Coherence Spectroscopy in the Condensed Phase: Insights into Molecular Structure, Environment, and Interactions

Tracking the conical intersection dynamics for the photoinduced Jahn-Teller switch of a Mn(iii) complex

Octahedral Mn(iii) ions predominantly exhibit an axially elongated Jahn-Teller (JT) distortion, which is responsible for their large uniaxial magnetic anisotropy. As a result, they are often used in the synthesis of single-molecule magnets (SMMs). Modulation of the JT distortion using femtosecond laser pulses could offer a route to controlling the magnetisation direction, and therefore is promising for the development of data storage devices that work on ultrafast timescales. Photoinduced switching of the distortion from an axially elongated to an axially compressed structure has been demonstrated for various Mn(iii) complexes. However, the dynamics around the region of the conical intersection for the photoinduced JT switch remains unclear. Here, ultrafast transient absorption spectra were recorded for solutions of tris(2,2,6,6-tetramethyl-3,5-heptanedionato)manganese(iii) (Mn(dpm)3) in ethanol to further explore the dynamics of the photoinduced JT switch. We observe the generation of a vibrational wavepacket on the excited state surface, which has a frequency of approximately 155 cm-1 and encompasses a JT-active vibrational mode. This coherent motion is maintained after passage through the conical intersection back to the ground state, which launches wavepackets along the ground state potential energy surface (PES) with frequencies of approximately 180 and 110 cm-1 that we assign to the elongated and compressed state, respectively. Inspection of the relative phases of the frequencies reveals phase shifts that are consistent with a one-mode reaction coordinate, and passes through the conical intersection at 1/4 and 3/4 of the excited state vibrational period. Our results provide direct insights into the non-adiabatic dynamics of Mn(iii) complexes, which can be used to guide the synthesis of optically controlled SMMs.

Role of Quantum Information in HEOM Trajectories

Open quantum systems often operate in the non-Markovian regime where a finite history of a trajectory is intrinsic to its evolution. The degree of non-Markovianity for a trajectory may be measured in terms of the amount of information flowing from the bath back into the system. In this study, we consider how information flows through the auxiliary density operators (ADOs) in the hierarchical equations of motion. We consider three cases for a range of baths, underdamped, intermediate, and overdamped. By understanding how information flows, we are able to determine the relative importance of different ADOs within the hierarchy. We show that ADOs sharing a common Matsubara axis behave similarly, while ADOs on different Matsubara axes behave differently. Using this knowledge, we are able to truncate hierarchies significantly, thus reducing the computation time, while obtaining qualitatively similar results. This is illustrated by comparing 2D electronic spectra for a molecule with an underdamped vibration subsumed into the bath spectral density.

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.

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.

Vibronic Coupling Drives the Ultrafast Internal Conversion in a Functionalized Free-Base Porphyrin

Internal conversion (IC) is a common radiationless transition in polyatomic molecules. Theory predicts that molecular vibrations assist IC between excited states, and ultrafast experiments can provide insight into their structure-function relationship. Here we elucidate the dynamics of the vibrational modes driving the IC process within the Q band of a functionalized porphyrin molecule. Through a combination of ultrafast multidimensional spectroscopies and theoretical modeling, we observe a 60 fs Qy-Qx IC and demonstrate that it is driven by the interplay among multiple high-frequency modes. Notably, we identify 1510 cm-1 as the leading tuning mode that brings the porphyrin to an optimal geometry for energy surface crossing. By employing coherent wave packet analysis, we highlight a set of short-lived vibrations (1200-1400 cm-1), promoting the IC within ≈60 fs. Furthermore, we identify one coupling mode (1350 cm-1) that is responsible for vibronic mixing within the Q states. Our findings indicate that porphyrin-core functionalization modulates IC effectively, offering new opportunities in photocatalysis and optoelectronics.

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.

