Measuring Coherently Coupled Intramolecular Vibrational and Charge-Transfer Dynamics with Two-Dimensional Vibrational-Electronic Spectroscopy

High-Spin State of a Ferrocene Electron Donor Revealed by Optical and X-ray Transient Absorption Spectroscopy

Ferrocene is one of the most common electron donors, and mapping its ligand-field excited states is critical to designing donor-acceptor (D-A) molecules with long-lived charge transfer states. Although 3(d-d) states are commonly invoked in the photophysics of ferrocene complexes, mention of the high-spin 5(d-d) state is scarce. Here, we provide clear evidence of 5(d-d) formation in a bimetallic D-A molecule, ferrocenyl cobaltocenium hexafluorophosphate ([FcCc]PF6). Femtosecond optical transient absorption (OTA) spectroscopy reveals two distinct electronic excited states with 30 and 500 ps lifetimes. Using a combination of ultraviolet, visible, near-infrared, and short-wave infrared probe pulses, we capture the spectral features of these states over an ultrabroadband range spanning 320 to 2200 nm. Time-dependent density functional theory (DFT) calculations of the lowest triplet and quintet states, both primarily Fe(II) (d-d) in character, qualitatively agree with the experimental OTA spectra, allowing us to assign the 30 ps state as the 3(d-d) state and the 500 ps state as the high-spin 5(d-d) state. To confirm the ferrocene-centered high-spin character of the 500 ps state, we performed X-ray transient absorption (XTA) spectroscopy at the Fe and Co K edges. The Fe K-edge XTA spectrum at 150 ps shows a red shift of the absorption edge that is consistent with an Fe(II) high-spin state, as supported by ab initio calculations. The transient signal detected at the Co K-edge is 50× weaker, confirming the ferrocene-centered character of the excited state. Fitting of the transient extended X-ray absorption fine structure region yields an Fe-C bond length increase of 0.25 ± 0.1 Å in the excited state, as expected for the high-spin state based on DFT. Altogether, these results demonstrate that the high-spin state of ferrocene should be considered when designing donor-acceptor assemblies for photocatalysis and photovoltaics.

Modeling Vibrational Sum Frequency Generation Spectra of Interfacial Water on a Gold Surface: The Role of the Fermi Resonance

Studying the hydrogen bonding structure of H2O at the metal-water interface is a highly complex yet fascinating endeavor. The intricate interactions and diverse orientations of water molecules on metal surfaces with varying potentials pose a significant challenge in elucidating the coupling between O-H stretching and H-O-H bending modes. In this study, we employed DFT-MD simulation to explore how the orientation of interfacial water molecules changes with the applied potential on the Au(111) surface. Based on the surface-specific velocity-velocity correlation function (ssVVCF) formula, we calculated vibrational sum frequency generation (VSFG) spectra for the O-H stretches. We found that three assigned peaks (∼3300, ∼3450, and 3650 cm-1) shifted toward lower frequencies as the potential moved toward more negative values. Our results align remarkably well with experimental Raman spectroscopy data. Notably, our VSFG analysis revealed a significant change in the VSFG spectra of the hydrogen-bonded O-H groups (∼3300 cm-1), switching from a negative to a positive sign with decreasing potential. This alteration suggests a substantial change in the orientation of these low-frequency O-H groups owing to their increased interactions with the Au surface. In contrast, the orientations of both the high-frequency O-H groups (∼3450 cm-1) and the dangling O-H groups (∼3650 cm-1) remained unaffected by the applied potentials. Furthermore, our analysis of the decomposed vibrational density of states (VDOS) for the H-O-H bending mode uncovered the coupling between the H-O-H bending and O-H stretching vibrations, known as the Fermi resonance. Our work suggests that the H-O-H bending vibration becomes restricted when water molecules transition from the ″one-H-down″ to the ″two-H-down″ conformation, leading to a redshift in the O-H stretching vibration through the Fermi resonance. By constructing the VSFG and decomposed VDOS spectra, we gained valuable insights into the structural changes that Raman spectra alone cannot fully interpret. Specifically, our analysis revealed the critical role of the Fermi resonance effect in shaping the spectroscopic signature of interfacial water molecules on the Au(111) surface.

