Two‐dimensional femtosecond vibrational spectroscopy of liquids

Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of a Single Molecule

Single-molecule fluorescence spectroscopy is a powerful method that avoids ensemble averaging, but its temporal resolution is limited by the fluorescence lifetime to nanoseconds at most. At the ensemble level, two-dimensional spectroscopy provides insight into ultrafast femtosecond processes, such as energy transfer and line broadening, even beyond the Fourier limit, by correlating pump and probe spectra. Here, we combine these two techniques and demonstrate coherent 2D spectroscopy of individual dibenzoterrylene (DBT) molecules at room temperature. We excite the molecule in a confocal microscope with a phase-modulated train of femtosecond pulses and detect the emitted fluorescence with single-photon counting detectors. Using a phase-sensitive detection scheme, we were able to measure the nonlinear 2D spectra of most of the DBT molecules that we studied. Our method is applicable to a wide range of single emitters and opens new avenues for understanding energy transfer in single quantum objects on ultrafast time scales.

Elucidating phonon dephasing mechanisms in layered perovskites with coherent Raman spectroscopies

Organic-inorganic hybrid perovskite quantum wells exhibit electronic structures with properties intermediate between those of inorganic semiconductors and molecular crystals. In these systems, periodic layers of organic spacer molecules occupy the interstitial spaces between perovskite sheets, thereby confining electronic excitations to two dimensions. Here, we investigate spectroscopic line broadening mechanisms for phonons coupled to excitons in lead-iodide layered perovskites with phenyl ethyl ammonium (PEA) and azobenzene ethyl ammonium (AzoEA) spacer cations. Using a modified Elliot line shape analysis for the absorbance and photoluminescence spectra, polaron binding energies of 11.2 and 17.5 meV are calculated for (PEA)2PbI4 and (AzoEA)2PbI4, respectively. To determine whether the polaron stabilization processes influence the dephasing mechanisms of coupled phonons, five-pulse coherent Raman spectroscopies are applied to the two systems under electronically resonant conditions. The prominence of inhomogeneous line broadening mechanisms detected in (AzoEA)2PbI4 suggests that thermal fluctuations involving the deformable organic phase broaden the distributions of phonon frequencies within the quantum wells. In addition, our data indicate that polaron stabilization primarily involves photoinduced reorganization of the organic phases for both systems, whereas the impulsively excited phonons represent less than 10% of the total polaron binding energy. The signal generation mechanisms associated with our fifth-order coherent Raman experiments are explored with a perturbative model in which cumulant expansions are used to account for time-coincident vibrational dephasing and polaron stabilization processes.

Gaining Insights into the Interplay between Optical and Magnetic Properties in Photoexcited Coordination Compounds

We describe early and recent advances in the fascinating field of combined magnetic and optical properties of inorganic coordination compounds and in particular of 3d-4f single molecule magnets. We cover various applied techniques which allow for the correlation of results obtained in the frequency and time domain in order to highlight the specific properties of these compounds and the future challenges towards multidimensional spectroscopic tools. An important point is to understand the details of the interplay of magnetic and optical properties through performing time-resolved studies in the presence of external fields especially magnetic ones. This will enable further exploration of this fundamental interactions i. e. the two components of electromagnetic radiation influencing optical properties.

Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.

Low-Frequency Spectra of Hydrated Ionic Liquids with Kosmotropic and Chaotropic Anions

In this study, we investigated the water concentration dependence of the intermolecular vibrations of two hydrated ionic liquids (ILs), cholinium dihydrogen phosphate ([ch][dhp]) and cholinium bromide ([ch]Br), using femtosecond Raman-induced Kerr effect spectroscopy (fs-RIKES). The anions of the former and latter hydrated ILs are kosmotropic and chaotropic, respectively. We found that the spectral peak of ∼50 cm-1 shifted to the low-frequency side in hydrated [ch][dhp], indicating the weakening of its intermolecular interactions. In contrast, no change in the peak frequency of the low-frequency band at ∼50 cm-1 was observed with increasing water concentration in hydrated [ch]Br. The vibrational density of states (VDOS) spectra generated from molecular dynamics (MD) simulations were in qualitative agreement with the experimental results. Decomposition analysis of the VDOS spectra for each component revealed that the red shift of the low-frequency band in the hydrated [ch][dhp] upon water addition was essentially due to the contributions of anions and water rather than that of the cholinium cation. We also found from the low-frequency spectra of the two hydrated ILs that they differed in the concentration dependence of the 180 cm-1 band, which is assigned as a hindered translational motion of water molecules combined to form O···O stretching motions. From the relationship between the peak frequency of the low-frequency band and the bulk parameter, which is the square root of the surface tension divided by the density, we found that the peak frequency in the hydrated IL with kosmotropic [dhp]- depends on the bulk parameter, similar to the case for an aqueous solution of the typical deep eutectic solvent reline. However, the peak frequency of the hydrated IL with chaotropic Br- is constant with the bulk parameter.