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

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

Development of Two-Dimensional Electronic-Vibrational Sum Frequency Generation (2D-EVSFG) for Vibronic and Solvent Couplings of Molecules at Interfaces and Surfaces

Many photoinduced excited states' relaxation processes and chemical reactions occur at interfaces and surfaces, including charge transfer, energy transfer, proton transfer, proton-coupled electron transfer, configurational dynamics, conical intersections, etc. Of them, interactions of electronic and vibrational motions, namely, vibronic couplings, are the main determining factors for the relaxation processes or reaction pathways. However, time-resolved electronic-vibrational spectroscopy for interfaces and surfaces is lacking. Here we develop interface/surface-specific two-dimensional electronic-vibrational sum frequency generation spectroscopy (2D-EVSFG) for time-dependent vibronic coupling of excited states at interfaces and surfaces. We further demonstrate the fourth-order technique by investigating vibronic coupling, solvent correlation, and time evolution of the coupling for photoexcited interface-active molecules, crystal violet (CV), at the air/water interface as an example. The two vibronic absorption peaks for CV molecules at the interface from the 2D-EVSFG experiments were found to be more prominent than their counterparts in bulk from 2D-EV. Quantitative analysis of the vibronic peaks in 2D-EVSFG suggested that a non-Condon process participates in the photoexcitation of CV at the interface. We further reveal vibrational solvent coupling for the zeroth level on the electronic state with respect to that on the ground state, which is directly related to the magnitude of its change in solvent reorganization energy. The change in the solvent reorganization energy at the interface is much smaller than that in bulk methanol. Time-dependent center line slopes (CLSs) of 2D-EVSFG also showed that kinetic behaviors of CV at the air/water interface are significantly different from those in bulk methanol. Our ultrafast 2D-EVSFG experiments not only offer vibrational information on both excited states and the ground state as compared with the traditional doubly resonant sum frequency generation and electronic-vibrational coupling but also provide vibronic coupling, dynamical solvent effects, and time evolution of vibronic coupling at interfaces.

Coherent Vibronic Wavepackets Show Structure-Directed Charge Flow in Host-Guest Donor-Acceptor Complexes

Designing and controlling charge transfer (CT) pathways in organic semiconductors are important for solar energy applications. To be useful, a photogenerated, Coulombically bound CT exciton must further separate into free charge carriers; direct observations of the detailed CT relaxation pathways, however, are lacking. Here, photoinduced CT and relaxation dynamics in three host-guest complexes, where a perylene (Per) electron donor guest is incorporated into two symmetric and one asymmetric extended viologen cyclophane acceptor hosts, are presented. The central ring in the extended viologen is either p-phenylene (ExV²⁺) or electron-rich 2,5-dimethoxy-p-phenylene (ExMeOV²⁺), resulting in two symmetric cyclophanes with unsubstituted or methoxy-substituted central rings, ExBox⁴⁺ and ExMeOBox⁴⁺, respectively, and an asymmetric cyclophane with one of the central viologen rings being methoxylated ExMeOVBox⁴⁺. Upon photoexcitation, the asymmetric host-guest ExMeOVBox⁴⁺ ⊃ Per complex exhibits directional CT toward the energetically unfavorable methoxylated side due to structural restrictions that facilitate strong interactions between the Per donor and the ExMeOV²⁺ side. The CT state relaxation pathways are probed using ultrafast optical spectroscopy by focusing on coherent vibronic wavepackets, which are used to identify CT relaxations along charge localization and vibronic decoherence coordinates. Specific low- and high-frequency nuclear motions are direct indicators of a delocalized CT state and the degree of CT character. Our results show that the CT pathway can be controlled by subtle chemical modifications of the acceptor host in addition to illustrating how coherent vibronic wavepackets can be used to probe the nature and time evolution of the CT states.

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

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

Time-Evolving Quantum Superpositions in Open Systems and the Rich Content of Coherence Maps

We discuss the general features of the time-evolving reduced density matrix (RDM) of multistate systems coupled to dissipative environments and show that many important aspects of the dynamics are visualized effectively and transparently through coherence maps, defined as snapshots of the real and imaginary components of the RDM on the square grid of system sites. In particular, the spread, signs, and shapes of the coherence maps collectively characterize the state of the system and the nature of the dynamics, as well as the equilibrium state. The topology of the system is readily reflected in its coherence map. Rows and columns show the composition of quantum superpositions, and their filling indicates the extent of the surviving coherence. Linear combinations of imaginary RDM elements specify instantaneous population derivatives. The main diagonal comprises the incoherent component of the dynamics, while the upper/lower triangular areas give rise to coherent contributions that increase the purity of the RDM. In open systems, the coherence map evolves to a band surrounding the principal diagonal whose width decreases with increasing temperature and dissipation strength. We illustrate these behaviors with examples of 10-site model molecular aggregates with Frenkel exciton couplings, where the electronic states of each monomer are coupled to harmonic vibrational baths.