A Spectroscopic Method for Distinguishing Two Novel Sandwich-Type Tungsten Oxide Cluster Compounds

This study introduces two novel sandwich-type tungsten-oxygen cluster compounds synthesized by hydrothermal methods, H4(C6H12N2H2)3{Na(H2O)2[Mn2(H2O)(GeW9O34)]}2 (Compound 1) and H2(C6H12N2H2)3.5{Na3(H2O)4[Co2(H2O)(GeW9O34)]2}·17H2O (Compound 2). The two compounds comprise cluster anions [GeW9O34]10- coordinated with transition metal atoms, either Mn or Co, and are stabilized by organic ligands. These compounds are crystallized in the hexagonal crystal system and P63/m space group. The two compounds were characterized through various techniques. Fourier transform infrared (IR) spectroscopy showed absorption peaks of anionic backbone vibrations of the Keggin cluster at 500-1000 cm-1, IR spectral peaks of δ(N-H) and νas(C-N) of the ligand triethylenediamine at 1000-2000 cm-1, and IR spectral peaks of the ligand νas(N-H) and νas(O-H) of water at 3000-3500 cm-1. Despite similar one-dimensional (1D) IR spectra due to the same cluster anions and similar molecular structures, the two compounds exhibited distinct responses in two-dimensional correlation spectroscopy with IR under magnetic and thermal perturbations. Under magnetic perturbation, Compound 1 showed a strong response peak for νas(W-Ob-W), while Compound 2 exhibited a strong response peak for νas(W=Od), possibly linked to differing magnetic particles. Similarly, Compound 1 displayed a strong response peak under thermal perturbation for νas(W-Oc-W). In contrast, Compound 2 showed a strong response peak for νas(W=Od); these results may be attributed to the different hydrogen bonding connections between the two compounds, which affect the groups in distinct ways through vibration and transmit these vibrations to the W-O bonds. The research presented in this paper expands the theoretical and experimental data of 2D correlation IR spectroscopy.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Simulating the isotropic Raman spectra of O-H stretching mode in liquid H2O based on a machine learning potential: the influence of vibrational couplings

In this study, we trained a deep potential (DP) for H2O, an accurate machine learning (ML) potential. We performed molecular dynamics (MD) simulations of liquid water using the DP model (or DeePMD simulations). Our results showed that the DP model exhibits DFT-level accuracy, and the DeePMD simulation is a promising approach for modeling the structural properties of liquid water. Based on the DeePMD simulation trajectories, we calculated the isotropic Raman spectra of the O-H stretching mode using the surface-specific velocity-velocity correlation function (ssVVCF), showing that the DeePMD/ssVVCF approach can correctly capture the bimodal characteristics of the experimental Raman spectra, with one peak located near 3400 cm-1 and the other near 3250 cm-1. The success of the DeePMD/ssVVCF approach should be credited to (1) the DFT-level accuracy of the DP model for H2O, (2) the ssVVCF formulation considering the coupling between vibrational modes, and (3) non-Condon effects. Furthermore, the DeePMD simulations revealed that the anharmonic interactions between the coupled water molecules in the first and second hydration shells should play an essential role in the strong mixing of the H-O-H bending mode and the O-H stretching mode, leading to the delocalization of the O-H stretching band. In particular, increasing the strength of hydrogen bonds would enhance the bend-stretch coupling, leading to the red-shifting of the O-H vibrational spectra and the increase in the intensity of the shoulder around 3250 cm-1.

