetimes in C3F-Azo-C6H/SSA and C3H-Azo-C6H/SSA hybrids in the film state, indicated the elevation of temperature of the microenvironment upon excitation of the chromophores, which demonstrated our previous hypothesis rationalizing that the high reactivity of isomerization in the hybrid film state is caused by heat trapping via multi-step dissipation of the excess energy. With the hybrid of a hydrocarbon analogue (C3H-Azo-C6H), a distinct difference in temperature gradient was found to show the crucial role of the perfluoroalkyl chain of the surfactant that traps the excess energy to retard its dissipation leading to three-dimensional morphological motion.

Ultrafast structural rearrangement dynamics induced by the photodetachment of phenoxide in aqueous solution

The elementary processes that accompany the interaction of ionizing radiation with biologically relevant molecules are of fundamental importance. However, the ultrafast structural rearrangement dynamics induced by the ionization of biomolecules in aqueous solution remain hitherto unknown. Here, we employ femtosecond optical pump-probe spectroscopy to elucidate the vibrational wave packet dynamics that follow the photodetachment of phenoxide, a structural mimic of tyrosine, in aqueous solution. Photodetachment of phenoxide leads to wave packet dynamics of the phenoxyl radical along 12 different vibrational modes. Eight of the modes are totally symmetric and support structural rearrangement upon electron ejection. Comparison to a previous photodetachment study of phenoxide in the gas phase reveals the important role played by the solvent environment in driving ultrafast structural reorganization induced by ionizing radiation. This work provides insight into the ultrafast molecular dynamics that follow the interaction of ionizing radiation with molecules in aqueous solution.

The interaction of biomolecules with ionizing radiation induces structural changes which are still largely unknown. The authors use femtosecond wave packet spectroscopy to observe ultrafast structural dynamics that follow the photodetachment of phenoxide in aqueous solution.

Gold Nanoclusters: Bridging Gold Complexes and Plasmonic Nanoparticles in Photophysical Properties

Recent advances in the determination of crystal structures and studies of optical properties of gold nanoclusters in the size range from tens to hundreds of gold atoms have started to reveal the grand evolution from gold complexes to nanoclusters and further to plasmonic nanoparticles. However, a detailed comparison of their photophysical properties is still lacking. Here, we compared the excited state behaviors of gold complexes, nanolcusters, and plasmonic nanoparticles, as well as small organic molecules by choosing four typical examples including the Au₁₀ complex, Au₂₅ nanocluster (1 nm metal core), 13 diameter Au nanoparticles, and Rhodamine B. To compare their photophysical behaviors, we performed steady-state absorption, photoluminescence, and femtosecond transient absorption spectroscopic measurements. It was found that gold nanoclusters behave somewhat like small molecules, showing both rapid internal conversion (<1 ps) and long-lived excited state lifetime (about 100 ns). Unlike the nanocluster form in which metal–metal transitions dominate, gold complexes showed significant charge transfer between metal atoms and surface ligands. Plasmonic gold nanoparticles, on the other hand, had electrons being heated and cooled (~100 ps time scale) after photo-excitation, and the relaxation was dominated by electron–electron scattering, electron–phonon coupling, and energy dissipation. In both nanoclusters and plasmonic nanoparticles, one can observe coherent oscillations of the metal core, but with different fundamental origins. Overall, this work provides some benchmarking features for organic dye molecules, organometallic complexes, metal nanoclusters, and plasmonic nanoparticles.

From Fundamental Theories to Quantum Coherences in Electron Transfer

Photoinduced electron transfer (ET) is a cornerstone of energy transduction from light to chemistry. The past decade has seen tremendous advances in the possible role of quantum coherent effects in the light-initiated energy and ET processes in chemical, biological, and materials systems. The prevalence of such coherence effects holds a promise to increase the efficiency and robustness of transport even in the face of energetic or structural disorder. A primary motive of this Perspective is to work out how to think about "coherence" in ET reactions. We will discuss how the interplay of basic parameters governing ET reactions-like electronic coupling, interactions with the environment, and intramolecular high-frequency quantum vibrations-impact coherences. This includes revisiting the insights from the seminal work on the theory of ET and time-resolved measurements on coherent dynamics to explore the role of coherences in ET reactions. We conclude by suggesting that in addition to optical spectroscopies, validating the functional role of coherences would require simultaneous mapping of correlated electron motion and atomically resolved nuclear structure.