B800-to-B850 relaxation of excitation energy in bacterial light harvesting: All-state, all-mode path integral simulations

We report fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodopseudomonas molischianum at room temperature. The exciton–vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll states of the B850 (inner) ring and the 8 states of the B800 (outer) ring with all available electronic couplings. The electronic states of each chromophore couple to 50 intramolecular vibrational modes with spectroscopically determined Huang–Rhys factors and to a weakly dissipative bath that models the biomolecular environment. Simulations of the excitation energy transfer following photoexcitation of various electronic eigenstates are performed using the numerically exact small matrix decomposition of the quasiadiabatic propagator path integral. We find that the energy relaxation process in the 24-state system is highly nontrivial. When the photoexcited state comprises primarily B800 pigments, a rapid intra-band redistribution of the energy sharply transitions to a significantly slower relaxation component that transfers 90% of the excitation energy to the B850 ring. The mixed character B850* state lacks the slow component and equilibrates very rapidly, providing an alternative energy transfer channel. This (and also another partially mixed) state has an anomalously large equilibrium population, suggesting a shift to lower energy by virtue of exciton–vibration coupling. The spread of the vibrationally dressed states is smaller than that of the eigenstates of the bare electronic Hamiltonian. The total population of the B800 band is found to decay exponentially with a 1/ e time of 0.5 ps, which is in good agreement with experimental results.

π-Stacking-Dependent Vibronic Couplings Drive Excited-State Dynamics in Perylenediimide Assemblies

Vibronic coupling, the interplay of electronic and nuclear vibrational motion, is considered a critical mechanism in photoinduced reactions such as energy transfer, charge transfer, and singlet fission. However, our understanding of how particular vibronic couplings impact excited-state dynamics is lacking due to the limited number of experimental studies of model molecular systems. Herein, we use two-dimensional electronic spectroscopy (2DES) to launch and interrogate a range of vibronic coherences in two distinct types of perylenediimide slip stacks─along the short and long molecular axes, which form either an excimer or a mixed state between the Frenkel exciton (FE) and charge transfer states. We explore the functionality of these vibronic coherences using quantum beatmaps, which display the Fourier amplitude signal oscillations as a function of pump and probe frequencies, along with knowledge of the characteristic signatures of the FE, ionic, and excimer species. We find that a low-frequency vibrational mode of the short-axis slip stack appears concomitantly with the formation of the excimer state, survives 2-fold longer than in the FE state in the reference monomer, and shows a phase shift compared to other modes. For the long-axis slip stacks, a pair of low-frequency modes coupled to a high-frequency coordinate of the FE state were found to play a critical role in mixed-state generation. Our findings thus experimentally reveal the complex and varying roles of vibronic couplings in tightly packed multimers undergoing a range of photoinduced processes.

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.

Synthetic Control of Exciton Dynamics in Bioinspired Cofacial Porphyrin Dimers

Understanding how the complex interplay among excitonic interactions, vibronic couplings, and reorganization energy determines coherence-enabled transport mechanisms is a grand challenge with both foundational implications and potential payoffs for energy science. We use a combined experimental and theoretical approach to show how a modest change in structure may be used to modify the exciton delocalization, tune electronic and vibrational coherences, and alter the mechanism of exciton transfer in covalently linked cofacial Zn-porphyrin dimers (meso-beta linked ABm-β and meso-meso linked AAm-m). While both ABm-β and AAm-m feature zinc porphyrins linked by a 1,2-phenylene bridge, differences in the interporphyrin connectivity set the lateral shift between macrocycles, reducing electronic coupling in ABm-β and resulting in a localized exciton. Pump-probe experiments show that the exciton dynamics is faster by almost an order of magnitude in the strongly coupled AAm-m dimer, and two-dimensional electronic spectroscopy (2DES) identifies a vibronic coherence that is absent in ABm-β. Theoretical studies indicate how the interchromophore interactions in these structures, and their system-bath couplings, influence excitonic delocalization and vibronic coherence-enabled rapid exciton transport dynamics. Real-time path integral calculations reproduce the exciton transfer kinetics observed experimentally and find that the linking-modulated exciton delocalization strongly enhances the contribution of vibronic coherences to the exciton transfer mechanism, and that this coherence accelerates the exciton transfer dynamics. These benchmark molecular design, 2DES, and theoretical studies provide a foundation for directed explorations of nonclassical effects on exciton dynamics in multiporphyrin assemblies.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer

We elucidate the influence of the system–bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

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.