Ultrafast transient vibrational action spectroscopy of cryogenically cooled ions

Ultrafast transient vibrational action spectra of cryogenically cooled Re(CO)3(CH3CN)3+ ions are presented. Nonlinear spectra were collected in the time domain by monitoring the photodissociation of a weakly bound N2 messenger tag as a function of delay times and phases between a set of three infrared pulses. Frequency-resolved spectra in the carbonyl stretch region show relatively strong bleaching signals that oscillate at the difference frequency between the two observed vibrational features as a function of the pump-probe waiting time. This observation is consistent with the presence of nonlinear pathways resulting from underlying cross-peak signals between the coupled symmetric-asymmetric C≡O stretch pair. The successful demonstration of frequency-resolved ultrafast transient vibrational action spectroscopy of dilute molecular ion ensembles provides an exciting, new framework for the study of molecular dynamics in isolated, complex molecular ion systems.

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.

Vibrationally resolved two-photon electronic spectra including vibrational pre-excitation: Theory and application to VIPER spectroscopy with two-photon excitation

Following up on our previous work on vibrationally resolved electronic absorption spectra including the effect of vibrational pre-excitation [von Cosel et al., J. Chem. Phys. 147, 164116 (2017)], we present a combined theoretical and experimental study of two-photon-induced vibronic transitions in polyatomic molecules that are probed in the VIbrationally Promoted Electronic Resonance experiment using two-photon excitation (2P-VIPER). In order to compute vibronic spectra, we employ time-independent and time-dependent methods based on the evaluation of Franck-Condon overlap integrals and Fourier transformations of time-domain correlation functions, respectively. The time-independent approach uses a generalized version of the FCclasses method, while the time-dependent approach relies on the analytical evaluation of Gaussian moments within the harmonic approximation, including Duschinsky rotation effects. For the Coumarin 6 dye, two-dimensional 2P-VIPER experiments involving excitation to the lowest-lying singlet excited state (S₁) are presented and compared with corresponding one-photon VIPER spectra. In both cases, coumarin ring modes and a CO stretch mode show VIPER activity, albeit with different relative intensities. Selective pre-excitation of these modes leads to a pronounced redshift of the low-frequency edge of the electronic absorption spectrum, which is a prerequisite for the VIPER experiment. Theoretical analysis underscores the role of interference between Franck-Condon and Herzberg-Teller effects in the two-photon experiment, which is at the root of the observed intensity distribution.

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.

Vibrational Modes Promoting Exciton Relaxation in the B850 Band of LH2

Exciton relaxation dynamics in multichromophore systems are often modeled using Redfield theory, where bath fluctuations mediate the relaxation among the exciton eigenstates. Identifying the vibrational or phonon modes that are implicated in exciton relaxation allows more detailed understanding of exciton dynamics. Here we focus on a well-studied light-harvesting II complex (LH2) isolated from the photosynthetic purple bacterium Rhodoblastus acidophilus strain 10050. Using two synchronized mode-locked lasers, we carried out a polarization-dependent two-dimensional electronic spectroscopy (2DES) study of an ultrafast exciton relaxation in the B850 band of LH2. 2DES data with different polarization configurations enable us to investigate the exciton relaxation between the k = ±1 exciton states. Then, we identify vibrational modes coupled to the exciton relaxation by analyzing the coherent wavepackets in the 2DES signals. Focusing on the coherent vibrational wavepackets, the data suggest that certain symmetry-breaking modes of monomeric units play a key role in exciton relaxation.

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.

Femtosecond X-ray Spectroscopy Directly Quantifies Transient Excited-State Mixed Valency

Quantifying charge delocalization associated with short-lived photoexcited states of molecular complexes in solution remains experimentally challenging, requiring local element specific femtosecond experimental probes of time-evolving electron transfer. In this study, we quantify the evolving valence hole charge distribution in the photoexcited charge transfer state of a prototypical mixed valence bimetallic iron-ruthenium complex, [(CN)₅Fe^IICNRu^III(NH₃)₅]^-, in water by combining femtosecond X-ray spectroscopy measurements with time-dependent density functional theory calculations of the excited-state dynamics. We estimate the valence hole charge that accumulated at the Fe atom to be 0.6 ± 0.2, resulting from excited-state metal-to-metal charge transfer, on an ∼60 fs time scale. Our combined experimental and computational approach provides a spectroscopic ruler for quantifying excited-state valency in solvated complexes.