Probing avoided crossings and conical intersections by two-pulse femtosecond stimulated Raman spectroscopy: Theoretical study

This study leverages two-pulse femtosecond stimulated Raman spectroscopy (2FSRS) to characterize molecular systems with avoided crossings (ACs) and conical intersections (CIs) in their low-lying excited electronic states. By simulating 2FSRS spectra of microscopically inspired ACs and CIs models, we demonstrate that 2FSRS not only delivers valuable information on the molecular parameters characterizing ACs and CIs but also helps distinguish between these two systems.

Beyond the Condon limit: Condensed phase optical spectra from atomistic simulations

While dark transitions made bright by molecular motions determine the optoelectronic properties of many materials, simulating such non-Condon effects in condensed phase spectroscopy remains a fundamental challenge. We derive a Gaussian theory to predict and analyze condensed phase optical spectra beyond the Condon limit. Our theory introduces novel quantities that encode how nuclear motions modulate the energy gap and transition dipole of electronic transitions in the form of spectral densities. By formulating the theory through a statistical framework of thermal averages and fluctuations, we circumvent the limitations of widely used microscopically harmonic theories, allowing us to tackle systems with generally anharmonic atomistic interactions and non-Condon fluctuations of arbitrary strength. We show how to calculate these spectral densities using first-principles simulations, capturing realistic molecular interactions and incorporating finite-temperature, disorder, and dynamical effects. Our theory accurately predicts the spectra of systems known to exhibit strong non-Condon effects (phenolate in various solvents) and reveals distinct mechanisms for electronic peak splitting: timescale separation of modes that tune non-Condon effects and spectral interference from correlated energy gap and transition dipole fluctuations. We further introduce analysis tools to identify how intramolecular vibrations, solute-solvent interactions, and environmental polarization effects impact dark transitions. Moreover, we prove an upper bound on the strength of cross correlated energy gap and transition dipole fluctuations, thereby elucidating a simple condition that a system must follow for our theory to accurately predict its spectrum.

Rapid-Scan Resonant Two-Dimensional Impulsive Stimulated Raman Spectroscopy of Excited States

Photochemical reactions occur in the electronically excited state, which is effectively represented by a multidimensional potential energy surface (PES) with a vast degree of freedom of nuclear coordinates. The elucidation of the intricate shape of the PES constitutes an important topic in the field of photochemistry and has long been studied both experimentally and theoretically. Recently, fully time-domain resonant two-dimensional Raman spectroscopy has emerged as a potentially powerful tool to provide unique information about the coupling between vibrational manifolds in the excited state. However, the wide application of this technique has been significantly hampered by the technical difficulties associated with experimental implementation and remains challenging. Herein, we demonstrate time-domain resonant two-dimensional impulsive stimulated Raman spectroscopy (2D-ISRS) of excited states using sub-10 fs pulses based on the rapid scan of the time delay, which facilitates the efficient collection of time-domain vibrational signals with high sensitivity. As a proof-of-principle experiment, we performed 2D-ISRS of 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-pentacene) in solution. Through 2D Fourier transformation of the high-quality time-time oscillatory signal, we obtained a 2D frequency-frequency correlation map of excited-state TIPS-pentacene in the broad frequency window of 0-2000 cm^-1. The data clearly resolve a number of cross peaks that signify the correlations among excited-state vibrational manifolds. The high capability of the rapid-scan-based 2D-ISRS spectrometer presented in this study enables the systematic investigation of various photochemical reaction systems, thereby further promoting the understanding and applications of this new multidimensional spectroscopy.