Solvent Effects on Ultrafast Photochemical Pathways

Photochemical reactions are increasingly being used for chemical and materials synthesis, for example, in photoredox catalysis, and generally involve photoexcitation of molecular chromophores dissolved in a liquid solvent. The choice of solvent influences the outcomes of the photochemistry because solute-solvent interactions modify the energies of and crossings between electronic states of the chromophores, and they affect the evolving structures of the photoexcited molecules. Ultrafast laser spectroscopy methods with femtosecond to picosecond time resolution can resolve the dynamics of these photoexcited molecules as they undergo structural and electronic changes, relax back to the ground state, dissipate their excess internal energy to the surrounding solvent, or undergo photochemical reactions. In this Account, we illustrate how experimental studies using ultrafast lasers can reveal the influences that different solvents or cosolutes exert on the photoinduced nonadiabatic dynamics of internal conversion and intersystem crossing in nonradiative relaxation pathways. Although the environment surrounding a solute molecule is rapidly changing, with fluctuations in the coordination to neighboring solvent molecules occurring on femtosecond or picosecond time scales, we show that it is possible to photoexcite selectively only those molecular chromophores transiently experiencing specific solute-solvent interactions such as intermolecular hydrogen bonding.The effects of different solvation environments on the photodynamics are illustrated using four selected examples of photochemical processes in which the solvent has a marked effect on the outcomes. We first consider two aromatic carbonyl compounds, benzophenone and acetophenone, which are known to undergo fast intersystem crossing to populate the first excited triplet state on time scales of a few picoseconds. We show that the nonadiabatic excited-state dynamics are modified by transient hydrogen bonding of the carbonyl group to a protic solvent or by coordination to a metal cation cosolute. We then examine how different solvents modify the competition between two alternative relaxation pathways in a photoexcited UVA-sunscreen molecule, diethylamino hydroxybenzoyl hexyl benzoate (DHHB). This relaxation back to the ground electronic state is an essential part of the effective operation of the sunscreen compound, but the dynamics are sensitive to the surrounding environment. Finally, we consider how solvents of different polarity affect the energies and lifetimes of excited states with locally excited or charge-transfer character in heterocyclic organic compounds used as excited-state electron donors for photoredox catalysis. With these and other examples, we seek to develop a molecular level understanding of how the choice of solution environment might be used to control the outcomes of photochemical reactions.

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.

Low-Frequency Vibronic Mixing Modulates the Excitation Energy Flow in Bacterial Light-Harvesting Complex II

Oscillatory features observed in two-dimensional electronic spectroscopy (2DES) manifest coherent vibrational and electronic dynamics and even the interplay of them. Recently, we developed a 2DES technique utilizing a pair of synchronized repetition-frequency-stabilized lasers, which enables the wide dynamic range measurements of 2DES signals rapidly. Here, we apply this dual-laser 2DES technique to investigate the electronic energy transfer (EET) process in bacterial light-harvesting complex II consisting of B800 and B850 circular aggregates at ambient temperature, and the coherent vibrational wavepakcet associated with the EET between the two aggregates are measured. Examining the principal component analysis of the time-resolved 2DES signal, we found that the EET from B800 to low-lying B850 states is modulated by a low-frequency (156 cm^-1) vibrational mode of the exciton donor (B800). This observation suggests that the donor transition density is modulated by this vibration, which, in turn, modulates the energy transfer dynamics.

2D Electronic Spectroscopic Techniques for Quantum Technology Applications

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

Measuring the Multiscale Dynamics, Structure, and Function of Biomolecules at Interfaces

The individual and collective structure and properties of biomolecules can change dramatically when they are localized at an interface. However, the small spatial extent of interfacial regions poses challenges to the detailed characterization of multiscale processes that dictate the structure and function of large biological units such as peptides, proteins, or nucleic acids. This Perspective surveys a broad set of tools that provide new opportunities to probe complex, dynamic interfaces across the vast range of temporal regimes that connect molecular-scale events to macroscopic observables. An emphasis is placed on the integration over multiple time scales, the use of complementary techniques, and the incorporation of external stimuli to control interfacial properties with spatial, temporal, and chemical specificity.