Time-Domain Vibrational Action Spectroscopy of Cryogenically Cooled, Messenger-Tagged Ions Using Ultrafast IR Pulses

Herein, we present the initial steps toward developing a framework that will enable the characterization of photoinitiated dynamics within large molecular ions in the gas phase with temporal and energy resolution. We combine the established techniques of tag-loss action spectroscopy on cryogenically trapped molecular ions with ultrafast vibrational spectroscopy by measuring the linear action spectrum of N₂-tagged protonated diglycine (GlyGlyH⁺·N₂) with an ultrafast infrared (IR) pulse pair. The presented time-domain data demonstrate that the excited-state vibrational populations in the tagged parent ions are modulated by the ultrafast IR pulse pair and encoded through the messenger tag-loss action response. The Fourier transform of the time-domain action interferograms yields the linear frequency-domain vibrational spectrum of the ion ensemble, and we show that this spectrum matches the linear spectrum collected in a traditional manner using a frequency-resolved IR laser. Time- and frequency-domain interpretations of the data are considered and discussed. Finally, we demonstrate the acquisition of nonlinear signals through cross-polarization pump-probe experiments. These results validate the prerequisite first steps of combining tag-loss action spectroscopy with two-dimensional IR spectroscopy for probing dynamics in gas-phase molecular ions.

Coherent Nonlinear Spectroscopy with Multiple Mode-Locked Lasers

Coherent multidimensional spectroscopy has been widely used to study the structure and dynamics of chemical and biological systems. Each ultrashort pulse from a single mode-locked laser is split into multiple pulses by beam splitters. Their arrival times at a given molecular sample are controlled with mechanical time-delay generators for time-resolved measurements of molecular responses. Such nonlinear vibrational, electronic, or vibrational-electronic spectroscopy can now be carried out with multiple mode-locked lasers with highly stabilized repetition and sometimes carrier-envelope-offset frequencies. By precisely controlling the repetition frequencies of multiple mode-locked lasers, one can achieve automatic delay time scanning, known as asynchronous optical sampling, to investigate various relaxation processes associated with photochemical or photobiological phenomena at one sweep in time. In this Perspective, the current developments and applications of multiple mode-locked laser-based techniques to time-resolved nonlinear spectroscopy of chromophores in condensed phases are discussed. The author's perspective on this approach is also presented.

Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang-Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra.

Multimode two-dimensional vibronic spectroscopy. I. Orientational response and polarization-selectivity

Two-dimensional Electronic-Vibrational (2D EV) spectroscopy and two-dimensional Vibrational-Electronic (2D VE) spectroscopy are among the newest additions to the coherent multidimensional spectroscopy toolbox, and they are directly sensitive to vibronic couplings. In this first of two papers, the complete orientational response functions are developed for a model system consisting of two coupled anharmonic oscillators and two electronic states in order to simulate polarization-selective 2D EV and 2D VE spectra with arbitrary combinations of linearly polarized electric fields. Here, we propose analytical methods to isolate desired signals within complicated spectra and to extract the relative orientation between vibrational and vibronic dipole moments of the model system using combinations of polarization-selective 2D EV and 2D VE spectral features. Time-dependent peak amplitudes of coherence peaks are also discussed as means for isolating desired signals within the time-domain. This paper serves as a field guide for using polarization-selective 2D EV and 2D VE spectroscopies to map coupled vibronic coordinates on the molecular frame.