Simulation of two-dimensional infrared Raman spectroscopy with application to proteins

Two-dimensional infrared Raman spectroscopy is a powerful technique for studying the structure and interaction in molecular and biological systems. Here, we present a new implementation of the simulation of the two-dimensional infrared Raman signals. The implementation builds on the numerical integration of the Schrödinger equation approach. It combines the prediction of dynamics from molecular dynamics with a map-based approach for obtaining Hamiltonian trajectories and response function calculations. The new implementation is tested on the amide-I region for two proteins, where one is dominated by α-helices and the other by β-sheets. We find that the predicted spectra agree well with experimental observations. We further find that the two-dimensional infrared Raman spectra at least of the studied proteins are much less sensitive to the laser polarization used compared to conventional two-dimensional infrared experiments. The present implementation and findings pave the way for future applications for the interpretation of two-dimensional infrared Raman spectra.

Discretized hierarchical equations of motion in mixed Liouville-Wigner space for two-dimensional vibrational spectroscopies of liquid water

A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space, with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.

Absolute excited state molecular geometries revealed by resonance Raman signals

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

Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems

The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems. Its applicability has so far been limited to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles, equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy, and long-time stability. Moreover, the technique can directly be implemented in other approaches such as Green's function, stochastic, and pseudomode formulations. As one highly nontrivial application, for the subohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.

Optically Induced Anisotropy in Time-Resolved Scattering: Imaging Molecular-Scale Structure and Dynamics in Disordered Media with Experiment and Theory

Time-resolved scattering experiments enable imaging of materials at the molecular scale with femtosecond time resolution. However, in disordered media they provide access to just one radial dimension thus limiting the study of orientational structure and dynamics. Here we introduce a rigorous and practical theoretical framework for predicting and interpreting experiments combining optically induced anisotropy and time-resolved scattering. Using impulsive nuclear Raman and ultrafast x-ray scattering experiments of chloroform and simulations, we demonstrate that this framework can accurately predict and elucidate both the spatial and temporal features of these experiments.

Low-frequency anharmonic couplings in bromoform revealed from 2D Raman-THz spectroscopy: from the liquid to the crystalline phase

Two-dimensional (2D) Raman-THz spectroscopy in the frequency up to 7 THz has been applied to study the crystalline beta-phase of bromoform (CHBr3). As for liquid CHBr3, cross peaks are observed, which however sharpen up in the crystalline sample and split into assignable sub-contributions. In the Raman dimension, the frequency positions of these cross peaks coincide with the intramolecular bending modes of the CHBr3 molecules, and in the THz dimension with the IR active lattice modes of the crystal. This work expands the applicability of this new 2D spectroscopic technique to solid samples at cryogenic temperatures. Furthermore, it provides new experimental evidence that the cross peaks indeed originate from the coupling between intra- and intermolecular vibrational modes.

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

Transient measurement of phononic states with covariance-based stochastic spectroscopy

We present a novel approach to transient Raman spectroscopy, which combines stochastic probe pulses and a covariance-based detection to measure stimulated Raman signals in alpha-quartz. A coherent broadband pump is used to simultaneously impulsively excite a range of different phonon modes, and the phase, amplitude, and energy of each mode are independently recovered as a function of the pump-probe delay by a noisy-probe and covariance-based analysis. Our experimental results and the associated theoretical description demonstrate the feasibility of 2D-Raman experiments based on the stochastic-probe schemes, with new capabilities not available in equivalent mean-value-based 2D-Raman techniques. This work unlocks the gate for nonlinear spectroscopies to capitalize on the information hidden within the noise and overlooked by a mean-value analysis.

Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrödinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.

Computational spectroscopy of complex systems

Numerous linear and non-linear spectroscopic techniques have been developed to elucidate structural and functional information of complex systems ranging from natural systems, such as proteins and light-harvesting systems, to synthetic systems, such as solar cell materials and light-emitting diodes. The obtained experimental data can be challenging to interpret due to the complexity and potential overlapping spectral signatures. Therefore, computational spectroscopy plays a crucial role in the interpretation and understanding of spectral observables of complex systems. Computational modeling of various spectroscopic techniques has seen significant developments in the past decade, when it comes to the systems that can be addressed, the size and complexity of the sample types, the accuracy of the methods, and the spectroscopic techniques that can be addressed. In this Perspective, I will review the computational spectroscopy methods that have been developed and applied for infrared and visible spectroscopies in the condensed phase. I will discuss some of the questions that this has allowed answering. Finally, I will discuss current and future challenges and how these may be addressed.