A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics

We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Influence of Vibronic Coupling on Ultrafast Singlet Fission in a Linear Terrylenediimide Dimer

Singlet fission (SF) is a photophysical process capable of boosting the efficiency of solar cells. Recent experimental investigations into the mechanism of SF provide evidence for coherent mixing between the singlet, triplet, and charge transfer basis states. Up until now, this interpretation has largely focused on electronic interactions; however, nuclear motions resulting in vibronic coupling have been suggested to support rapid and efficient SF in organic chromophore assemblies. Further information about the complex interactions between vibronic excited states is needed to understand the potential role of this coupling in SF. Here, we report mixed singlet and correlated triplet pair states giving rise to sub-50 fs SF in a terrylene-3,4:11,12-bis(dicarboximide) (TDI) dimer in which the two TDI molecules are covalently linked by a direct N-N connection at one of their imide positions, leading to a linear dimer with perpendicular TDI π systems. We observe the transfer of low-frequency coherent wavepackets between the initial predominantly singlet states to the product triplet-dominated states. This implies a non-negligible dependence of SF on nonadiabatic coupling in this dimer. We interpret our experimental results in the framework of a modified Holstein Hamiltonian, which predicts that vibronic interactions between low-frequency singlet modes and high-frequency correlated triplet pair motions lead to mixing of the pure basis states. These results highlight how nonadiabatic mixing can shape the complex potential energy landscape underlying ultrafast SF.

Development of interface-/surface-specific two-dimensional electronic spectroscopy

Structures, kinetics, and chemical reactivities at interfaces and surfaces are key to understanding many of the fundamental scientific problems related to chemical, material, biological, and physical systems. These steady-state and dynamical properties at interfaces and surfaces require even-order techniques with time-resolution and spectral-resolution. Here, we develop fourth-order interface-/surface-specific two-dimensional electronic spectroscopy, including both two-dimensional electronic sum frequency generation (2D-ESFG) spectroscopy and two-dimensional electronic second harmonic generation (2D-ESHG) spectroscopy, for structural and dynamics studies of interfaces and surfaces. The 2D-ESFG and 2D-ESHG techniques were based on a unique laser source of broadband short-wave IR from 1200 nm to 2200 nm from a home-built optical parametric amplifier. With the broadband short-wave IR source, surface spectra cover most of the visible light region from 480 nm to 760 nm. A translating wedge-based identical pulses encoding system (TWINs) was introduced to generate a phase-locked pulse pair for coherent excitation in the 2D-ESFG and 2D-ESHG. As an example, we demonstrated surface dark states and their interactions of the surface states at p-type GaAs (001) surfaces with the 2D-ESFG and 2D-ESHG techniques. These newly developed time-resolved and interface-/surface-specific 2D spectroscopies would bring new information for structure and dynamics at interfaces and surfaces in the fields of the environment, materials, catalysis, and biology.

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.

Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N ² logic variables per N level system. This is how massive parallelism is achieved in that there are N ² potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N ² expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. Here, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

An excited state dynamics driven reaction: wavelength-dependent photoisomerization quantum yields in [Ru(bpy)2(dmso)2]2

We report the excited-state behavior of a structurally simple bis-sulfoxide complex, cis-S,S-[Ru(bpy)2(dmso)2]2+, as investigated by femtosecond pump-probe spectroscopy. The results reveal that a single photon prompts phototriggered isomerization of one or both dmso ligands to yield a mixture of cis-S,O-[Ru(bpy)2(dmso)2]2+ and cis-O,O-[Ru(bpy)2(dmso)2]2+. The quantum yields of isomerization of each product and relative product distribution are dependent upon the excitation wavelength, with longer wavelengths favoring the double isomerization product, cis-O,O-[Ru(bpy)2(dmso)2]2+. Transient absorption measurements on cis-O,O-[Ru(bpy)2(dmso)2]2+ do not reveal an excited-state isomerization pathway to produce either the S,O or S,S isomers. Femtosecond pulse shaping experiments reveal no change in the product distribution. Pump-repump-probe transient absorption spectroscopy of cis-S,S-[Ru(bpy)2(dmso)2]2+ shows that a pump-repump time delay of 3 ps dramatically alters the S,O : O,O product ratio; pump-repump-probe transient absorption spectroscopy of cis-O,O-[Ru(bpy)2(dmso)2]2+ with a time delay of 3 ps uncovers an excited-state isomerization pathway to produce the S,O isomer. In conjunction with low-temperature steady-state emission spectroscopy, these results are interpreted in the context of an excited-state bifurcating pathway, in which the isomerization product distribution is determined not by thermodynamics, but rather as a dynamics driven reaction.