Direct observation of coherent femtosecond solvent reorganization coupled to intramolecular electron transfer

It is well known that the solvent plays a critical role in ultrafast electron-transfer reactions. However, solvent reorganization occurs on multiple length scales, and selectively measuring short-range solute-solvent interactions at the atomic level with femtosecond time resolution remains a challenge. Here we report femtosecond X-ray scattering and emission measurements following photoinduced charge-transfer excitation in a mixed-valence bimetallic (FeⁱⁱRuⁱⁱⁱ) complex in water, and their interpretation using non-equilibrium molecular dynamics simulations. Combined experimental and computational analysis reveals that the charge-transfer excited state has a lifetime of 62 fs and that coherent translational motions of the first solvation shell are coupled to the back electron transfer. Our molecular dynamics simulations identify that the observed coherent translational motions arise from hydrogen bonding changes between the solute and nearby water molecules upon photoexcitation, and have an amplitude of tenths of ångströms, 120-200 cm^-1 frequency and ~100 fs relaxation time. This study provides an atomistic view of coherent solvent reorganization mediating ultrafast intramolecular electron transfer.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and interprotein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an all-encompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semiempirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

Photon echoes and two dimensional spectra of the amide I band of proteins measured by femtosecond IR - Raman spectroscopy

Infrared (IR) and Raman spectroscopy are fundamental techniques in chemistry, allowing the convenient determination of bond specific chemical composition and structure. Over the last decades, ultrafast multidimensional IR approaches using sequences of femtosecond IR pulses have begun to provide a new means of gaining additional information on molecular vibrational couplings, distributions of molecular structures and ultrafast molecular structural dynamics. In this contribution, new approaches to measuring multidimensional spectra involving IR and Raman processes are presented and applied to the study of the amide I band of proteins. Rephasing of the amide I band is observed using dispersed IR-Raman photon echoes and frequency domain 2D-IR-Raman spectra are measured by use of a mid-IR pulse shaper or over a broader spectral range using a tuneable picosecond laser. A simple pulse shaping approach to performing heterodyned time-domain Fourier Transform 2D-IR-Raman spectroscopy is introduced, revealing that the 2D-IR-Raman spectra distinguish homogeneous and inhomogeneous broadening in the same way as the well-established methods of 2D-IR spectroscopy. Across all datasets, the unique dependence of the amide I data on the IR and Raman strengths, vibrational anharmonicities and inhomogeneous broadening provides a fascinating spectroscopic view of the amide I band.

New ultrafast 2D-IR-Raman photon echo spectroscopy techniques are introduced and applied to the structural analysis of proteins.

Determining the Orientation and Vibronic Couplings between Electronic and Vibrational Coordinates with Polarization-Selective Two-Dimensional Vibrational-Electronic Spectroscopy

We experimentally demonstrate polarization-selective two-dimensional (2D) vibrational-electronic (VE) spectroscopy on a transition-metal mixed-valence complex where the cyanide stretching vibrations are coupled to the metal-to-metal charge-transfer transition. A simultaneous fitting of the parallel and crossed polarized 2D VE spectra quantifies the relative vibronic coupling strengths and angles between the charge-transfer transition and three coupled cyanide stretching vibrations in a mode-specific manner. In particular, we find that the bridging vibration, which modulates the distance between the transition-metal centers, is oriented nearly parallel to the charge-transfer axis and is 9 times more strongly coupled to the electronic transition than the radial vibration, which is oriented almost perpendicular to the charge-transfer axis. The results from this experiment allow us to map the spectroscopically observed vibronic coordinates onto the molecular frame providing a general method to spatially resolve vibronic energy transfer on a femtosecond time scale.

Vibronic coherence evolution in multidimensional ultrafast photochemical processes

The complex choreography of electronic, vibrational, and vibronic couplings used by photoexcited molecules to transfer energy efficiently is remarkable, but an unambiguous description of the temporally evolving vibronic states governing these processes has proven experimentally elusive. We use multidimensional electronic-vibrational spectroscopy to identify specific time-dependent excited state vibronic couplings involving multiple electronic states, high-frequency vibrations, and low-frequency vibrations which participate in ultrafast intersystem crossing and subsequent relaxation of a photoexcited transition metal complex. We discover an excited state vibronic mechanism driving long-lived charge separation consisting of an initial electronically-localized vibrational wavepacket which triggers delocalization onto two charge transfer states after propagating for ~600 femtoseconds. Electronic delocalization consequently occurs through nonadiabatic internal conversion driven by a 50 cm^-1 coupling resulting in vibronic coherence transfer lasting for ~1 picosecond. This study showcases the power of multidimensional electronic-vibrational spectroscopy to elucidate complex, non-equilibrium energy and charge transfer mechanisms involving multiple molecular coordinates.