Direct comparison of amplitude and geometric measures of spectral inhomogeneity using phase-cycled 2D-IR spectroscopy

Two-dimensional infrared (2D-IR) spectroscopy provides access to equilibrium dynamics with the extraction of the frequency-fluctuation correlation function (FFCF) from the measured spectra. Several different methods of obtaining the FFCF from experimental spectra, such as the center line slope (CLS), ellipticity, phase slope, and nodal line slope, all depend on the geometrical nature of the 2D line shape and necessarily require spectral extent in order to achieve a measure of the FFCF. Amplitude measures, on the other hand, such as the inhomogeneity index, rely only on signal amplitudes and can, in principle, be computed using just a single point in a 2D spectrum. With a pulse shaper-based 2D-IR spectrometer, in conjunction with phase cycling, we separate the rephasing and nonrephasing signals used to determine the inhomogeneity index. The same measured data provide the absorptive spectrum, needed for the CLS. Both methods are applied to two model molecular systems: tungsten hexacarbonyl (WCO₆) and methylcyclopentadienyl manganese tricarbonyl [Cp'Mn(CO)₃, MCMT]. The three degenerate IR modes of W(CO)₆ lack coherent modulation or noticeable intramolecular vibrational redistribution (IVR) and are used to establish a baseline comparison. The two bands of the MCMT tripod complex include intraband coherences and IVR as well as likely internal torsional motion on a few-picosecond time scale. We find essentially identical spectral diffusion, but faster, non-equilibrium dynamics lead to differences in the FFCFs extracted with the two methods. The inhomogeneity index offers an advantage in cases where spectra are complex and energy transfer can mimic line shape changes due to frequency fluctuations.

Frequency comb-based multidimensional coherent spectroscopy bridges the gap between fundamental science and cutting-edge technology

Optical multidimensional coherent spectroscopy (MDCS) has become a powerful and routine technique for studying optical properties of a wide range of materials. However, current implementations of MDCS have spectral resolution and acquisition speed limitations. In this Perspective, I describe how frequency comb technology can be used to overcome the limitations and also show the recent progress that has been made in this field.

Full molecular dynamics simulations of molecular liquids for single-beam spectrally controlled two-dimensional Raman spectroscopy

Single-beam spectrally controlled (SBSC) two-dimensional (2D) Raman spectroscopy is a unique 2D vibrational measurement technique utilizing trains of short pulses that are generated from a single broadband pulse by pulse shaping. This approach overcomes the difficulty of 2D Raman spectroscopy in dealing with small-signal extraction and avoids complicated low-order cascading effects, thus providing a new possibility for measuring the intramolecular and intermolecular modes of molecular liquids using fifth-order 2D Raman spectroscopy. Recently, for quantitatively investigating the mode-mode coupling mechanism, Hurwitz et al. [Opt. Express 28, 3803 (2020)] have developed a new pulse design for this measurement to separate the contributions of the fifth- and third-order polarizations, which are often overlapped in the original single-beam measurements. Here, we describe a method for simulating these original measurements and the new 2D Raman measurements on the basis of a second-order response function approach. We carry out full molecular dynamics simulations for carbon tetrachloride and liquid water using an equilibrium-nonequilibrium hybrid algorithm, with the aim of explaining the key features of the SBSC 2D Raman spectroscopic method from a theoretical point of view. The predicted signal profiles and intensities provide valuable information that can be applied to 2D spectroscopy experiments, allowing them to be carried out more efficiently.

Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

Observation of Ultrafast Coherence Transfer and Degenerate States with Polarization-Controlled Two-Dimensional Electronic Spectroscopy

Optical spectroscopy is a powerful tool to interrogate quantum states of matter. We present simulation results for the cross-polarized two-dimensional electronic spectra of the light-harvesting system LH2 of purple bacteria. We identify a spectral feature on the diagonal, which we assign to ultrafast coherence transfer between degenerate states. The implication for the interpretation of previous experiments on different systems and the potential use of this feature are discussed. In particular, we foresee that this kind of feature will be useful for identifying mixed degenerate states and for identifying the origin of symmetry breaking disorder in systems like LH2. Furthermore, this may help identify both vibrational and electronic states in biological systems such as proteins and solid-state materials such as hybrid perovskites.