Interface-Specific Two-Dimensional Electronic Sum Frequency Generation Spectroscopy

High even-order surface/interface specific spectroscopy has the potential to provide more structural and dynamical information about surfaces and interfaces. In this work, we developed a novel fourth-order interface-specific two-dimensional electronic sum frequency generation (2D-ESFG) for structures and dynamics at surfaces and interfaces. A translating wedge-based identical pulses encoding system (TWINs) was introduced to generate phase-locked pulse pairs for coherent pump beams in 2D-ESFG. As a proof-of-principle experiment, fourth-order 2D-ESFG spectroscopy was used to demonstrate couplings of surface states for both n-type and p-type GaAs (100). We found surface dark state within the bandgap of the GaAs in 2D-ESFG spectra, which could not be observed in one-dimensional ESFG spectra. To our best knowledge, this is a first demonstration of interface-specific two-dimensional electronic spectroscopy. The development of the 2D-ESFG spectroscopy will provide new structural probes of spectral diffusion, conformational dynamics, energy transfer, and charge transfer for surfaces and interfaces.

Ultrafast XANES Monitors Femtosecond Sequential Structural Evolution in Photoexcited Coenzyme B12

Polarized X-ray absorption near-edge structure (XANES) at the Co K-edge and broadband UV-vis transient absorption are used to monitor the sequential evolution of the excited-state structure of coenzyme B₁₂ (adenosylcobalamin) over the first picosecond following excitation. The initial state is characterized by sub-100 fs sequential changes around the central cobalt. These are polarized first in the y-direction orthogonal to the transition dipole and 50 fs later in the x-direction along the transition dipole. Expansion of the axial bonds follows on a ca. 200 fs time scale as the molecule moves out of the Franck-Condon active region of the potential energy surface. On the same 200 fs time scale there are electronic changes that result in the loss of stimulated emission and the appearance of a strong absorption at 340 nm. These measurements provide a cobalt-centered movie of the excited molecule as it evolves to the local excited-state minimum.

Steric Interactions Impact Vibronic and Vibrational Coherences in Perylenediimide Cyclophanes

Designing molecular systems that exploit vibronic coherence to improve light harvesting efficiencies relies on understanding how interchromophoric interactions, such as van der Waals forces and dipolar coupling, influence these coherences in multichromophoric arrays. However, disentangling these interactions requires studies of molecular systems with tunable structural relationships. Here, we use a combination of two-dimensional electronic spectroscopy and femtosecond stimulated Raman spectroscopy to investigate the role of steric hindrance between chromophores in driving changes to vibronic and vibrational coherences in a series of substituted perylenediimide (PDI) cyclophane dimers. We report significant differences in the frequency power spectra from the cyclophane dimers versus the corresponding monomer reference. We attribute these differences to distortion of the PDI cores from steric interactions between the substituents. These results highlight the importance of considering structural changes when rationalizing vibronic coupling in multichromophoric systems.

Quantum dynamics of vibration-assisted excitation energy transfer in phycobiliprotein light-harvesting complex

Phycobiliprotein is a light-harvesting complex containing linear tetrapyrrole bilin pigments that are responsible for absorption and funneling the sun's energy in cryptophytes algae. In particular, the protein structure determines relative positions and orientations of the pigments and thus controls energy transfer pathways. The present research reveals the impact of molecular vibrations (in the 850-2700 cm^-1 region) on excitation energy transfer in phycobiliprotein. The analysis of the excitation energy transfer pathways indicates a possibility of the coherent mechanism of energy transfer (delocalization) in central dihydrobiliverdin pigments and incoherent vibration-assisted energy transfer to peripheral phycocyanobilin pigments at a sub-picosecond time scale. A computational approach that enables modeling the dynamics of the excitation energy transfer with the quantum master equation formalism employing Huang-Rhys factors to describe electronic-vibrational coupling has been developed. The computational methodology has been implemented in PyFREC software.

