Vibrational Dephasing along the Reaction Coordinate of an Electron Transfer Reaction

Anharmonically Coupled Vibrational Scaffolds for Energy Dissipation in a Terpyridine-Aldehyde Ligand

The role of intramolecular vibrational energy redistribution is critical when considering the thermal properties of coordination complexes. The interactions and redistribution of vibrational energy can be uncovered through the use of two-dimensional infrared (2D IR) spectroscopy by observing the cross-peaks between different vibrational signatures. In this study, the energetic landscape consisting of the vibrations of [6,2':6',2″-terpyridine]-2-carbaldehyde (terpyCHO) is studied directly in the region between 1400 and 1740 cm-1. Information on the anharmonic coupling between different groups of vibrations estimates the delocalization in the detected normal modes. The delocalization of the aldehyde stretch is directly comparable to that calculated from density functional theory (DFT) calculations and local mode analysis via the LModeA program, a freeware that can characterize the normal modes in terms of a nonredundant set of local modes. Tracking of the relative cross-peak intensities as a function of the waiting time reveals a complex network of energy exchange pathways responsible for energy dissipation and vibrational dephasing. These dynamics reveal the aldehyde to be an efficient inlet and outlet of vibrational energy flow and the C-H bends as energetic dumps with the pyridine ring stretches acting as bridging modes between them. Finally, signatures of vibrational coherences are observed in the diagonal peak dynamics of the 2D IR data, further revealing a network of couplings to lower energy modes that mediate this energy exchange. These findings provide new insights into the energetic landscape of organic molecules potentially useful as ligands in single molecule magnets.

Tracking nuclear wave packets in excited-state reactions via quantum mechanics/molecular dynamics simulations

Nuclear wave packets (NWPs) in electronically excited states generated by ultrashort laser pulses can persist through photochemical processes and be detected in the product state. The NWPs that are coupled with the reaction dynamics undergo changes during the process and provide crucial insights into potential energy surfaces and molecular reaction dynamics. We present a computational method to calculate NWPs in the products of ultrafast photochemical processes by projecting nuclear displacements, obtained via Born-Oppenheimer molecular dynamics simulations, onto the normal modes of the reaction product state. Applying this approach to the excited-state intramolecular proton transfer reaction of 10-hydroxybenzo[h]quinoline, we successfully reproduced the experimentally observed NWPs in the reaction product, which were measured by time-resolved fluorescence of the product state with high fidelity. This significant achievement enables the analysis of individual normal mode motions following photoexcitation in chemical and physical processes. By integrating highly time-resolved spectroscopy with computational modeling, this method provides an effective approach to investigate the excited-state potential energy surfaces and the associated nuclear dynamics.

Ultrafast Spectroscopy and Dynamics of Photoredox Catalysis

Photoredox catalysis has emerged as a powerful platform for chemical synthesis, utilizing chromophore excited states as selective energy stores to surmount chemical activation barriers toward making desirable products. Developments in this field have pushed synthetic chemists to design and discover new photocatalysts with novel and impactful photoreactivity but also with uncharacterized excited states and only an approximate mechanistic understanding. This review highlights specific instances in which ultrafast spectroscopies dissected the photophysical and photochemical dynamics of new classes of photoredox catalysts and their photochemical reactions. After briefly introducing the photophysical processes and ultrafast spectroscopic methods central to this topic, the review describes selected recent examples that evoke distinct classes of photoredox catalysts with demonstrated synthetic utility and ultrafast spectroscopic characterization. This review cements the significant role of ultrafast spectroscopy in modern photocatalyzed organic transformations and institutionalizes the developing intersection of synthetic organic chemistry and physical chemistry.