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.

Vibronic Wavepackets and Energy Transfer in Cryptophyte Light-Harvesting Complexes

Determining the key features of high-efficiency photosynthetic energy transfer remains an ongoing task. Recently, there has been evidence for the role of vibronic coherence in linking donor and acceptor states to redistribute oscillator strength for enhanced energy transfer. To gain further insights into the interplay between vibronic wavepackets and energy-transfer dynamics, we systematically compare four structurally related phycobiliproteins from cryptophyte algae by broad-band pump-probe spectroscopy and extend a parametric model based on global analysis to include vibrational wavepacket characterization. The four phycobiliproteins isolated from cryptophyte algae are two "open" structures and two "closed" structures. The closed structures exhibit strong exciton coupling in the central dimer. The dominant energy-transfer pathway occurs on the subpicosecond timescale across the largest energy gap in each of the proteins, from central to peripheral chromophores. All proteins exhibit a strong 1585 cm^-1 coherent oscillation whose relative amplitude, a measure of vibronic intensity borrowing from resonance between donor and acceptor states, scales with both energy-transfer rates and damping rates. Central exciton splitting may aid in bringing the vibronically linked donor and acceptor states into better resonance resulting in the observed doubled rate in the closed structures. Several excited-state vibrational wavepackets persist on timescales relevant to energy transfer, highlighting the importance of further investigation of the interplay between electronic coupling and nuclear degrees of freedom in studies on high-efficiency photosynthesis.

Coherent wavepackets in the Fenna-Matthews-Olson complex are robust to excitonic-structure perturbations caused by mutagenesis

Femtosecond pulsed excitation of light-harvesting complexes creates oscillatory features in their response. This phenomenon has inspired a large body of work aimed at uncovering the origin of the coherent beatings and possible implications for function. Here we exploit site-directed mutagenesis to change the excitonic level structure in Fenna-Matthews-Olson (FMO) complexes and compare the coherences using broadband pump-probe spectroscopy. Our experiments detect two oscillation frequencies with dephasing on a picosecond timescale-both at 77 K and at room temperature. By studying these coherences with selective excitation pump-probe experiments, where pump excitation is in resonance only with the lowest excitonic state, we show that the key contributions to these oscillations stem from ground-state vibrational wavepackets. These experiments explicitly show that the coherences-although in the ground electronic state-can be probed at the absorption resonances of other bacteriochlorophyll molecules because of delocalization of the electronic excitation over several chromophores.

Vibronically coherent ultrafast triplet-pair formation and subsequent thermally activated dissociation control efficient endothermic singlet fission

Singlet exciton fission (SF), the conversion of one spin-singlet exciton (S₁) into two spin-triplet excitons (T₁), could provide a means to overcome the Shockley-Queisser limit in photovoltaics. SF as measured by the decay of S₁ has been shown to occur efficiently and independently of temperature, even when the energy of S₁ is as much as 200 meV less than that of 2T₁. Here we study films of triisopropylsilyltetracene using transient optical spectroscopy and show that the triplet pair state (TT), which has been proposed to mediate singlet fission, forms on ultrafast timescales (in 300 fs) and that its formation is mediated by the strong coupling of electronic and vibrational degrees of freedom. This is followed by a slower loss of singlet character as the excitation evolves to become only TT. We observe the TT to be thermally dissociated on 10-100 ns timescales to form free triplets. This provides a model for 'temperature-independent' efficient TT formation and thermally activated TT separation.