"On-The-Fly" Calculation of the Vibrational Sum-Frequency Generation Spectrum at the Air-Water Interface

In the present work, we provide an electronic structure based method for the "on-the-fly" determination of vibrational sum frequency generation (v-SFG) spectra. The predictive power of this scheme is demonstrated at the air-water interface. While the instantaneous fluctuations in dipole moment are obtained using the maximally localized Wannier functions, the fluctuations in polarizability are approximated to be proportional to the second moment of Wannier functions. The spectrum henceforth obtained captures the signatures of hydrogen bond stretching, bending, as well as low-frequency librational modes.

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.

A Feynman diagram description of the 2D-Raman-THz response of amorphous ice

The 2D-Raman-THz response in all possible time-orderings (Raman-THz-THz, THz-Raman-THz, and THz-THz-Raman) of amorphous water ice is calculated in two ways: from atomistic molecular dynamics simulations and with the help of a Feynman diagram model, the latter of which power-expands the potential energy surface and the dipole and polarizability surfaces up to leading order. Comparing both results allows one to dissect the 2D-Raman-THz response into contributions from mechanical anharmonicity, as well as electrical dipole and polarizability anharmonicities. Mechanical anharmonicity dominates the 2D-Raman-THz response of the hydrogen-bond stretching and hydrogen-bond bending bands of water, and dipole anharmonicity dominates that of the librational band, while the contribution of polarizability anharmonicity is comparably weak. A distinct echo of the hydrogen-bond stretching band is observed for the THz-Raman-THz pulse sequence, again dominated by mechanical anharmonicity. A peculiar mechanism is discussed, which is based on the coupling between the many normal modes within the hydrogen-bond stretching band and which will inevitably generate such an echo for an amorphous structure.

Two-dimensional Raman spectroscopy of Lennard-Jones liquids via ring-polymer molecular dynamics

The simulation of multidimensional vibrational spectroscopy of condensed-phase systems including nuclear quantum effects is challenging since full quantum-mechanical calculations are still intractable for large systems comprising many degrees of freedom. Here, we apply the recently developed double Kubo transform (DKT) methodology in combination with ring-polymer molecular dynamics (RPMD) for evaluating multi-time correlation functions [K. A. Jung et al., J. Chem. Phys. 148, 244105 (2018)], providing a practical method for incorporating nuclear quantum effects in nonlinear spectroscopy of condensed-phase systems. We showcase the DKT approach in the simulation of the fifth-order two-dimensional (2D) Raman spectroscopy of Lennard-Jones liquids as a prototypical example, which involves nontrivial nonlinear spectroscopic observables of systems described by anharmonic potentials. Our results show that the DKT can faithfully reproduce the 2D Raman response of liquid xenon at high temperatures, where the system behaves classically. In contrast, liquid neon at low temperatures exhibits moderate but discernible nuclear quantum effects in the 2D Raman response compared to the responses obtained with classical molecular dynamics approaches. Thus, the DKT formalism in combination with RPMD simulations enables simulations of multidimensional optical spectroscopy of condensed-phase systems that partially account for nuclear quantum effects.

Hierarchical equations of motion method based on Fano spectrum decomposition for low temperature environments

The hierarchical equations of motion (HEOM) method has become one of the most popular methods for the studies of the open quantum system. However, its applicability to systems at ultra-low temperatures is largely restrained by the enormous computational cost, which is caused by the numerous exponential functions required to accurately characterize the non-Markovian memory of the reservoir environment. To overcome this problem, a Fano spectrum decomposition (FSD) scheme has been proposed recently [Cui et al., J. Chem. Phys. 151, 024110 (2019)], which expands the reservoir correlation functions using polynomial-exponential functions and hence greatly reduces the size of the memory basis set. In this work, we explicitly establish the FSD-based HEOM formalisms for both bosonic and fermionic environments. The accuracy and efficiency of the FSD-based HEOM are exemplified by the calculated low-temperature dissipative dynamics of a spin-boson model and the dynamic and static properties of a single-orbital Anderson impurity model in the Kondo regime. The encouraging numerical results highlight the practicality and usefulness of the FSD-based HEOM method for general open systems at ultra-low temperatures.