A numerically exact description of ultrafast vibrational decoherence in vibration-coupled electron transfer

Broadband pump-probe spectroscopy has been widely used to measure vibrational decoherence associated with the reaction coordinate in photoinduced ultrafast vibration-coupled electron transfer (VCET) reactions. These experiments provide insight into the interplay of intramolecular coordinates along the reaction coordinate. However, a general theoretical foundation for analyzing, and even for explaining rigorously, these data is lacking. In this work, we study vibrational decoherence in a model VCET reaction using the nearly exact time-dependent density matrix renormalization group simulation method. We explore how analyzing the density matrix with quantum information measures can help elucidate the evolution of vibrational coherence in simulations of dynamics. We examine how vibrational coherence is affected by electron transfer on the timescale of approximately 100 femtoseconds. Our results suggest that electron transfer, in the nonadiabatic model, changes the vibrational equilibrium position abruptly-an example of a "quantum quench" event. This explains the concomitant vibrational decoherence. We find that abrupt vibrational decoherence can be mitigated by wavepacket motion occurring on the timescale of the electron transfer.

Coherence in Chemistry: Foundations and Frontiers

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

From Coherence to Function: Exploring the Connection in Chemical Systems

ConspectusThe role of quantum mechanical coherences or coherent superposition states in excited state processes has received considerable attention in the last two decades largely due to advancements in ultrafast laser spectroscopy. These coherence effects hold promise for enhancing the efficiency and robustness of functionally relevant processes, even when confronted with energy disorder and environmental fluctuations. Understanding coherence deeply drives us to unravel mechanisms and dynamics controlled by order and synchronization at a quantum mechanical level, envisioning optical control of coherence to enhance functions or create new ones in molecular and material systems. In this frontier, the interplay between electronic and vibrational dynamics, specifically the influence of vibrations in directing electronic dynamics, has emerged as the leading principle. Here, two energetically disparate quantum degrees of freedom work in-sync to dictate the trajectory of an excited state reaction. Moreover, with the vibrational degree being directly related to the structural composition of molecular or material systems, new molecular designs could be inspired by tailoring certain structural elements.In the realm of chemical kinetics, our understanding of the dynamics of chemical transformations is underpinned by fundamental theories, such as transition state theory, activated rate theory, and Marcus theory. These theories elucidate reaction rates by considering the energy barriers that must be overcome for reactants to transform into products. Those barriers are surmounted by the stochastic nature of energy gap fluctuations within reacting systems, emphasizing that the reaction coordinate, the pathway from reactants to products, is not rigidly defined by a specific vibrational motion but encompasses a diverse array of molecular motions. While less is known about the involvement of specific intramolecular vibrational modes, their significance in certain cases cannot be overlooked.In this Account, we summarize key experimental findings that offer deeper insights into the complex electronic-vibrational trajectories encompassing excited states afforded from state-of-the-art ultrafast laser spectroscopy in three exemplary processes: photoinduced electron transfer, singlet-triplet intersystem crossing, and intramolecular vibrational energy flow in molecular systems. We delve into the rapid decoherence, or loss of phase and amplitude correlations, of vibrational coherences along promoter vibrations during subpicosecond intersystem crossing dynamics in a series of binuclear platinum complexes. This rapid decoherence illustrates the vibration-driven reactive pathways from the Franck-Condon state to the curve crossing region. We also explore the generation of new vibrational coherences induced by impulsive reaction dynamics rather than by the laser pulse in these systems, which sheds light on specific energy dissipation pathways and thereby on the progression of the reaction trajectory in the vicinity of the curve crossing on the product side. Another property of vibrational coherences, amplitude, reveals how energy can flow from one vibration to another in the electronic excited state of a terpyridine-molybdenum complex hosting a nonreactive dinitrogen substrate. A slight change in vibrational energy triggers a quasi-resonant interaction, leading to constructive wavepacket interference and ultimately intramolecular vibrational redistribution from a Franck-Condon active terpyridine vibration to a dinitrogen stretching vibration, energizing the dinitrogen bond.

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.

Nitrile Vibrational Lifetimes as Probes of Local Electric Fields

Optical measurements of electric fields have wide-ranging applications in the fields of chemistry and biology. Previously, such measurements focused on shifts in intensity or frequency. Here, we show that nitrile vibrational lifetimes can report local electric fields through ultrasensitive picosecond mid-infrared-near-infrared double-resonance fluorescence spectro-microscopy on Rhodamine 800. Using a robust convolution fitting approach, we observe that the nitrile vibrational lifetimes are strongly linearly correlated (R2 = 0.841) with solvent reaction fields. Supported by density functional theory, we rationalize this trend through a doorway model of intramolecular vibrational energy redistribution. This work provides new fundamental insights into the nature of vibrational energy flow in large polyatomic molecular systems and establishes a theoretical basis for electric field sensing with vibrational lifetimes, offering a new experimental dimension for probing intracellular electrostatics.