Ultrafast photoinduced energy and charge transfer

After presenting the basic theoretical models of excitation energy transfer and charge transfer, I describe some of the novel experimental methods used to probe them. Finally, I discuss recent results concerning ultrafast energy and charge transfer in biological systems, in chemical systems and in photovoltaics based on sensitized transition metal oxides.

Multispectral multidimensional spectrometer spanning the ultraviolet to the mid-infrared

Multidimensional spectroscopy is the optical analog to nuclear magnetic resonance, probing dynamical processes with ultrafast time resolution. At optical frequencies, the technical challenges of multidimensional spectroscopy have hindered its progress until recently, where advances in laser sources and pulse-shaping have removed many obstacles to its implementation. Multidimensional spectroscopy in the visible and infrared (IR) regimes has already enabled respective advances in our understanding of photosynthesis and the structural rearrangements of liquid water. A frontier of ultrafast spectroscopy is to extend and combine multidimensional techniques and frequency ranges, which have been largely restricted to operating in the distinct visible or IR regimes. By employing two independent amplifiers seeded by a single oscillator, it is straightforward to span a wide range of time scales (femtoseconds to seconds), all of which are often relevant to the most important energy conversion and catalysis problems in chemistry, physics, and materials science. Complex condensed phase systems have optical transitions spanning the ultraviolet (UV) to the IR and exhibit dynamics relevant to function on time scales of femtoseconds to seconds and beyond. We describe the development of the Multispectral Multidimensional Nonlinear Spectrometer (MMDS) to enable studies of dynamical processes in atomic, molecular, and material systems spanning femtoseconds to seconds, from the UV to the IR regimes. The MMDS employs pulse-shaping methods to provide an easy-to-use instrument with an unprecedented spectral range that enables unique combination spectroscopies. We demonstrate the multispectral capabilities of the MMDS on several model systems.

Implementation of continuous fast scanning detection in femtosecond Fourier-transform two-dimensional vibrational-electronic spectroscopy to decrease data acquisition time

Femtosecond Fourier transform two-dimensional vibrational-electronic (2D VE) spectroscopy is a recently developed third-order nonlinear spectroscopic technique to measure coupled electronic and vibrational motions in the condensed phase. The viability of femtosecond multidimensional spectroscopy as an analytical tool requires improvements in data collection and processing to enhance the signal-to-noise ratio and increase the amount of data collected in these experiments. Here a continuous fast scanning technique for the efficient collection of 2D VE spectroscopy is described. The resulting 2D VE spectroscopic method gains sensitivity by reducing the effect of laser drift, as well as decreasing the data collection time by a factor of 10 for acquiring spectra with a high signal-to-noise ratio within 3 dB of the more time intensive step scanning methods. This work opens the door to more comprehensive studies where 2D VE spectra can be collected as a function of external parameters such as temperature, pH, and polarization of the input electric fields.

Electronic Interactions in the Bacterial Reaction Center Revealed by Two-Color 2D Electronic Spectroscopy

The bacterial reaction center (BRC) serves as an important model system for understanding the charge separation processes in photosynthesis. Knowledge of the electronic structure of the BRC is critical for understanding its charge separation mechanism. While it is well-accepted that the "special pair" pigments are strongly coupled, the degree of coupling among other BRC pigments has been thought to be relatively weak. Here we study the W(M250)V mutant BRC by two-color two-dimensional electronic spectroscopy to correlate changes in the Q _x region with excitation of the Q _y transitions. The resulting Q _y-Q _x cross-peaks provide a sensitive measure of the electronic interactions throughout the BRC pigment network and complement one-color 2D studies in which such interactions are often obscured by energy transfer and excited-state absorption signals. Our observations should motivate the refinement of electronic structure models of the BRC to facilitate improved understanding of the charge separation mechanism.