Single beam low frequency 2D Raman spectroscopy

Low frequency Raman spectroscopy resolves the slow vibrations resulting from collective motions of molecular structures. This frequency region is extremely challenging to access via other multidimensional methods such as 2D-IR. In this paper, we describe a new scheme which measures 2D Raman spectra in the low frequency regime. We separate the pulse into a spectrally shaped pump and a transform-limited probe, which can be distinguished by their polarization states. Low frequency 2D Raman spectra in liquid tetrabromoethane are presented, revealing coupling dynamics at frequencies as low as 115 cm^-1. The experimental results are supported by numerical simulations which replicate the key features of the measurement. This method opens the door for the deeper exploration of vibrational energy surfaces in complex molecular structures.

Broadband Impulsive Stimulated Raman Scattering Based on a Chirped Detection

In impulsive stimulated Raman scattering, vibrational oscillations, coherently stimulated by a femtosecond Raman pulse, are monitored in real time and read out as intensity modulations in the transmission of a temporally delayed probe pulse. Critically, in order to retrieve broadband Raman spectra, a fine sampling of the time delays between the Raman and probe pulses is required, making conventional ISRS ineffective for probing irreversible phenomena and/or weak scatterers typically demanding long acquisition times, with signal-to-noise ratios that crucially depend on the pulse fluences and overlap stabilities. To overcome such limitations, here we introduce the chirped-based impulsive stimulated raman scattering (CISRS) technique. Specifically, we show how introducing a chirp in the probe pulse can be exploited for recording the Raman information without the need to scan over the Raman-probe pulse delay. We then experimentally demonstrate with a few examples how to use the introduced scheme to measure Raman spectra.

Manipulating nonadiabatic conical intersection dynamics by optical cavities

Optical cavities hold great promise to manipulate and control the photochemistry of molecules. We demonstrate how molecular photochemical processes can be manipulated by strong light-matter coupling. For a molecule with an inherent conical intersection, optical cavities can induce significant changes in the nonadiabatic dynamics by either splitting the pristine conical intersections into two novel polaritonic conical intersections or by creating light-induced avoided crossings in the polaritonic surfaces. This is demonstrated by exact real-time quantum dynamics simulations of a three-state two-mode model of pyrazine strongly coupled to a single cavity photon mode. We further explore the effects of external environments through dissipative polaritonic dynamics computed using the hierarchical equation of motion method. We find that cavity-controlled photochemistry can be immune to external environments. We also demonstrate that the polariton-induced changes in the dynamics can be monitored by transient absorption spectroscopy.

Signatures of Intra- and Intermolecular Vibrational Coupling in Halogenated Liquids Revealed by Two-Dimensional Raman-Terahertz Spectroscopy

Hybrid two-dimensional (2D) Raman-terahertz spectroscopy with the Raman-terahertz-terahertz (RTT) pulse sequence is used to explore the ultrafast intra- and intermolecular degrees of freedom of liquid bromoform (CHBr₃) in the frequency range of 1-8 THz. Cross peaks observed in these 2D spectra are assigned to the coupling between the narrow intramolecular modes of the molecules and the much broader intermolecular degrees of freedom of the liquid. This assignment is based on the frequency position of the cross peaks; however, it is shown that these frequency positions can be deduced accurately only when properly taking into account the convolution of the molecular response with the instrument response function of the experimental setup, the latter of which distorts the 2D spectra considerably. The assignment is supported by additional experiments on diiodomethane (CH₂I₂), which has only one intramolecular mode in the frequency range of the experiment, and hence excludes the possibility of intramolecular couplings.

Fifth-order time-domain Raman spectroscopy of photoactive yellow protein for visualizing vibrational coupling in its excited state

We report fifth-order time-domain Raman spectroscopy of photoactive yellow protein (PYP), with the aim to visualize vibrational coupling in its excited state. After the ultrashort actinic pump pulse prepared the vibrational coherence and population in the excited state, the evolving vibrational structure was tracked by time-resolved impulsive stimulated Raman spectroscopy using sub-7-fs pulses. The obtained fifth-order time-domain Raman data were translated to a two-dimensional (2D) frequency-frequency correlation map, which visualizes the correlation between low- and high-frequency vibrational modes of the excited state. The 2D map of PYP reveals a cross peak, indicating the coupling between the phenolic C─O stretch mode of the chromophore and the low-frequency modes (~160 cm^-1), assignable to the intermolecular motions involving the surrounding hydrogen-bonded amino acids. The unveiled coupling suggests the importance of the low-frequency vibrational motion in the primary photoreaction of PYP, highlighting the unique capability of this spectroscopic approach for studying ultrafast reaction dynamics.