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.

Time-resolved vibrational dynamics: Novel opportunities for sensing and imaging

The evolution of time-resolved spectroscopies has resulted in significant advancements across numerous scientific disciplines, particularly those concerned with molecular electronic states. However, the intricacy of molecular vibrational spectroscopies, which provide comprehensive molecular-level information within complex structures, has presented considerable challenges due to the ultrashort dephasing time. Over recent decades, an increasing focus has been placed on exploring the temporal progression of bond vibrations, thereby facilitating an improved understanding of energy redistribution within and between molecules. This review article focuses on an array of time-resolved detection methodologies, each distinguished by unique technological attributes that offer exclusive capabilities for investigating the physical phenomena propelled by molecular vibrational dynamics. In summary, time-resolved vibrational spectroscopy emerges as a potent instrument for deciphering the dynamic behavior of molecules. Its potential for driving future progress across fields as diverse as biology and materials science is substantial, marking a promising future for this innovative tool.

What is cooking in your kitchen: seeing "invisible" with time-resolved coherent anti-Stokes Raman spectroscopy

Cooking oil is a critical component of human food and its main component, lipid, is influential to health, but assessing its authenticity and quality can be challenging due to its complex chemical composition. In this study, we introduce a novel application of time-resolved coherent anti-Stokes Raman scattering (T-CARS) spectroscopy for detecting adulteration and understanding the mechanisms of lipid oxidation in various cooking oils. Our research surpasses the limitations of conventional spontaneous Raman spectroscopy, demonstrating that intra-molecular interactions from unsaturated bonds in triglycerides significantly influence vibrational dephasing time. We observed that these dephasing times, although diverse initially, converge to a similar value after heating cycles. Notably, a longer vibrational dephasing of the CH2 symmetric stretching mode was found to correlate with a higher lipid oxidation rate. These findings underscore the potential of T-CARS in identifying and characterizing subtle molecular interactions, offering a transformative approach to understanding molecular dynamics. This research paves the way for broader applications of T-CARS across fields such as chemistry, biomedicine, and material science, marking a significant advancement in the development of innovative analytical techniques.

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.

Equatorial restriction of the photoinduced Jahn-Teller switch in Mn(iii)-cyclam complexes

Ultrafast transient absorption spectra were recorded for solutions of [Mn^III(cyclam)(H₂O)(OTf)][OTf]₂ (cyclam = 1,4,8,11-tetraazacyclotetradecane and OTf = trifluoromethanesulfonate) in water to explore the possibility to restrict the equatorial expansion following photoexcitation of the d_xy ← d_z² electronic transition, often resulting in a switch from axial to equatorial Jahn-Teller distortion in Mn^III complexes. Strong oscillations were observed in the excited state absorption signal and were attributed to an excited state wavepacket. The structural rigidity of the cyclam ligand causes a complex reaction coordinate with frequencies of 333, 368, 454 and 517 cm^-1, and a significantly shorter compressed-state lifetime compared to other Mn^III complexes with less restricted equatorial ligands. Complementary density functional theory quantum chemistry calculations indicate a switch from an axially elongated to a compressed structure in the first excited quintet state Q₁, which is accompanied by a modulation of the axial tilt angle. Computed harmonic frequencies for the axial stretching mode (∼379 cm^-1) and the equatorial expansions (∼410 and 503 cm^-1) of the Q₁ state agree well with the observed coherences and indicate that the axial bond length contraction is significantly larger than the equatorial expansion, which implies a successful restriction of the wavepacket motion. The weak oscillation observed around 517 cm^-1 is assigned to a see-saw motion of the axial tilt (predicted ∼610 cm^-1). The results provide insights into the structural perturbations to the molecular evolution along excited state potential energy surfaces of Mn^III octahedral complexes and can be used to guide the synthesis of optically controlled Mn^III-based single-molecule magnets.