Optical spectra in the condensed phase: Capturing anharmonic and vibronic features using dynamic and static approaches

Simulating optical spectra in the condensed phase remains a challenge for theory due to the need to capture spectral signatures arising from anharmonicity and dynamical effects, such as vibronic progressions and asymmetry. As such, numerous simulation methods have been developed that invoke different approximations and vary in their ability to capture different physical regimes. Here, we use several models of chromophores in the condensed phase and ab initio molecular dynamics simulations to rigorously assess the applicability of methods to simulate optical absorption spectra. Specifically, we focus on the ensemble scheme, which can address anharmonic potential energy surfaces but relies on the applicability of extreme nuclear-electronic time scale separation; the Franck-Condon method, which includes dynamical effects but generally only at the harmonic level; and the recently introduced ensemble zero-temperature Franck-Condon approach, which straddles these limits. We also devote particular attention to the performance of methods derived from a cumulant expansion of the energy gap fluctuations and test the ability to approximate the requisite time correlation functions using classical dynamics with quantum correction factors. These results provide insights as to when these methods are applicable and able to capture the features of condensed phase spectra qualitatively and, in some cases, quantitatively across a range of regimes.

Open system dynamics using Gaussian-based multiconfigurational time-dependent Hartree wavefunctions: Application to environment-modulated tunneling

A variational approach for the quantum dynamics of statistical mixtures is developed, which is based upon the representation of the natural states of the mixture in terms of hybrid Gaussian-based Multiconfiguration Time-Dependent Hartree (G-MCTDH) wavefunctions. The method, termed ρG-MCTDH, is combined with a treatment of dissipation and decoherence based on the nonstochastic open-system Schrödinger equations. The performance and the convergence properties of the approach are illustrated for a two-dimensional tunneling system, where the primary tunneling coordinate, represented by flexible single-particle functions, is resonantly coupled to a second harmonic mode, represented by Gaussian wave packets. The harmonic coordinate is coupled to the environment and two different processes are studied: (i) vibrational relaxation at zero temperature described by a master equation in the Lindblad form and (ii) thermalization induced by the Caldeira-Leggett master equation. In the second case, the evolution from a quantum tunneling regime to a quasistationary classical-limit distribution, driven by the heat bath, is visualized using a flux analysis.

Understanding the influence of disorder on the exciton dynamics and energy transfer in Zn-phthalocyanine H-aggregates

The photophysics of 9(19),16(17),23(24)-tri-tert-butyl-2-[ethynyl-(4-carboxymethyl)phenyl]phthalocyaninatozinc(ii) and its H-aggregates is studied in different solvents by means of ultrafast non-linear optical spectroscopy and computational modeling. In non-coordinating solvents, both stationary and time-resolved spectroscopies highlight the formation of extended molecular aggregates, whose dimension and spectral properties depends on the concentration. In all the explored experimental conditions, time-resolved transient absorption experiments show multi exponential decay of the signals. Additional insights into the excited state relaxation mechanisms of the system is obtained with 2D electronic spectroscopy, which is employed to compare the deactivation channels in the absence or presence of aggregates. In ethanol and diethylether, where only monomers are present, an ultrafast relaxation process among the two non-degenerate Q-states of the molecule is evidenced by the appearance of a cross peak in the 2D-maps. In chloroform or CCl4, where disordered H-aggregates are formed, an energy transfer channel among aggregates with different composition and size is observed, leading to the non-radiative decay towards the lower energy dark state of the aggregates. Efficient coupling between less and more aggregated species is highlighted in two-dimensional electronic spectra by the appearance of a cross peak. The kinetics and intensity of the latter depend on the concentration of the solution. Finally, the linear spectroscopic properties of the aggregate are reproduced using a simplified structural model of an extended aggregate, based on Frenkel Hamiltonian Calculations and on an estimate of the electronic couplings between each dimer composing the aggregate computed at DFT level.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.