Impact of nuclear quantum effects on the structural inhomogeneity of liquid water

The 2D Raman-terahertz (THz) response of liquid water is studied in dependence of temperature and isotope substitution ([Formula: see text]O, [Formula: see text]O, and [Formula: see text]O). In either case, a very short-lived (i.e., between 75 and 95 fs) echo is observed that reports on the inhomogeneity of the low-frequency intermolecular modes and hence, on the heterogeneity of the hydrogen bond networks of water. The echo lifetime slows down by about 20% when cooling the liquid from room temperature to the freezing point. Furthermore, the echo lifetime of [Formula: see text]O is [Formula: see text] slower than that of [Formula: see text]O, and both can be mapped on each other by introducing an effective temperature shift of [Formula: see text] K. In contrast, the temperature-dependent echo lifetimes of [Formula: see text]O and [Formula: see text]O are the same within error. [Formula: see text]O and [Formula: see text]O have identical masses, yet [Formula: see text]O is much closer to [Formula: see text]O in terms of nuclear quantum effects. It is, therefore, concluded that the echo is a measure of the structural inhomogeneity of liquid water induced by nuclear quantum effects.

Conducting Excitation and Emission Spectra in the IR Regime: Frequency-Domain Time-Resolved Vibrational Four Wave Mixing Spectroscopy

We report new features of recently developed ultrafast coherent multidimensional spectroscopy (CMDS), an optical analogue to multidimensional NMR. By using both frequency- and time-domain nonlinear four wave mixing methods, CMDS is able to directly observe coherence transfer (CT), the coherent quantum mechanical analogue of population relaxation. Using a mixture of acetonitrile and magnesium perchlorate (1.0 M) as a model system, we demonstrated that this one color- and population-involving CT process makes CMDS capable of measuring samples with features that mimic excitation and emission spectral measurements in fluorescence spectroscopy. With the new capabilities, one might develop CMDS into a versatile vibrational tool for revealing the role of coherence as a design element in realizing a function. Furthermore, CT-based vibrational resonance energy transfer (VRET) methods may be developed for label-free biosensing and imaging, such as those demonstrated by fluorescence resonance energy transfer (FRET).

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.

Structural analysis of transient reaction intermediate in formic acid dehydrogenation catalysis using two-dimensional IR spectroscopy

The molecular structure of a catalytically active key intermediate is determined in solution by employing 2D IR spectroscopy measuring vibrational cross-angles. The formate intermediate (2) in the formic acid dehydrogenation reaction catalyzed by a phosphorus-nitrogen PN3P-Ru catalyst is elucidated. Our spectroscopic studies show that the complex features a formate ion directly attached to the Ru center as a ligand, and a proton added to the imine arm of the dearomatized PN3P* ligand. During the catalytic process, the imine arms are not only reversibly protonated and deprotonated, but also interacting with the protic substrate molecules, effectively serving as the local proton buffer to offer remarkable stability with a turnover number (TON) over one million.

Coupling between intra- and intermolecular motions in liquid water revealed by two-dimensional terahertz-infrared-visible spectroscopy

The interaction between intramolecular and intermolecular degrees of freedom in liquid water underlies fundamental chemical and physical phenomena such as energy dissipation and proton transfer. Yet, it has been challenging to elucidate the coupling between these different types of modes. Here, we report on the direct observation and quantification of the coupling between intermolecular and intramolecular coordinates using two-dimensional, ultra-broadband, terahertz-infrared-visible (2D TIRV) spectroscopy and molecular dynamics calculations. Our study reveals strong coupling of the O-H stretch vibration, independent of the degree of delocalization of this high-frequency mode, to low-frequency intermolecular motions over a wide frequency range from 50 to 250 cm-1, corresponding to both the intermolecular hydrogen bond bending (≈ 60 cm-1) and stretching (≈ 180 cm-1) modes. Our results provide mechanistic insights into the coupling of the O-H stretch vibration to collective, delocalized intermolecular modes.