Excited-State THz Vibrations in Aggregates of PtII Complexes Contribute to the Enhancement of Near-Infrared Emission Efficiencies

The exploration of deactivation mechanisms for near-infrared(NIR)-emissive organic molecules has been a key issue in chemistry, materials science and molecular biology. In this study, based on transient absorption spectroscopy and transient grating photoluminescence spectroscopy, we demonstrate that the aggregated PtII complex 4H (efficient NIR emitter) exhibits collective out-of-plane motions with a frequency of 32 cm-1 (0.96 THz) in the excited states. Importantly, similar THz characteristics were also observed in analogous PtII complexes with prominent NIR emission efficiency. The conservation of THz motions enables excited-state deactivation to proceed along low-frequency vibrational coordinates, contributing to the suppression of nonradiative decay and remarkable NIR emission. These novel results highlight the significance of excited-state vibrations in nonradiative processes, which serve as a benchmark for improving device performance.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Dephasing Dynamics across Different Local Vibrational Modes and Crystalline Environments

The perturbed free induction decay (PFID) observed in ultrafast infrared spectroscopy was used to unveil the rates at which different vibrational modes of the same atomic-scale defect can interact with their environment. The N_{3}VH^{0} defect in diamond provided a model system, allowing a comparison of stretch and bend vibrational modes within different crystal lattice environments. The observed bend mode (first overtone) exhibited dephasing times T_{2}=2.8(1)  ps, while the fundamental stretch mode had surprisingly faster dynamics T_{2}<1.7  ps driven by its more direct perturbation of the crystal lattice, with increased phonon coupling. Further, at high defect concentrations the stretch mode's dephasing rate was enhanced. The ability to reliably measure T_{2} via PFID provides vital insights into how vibrational systems interact with their local environment.

Ultrafast Symmetry-Breaking Charge Separation in a Perylene Bisimide Dimer Enabled by Vibronic Coupling and Breakdown of Adiabaticity

Perylene bisimides (PBIs) have received great attention in their applicability to optoelectronics. Especially, symmetry-breaking charge separation (SB-CS) in PBIs has been investigated to mimic the efficient light capturing and charge generation in natural light-harvesting systems. However, unlike ultrafast CS dynamics in donor-acceptor heterojunction materials, ultrafast SB-CS in a stacked homodimer has still been challenging due to excimer formation in the absence of rigidifying surroundings such as a special pair in the natural systems. Herein, we present the detailed mechanism of ultrafast photoinduced SB-CS occurring in a 1,7-bis(N-pyrrolidinyl) PBI dimer within a cyclophane. Through narrow-band and broad-band transient absorption spectroscopy, we demonstrate that ultrafast SB-CS in the dimer is enabled by the combination of (1) vibrationally coherent charge-transfer resonance-enhanced excimer formation and (2) breakdown of adiabaticity (formation of SB-CS diabats) in the excimer state via structural and solvent fluctuation. Quantum chemical calculations also underpin that the participation of strong electron-donating substituents in overall vibrational modes plays a crucial role in triggering the ultrafast SB-CS. Therefore, our work provides an alternative route to facilitate ultrafast SB-CS in PBIs and thereby establishes a novel strategy for the design of optoelectronic materials.

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.

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.

Reaction dynamics studied via femtosecond X-ray liquidography at X-ray free-electron lasers

X-ray free-electron lasers (XFELs) provide femtosecond X-ray pulses suitable for pump–probe time-resolved studies with a femtosecond time resolution. Since the advent of the first XFEL in 2009, recent years have witnessed a great number of applications with various pump–probe techniques at XFELs. Among these, time-resolved X-ray liquidography (TRXL) is a powerful method for visualizing structural dynamics in the liquid solution phase. Here, we classify various chemical and biological molecular systems studied via femtosecond TRXL (fs-TRXL) at XFELs, depending on the focus of the studied process, into (i) bond cleavage and formation, (ii) charge distribution and electron transfer, (iii) orientational dynamics, (iv) solvation dynamics, (v) coherent nuclear wavepacket dynamics, and (vi) protein structural dynamics, and provide a brief review on each category. We also lay out a plausible roadmap for future fs-TRXL studies for areas that have not been explored yet.

Femtosecond X-ray liquidography using X-ray free-electron lasers (XFELs) visualizes various aspects of reaction dynamics.