Signatures of vibronic coupling in two-dimensional electronic-vibrational and vibrational-electronic spectroscopies

Two-Dimensional Electronic-Vibrational (2D EV) spectroscopy and Two-Dimensional Vibrational-Electronic (2D VE) spectroscopy are new coherent four-wave mixing spectroscopies that utilize both electronically resonant and vibrationally resonant field-matter interactions to elucidate couplings between electronic and vibrational degrees of freedom. A system Hamiltonian is developed here to lay a foundation for interpreting the 2D EV and 2D VE signals that arise from a vibronically coupled molecular system in the condensed phase. A molecular system consisting of one anharmonic vibration and two electronic states is modeled. Equilibrium displacement of the vibrational coordinate and vibrational frequency shifts upon excitation to the first electronic excited state are included in our Hamiltonian through linear and quadratic vibronic coupling terms. We explicitly consider the nuclear dependence of the electronic transition dipole moment and demonstrate that these spectroscopies are sensitive to non-Condon effects. A series of simulations of 2D EV and 2D VE spectra obtained by varying parameters of the system, system-bath, and interaction Hamiltonians demonstrate that one of the following conditions must be met to observe signals: (1) non-zero linear and/or quadratic vibronic coupling in the electronic excited state, (2) vibrational-coordinate dependence of the electronic transition dipole moment, or (3) electronic-state-dependent vibrational dephasing dynamics. We explore how these vibronic interactions are manifested in the positions, amplitudes, and line shapes of the peaks in 2D EV and 2D VE spectroscopies.

Two-Dimensional Spectroscopy Is Being Used to Address Core Scientific Questions in Biology and Materials Science

Two-dimensional spectroscopy is a powerful tool for extracting structural and dynamic information from a wide range of chemical systems. We provide a brief overview of the ways in which two-dimensional visible and infrared spectroscopies are being applied to elucidate fundamental details of important processes in biological and materials science. The topics covered include amyloid proteins, photosynthetic complexes, ion channels, photovoltaics, batteries, as well as a variety of promising new methods in two-dimensional spectroscopy.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Ultrafast structural molecular dynamics investigated with 2D infrared spectroscopy methods

Ultrafast, multi-dimensional infrared (IR) spectroscopy has been advanced in recent years to a versatile analytical tool with a broad range of applications to elucidate molecular structure on ultrafast timescales, and it can be used for samples in a many different environments. Following a short and general introduction on the benefits of 2D IR spectroscopy, the first part of this chapter contains a brief discussion on basic descriptions and conceptual considerations of 2D IR spectroscopy. Outstanding classical applications of 2D IR are used afterwards to highlight the strengths and basic applicability of the method. This includes the identification of vibrational coupling in molecules, characterization of spectral diffusion dynamics, chemical exchange of chemical bond formation and breaking, as well as dynamics of intra- and intermolecular energy transfer for molecules in bulk solution and thin films. In the second part, several important, recently developed variants and new applications of 2D IR spectroscopy are introduced. These methods focus on (i) applications to molecules under two- and three-dimensional confinement, (ii) the combination of 2D IR with electrochemistry, (iii) ultrafast 2D IR in conjunction with diffraction-limited microscopy, (iv) several variants of non-equilibrium 2D IR spectroscopy such as transient 2D IR and 3D IR, and (v) extensions of the pump and probe spectral regions for multi-dimensional vibrational spectroscopy towards mixed vibrational-electronic spectroscopies. In light of these examples, the important open scientific and conceptual questions with regard to intra- and intermolecular dynamics are highlighted. Such questions can be tackled with the existing arsenal of experimental variants of 2D IR spectroscopy to promote the understanding of fundamentally new aspects in chemistry, biology and materials science. The final part of the chapter introduces several concepts of currently performed technical developments, which aim at exploiting 2D IR spectroscopy as an analytical tool. Such developments embrace the combination of 2D IR spectroscopy and plasmonic spectroscopy for ultrasensitive analytics, merging 2D IR spectroscopy with ultra-high-resolution microscopy (nanoscopy), future variants of transient 2D IR methods, or 2D IR in conjunction with microfluidics. It is expected that these techniques will allow for groundbreaking research in many new areas of natural sciences.

Fourier transform two-dimensional electronic-vibrational spectroscopy using an octave-spanning mid-IR probe

The development of coherent Fourier transform two-dimensional electronic-vibrational (2D EV) spectroscopy with acousto-optic pulse-shaper-generated near-UV pump pulses and an octave-spanning broadband mid-IR probe pulse is detailed. A 2D EV spectrum of a silicon wafer demonstrates the full experimental capability of this experiment, and a 2D EV spectrum of dissolved hexacyanoferrate establishes the viability of our 2D EV experiment for studying condensed phase molecular ensembles.

Two-dimensional vibrational-electronic spectroscopy

Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([Fe(III)(CN)6](3-) dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5Fe(II)CNRu(III)(NH3)5](-) dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

Investigating vibrational relaxation in cyanide-bridged transition metal mixed-valence complexes using two-dimensional infrared and infrared pump-probe spectroscopies

Using polarization-selective two-dimensional infrared (2D IR) and infrared pump-probe spectroscopies, we study vibrational relaxation of the four cyanide stretching (νCN) vibrations found in [(NH3)5Ru(III)NCFe(II)(CN)5](-) (FeRu) dissolved in D2O or formamide and [(NC)5Fe(II)CNPt(IV)(NH3)4NCFe(II)(CN)5](4-) (FePtFe) dissolved in D2O. These cyanide-bridged transition metal complexes serve as models for understanding the role high frequency vibrational modes play in metal-to-metal charge transfers over a bridging ligand. However, there is currently little information about vibrational relaxation and dephasing dynamics of the anharmonically coupled νCN modes in the electronic ground state of these complexes. IR pump-probe experiments reveal that the vibrational lifetimes of the νCN modes are ∼2 times faster when FeRu is dissolved in D2O versus formamide. They also reveal that the vibrational lifetimes of the νCN modes of FePtFe in D2O are almost four times as long as for FeRu in D2O. Combined with mode-specific relaxation dynamics measured from the 2D IR experiments, the IR pump-probe experiments also reveal that intramolecular vibrational relaxation is occurring in all three systems on ∼1 ps timescale. Center line slope dynamics, which have been shown to be a measure of the frequency-frequency correlation function, reveal that the radial, axial, and trans νCN modes exhibit a ∼3 ps timescale for frequency fluctuations. This timescale is attributed to the forming and breaking of hydrogen bonds between each mode and the solvent. The results presented here along with our previous work on FeRu and FePtFe reveal a picture of coupled anharmonic νCN modes where the spectral diffusion and vibrational relaxation dynamics depend on the spatial localization of the mode on the molecular complex and its specific interaction with the solvent.

Watching the dynamics of electrons and atoms at work in solar energy conversion

The photochemical reactions performed by transition metal complexes have been proposed as viable routes towards solar energy conversion and storage into other forms that can be conveniently used in our everyday applications. In order to develop efficient materials, it is necessary to identify, characterize and optimize the elementary steps of the entire process on the atomic scale. To this end, we have studied the photoinduced electronic and structural dynamics in two heterobimetallic ruthenium–cobalt dyads, which belong to the large family of donor–bridge–acceptor systems. Using a combination of ultrafast optical and X-ray absorption spectroscopies, we can clock the light-driven electron transfer processes with element and spin sensitivity. In addition, the changes in local structure around the two metal centers are monitored. These experiments show that the nature of the connecting bridge is decisive for controlling the forward and the backward electron transfer rates, a result supported by quantum chemistry calculations. More generally, this work illustrates how ultrafast optical and X-ray techniques can disentangle the influence of spin, electronic and nuclear factors on the intramolecular electron transfer process. Finally, some implications for further improving the design of bridged sensitizer-catalysts utilizing the presented methodology are outlined.