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

Cutting through the Noise: Extracting Dynamics from Ultrafast Spectra Using Dynamic Mode Decomposition

Coherent multidimensional spectroscopy provides experimental access to molecular structure and subpicosecond dynamics in solution. Dynamics are typically inferred from the evolution of lineshapes over a function of waiting time. Numerous spectral analysis methods, such as center/nodal line slope, have been developed to extract these dynamics. However, the extracted dynamics can depend heavily on subjective choices, such as the region selected for CLS analysis or the chosen models. In this study, we introduce a novel approach to extracting dynamics from ultrafast two-dimensional infrared (2D IR) spectra by using dynamic mode decomposition (DMD). As a data-driven method, DMD directly extracts spatiotemporal structures from the complex 2D IR spectra. We evaluated the performance of DMD in simulated and experimental spectra containing overlapped peaks. We show that DMD can retrieve the dynamics of overlapped transitions and cross peaks that are typically challenging to extract with traditional methods. In addition, we demonstrate that combining conditional generative adversarial neural networks with DMD can recover dynamics even at low signal-to-noise ratios. DMD methods do not require preliminary assumptions and can be readily extended to other multidimensional spectroscopies.

Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality

Two-dimensional spectroscopic techniques combining terahertz (THz), infrared (IR), and visible pulses offer a wealth of information about coupling among vibrational modes in molecular liquids, thus providing a promising probe of their local structure. However, the capabilities of these spectroscopies are still largely unexplored due to experimental limitations and inherently weak nonlinear signals. Here, through a combination of equilibrium-nonequilibrium molecular dynamics (MD) and a tailored spectrum decomposition scheme, we identify a relationship between the tetrahedral order of liquid water and its two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship can explain the temperature dependence of the spectral features corresponding to the anharmonic coupling between low-frequency intermolecular and high-frequency intramolecular vibrational modes of water. In light of these results, we propose new experiments and discuss the implications for the study of tetrahedrality of liquid water.

Low-frequency anharmonic couplings in crystalline bromoform: Theory

Theoretical calculations of the low-frequency anharmonic couplings of the β-phase of crystalline bromoform are presented based on density functional theory quantum chemistry calculations. The electrical and mechanical anharmonicities between intra- and intermolecular modes are calculated, revealing that the electrical anharmonicity dominates the cross-peak intensities in the 2D Raman-THz response and crystalline, as well as liquid, bromoform. Furthermore, the experimentally observed difference in relative cross-peak intensities between the two intramolecular modes of bromoform and the intermolecular modes can be explained by the C_3v-symmetry of bromoform in combination with orientational averaging. The good agreement with the experimental results provides further evidence for our interpretation that the 2D Raman-THz response of bromoform is, indeed, related to the anharmonic coupling between the intra- and intermolecular modes.

Mapping LiNbO_{3} Phonon-Polariton Nonlinearities with 2D THz-THz-Raman Spectroscopy

Two-dimensional terahertz-terahertz-Raman spectroscopy can provide insight into the anharmonicities of low-energy phonon modes-knowledge of which can help develop strategies for coherent control of material properties. Measurements on LiNbO_{3} reveal THz and Raman nonlinear transitions between the E(TO_{1}) and E(TO_{3}) phonon polaritons. Distinct coherence pathways are observed with different THz polarizations. The observed pathways suggest that the origin of the third-order nonlinear responses is due to mechanical anharmonicities, as opposed to electronic anharmonicities. Further, we confirm that the E(TO_{1}) and E(TO_{3}) phonon polaritons are excited through resonant one-photon THz excitation.

Generative Adversarial Neural Networks for Denoising Coherent Multidimensional Spectra

Ultrafast spectroscopy often involves measuring weak signals and long data acquisition times. Spectra are typically collected as a "pump-probe" spectrum by measuring differences in intensity across laser shots. Shot-to-shot intensity fluctuations are most often the primary source of noise in ultrafast spectroscopy. Here, we present a novel approach for denoising ultrafast two-dimensional infrared (2D IR) spectra using conditional generative adversarial neural networks (cGANNs). The cGANN approach is able to eliminate shot-to-shot noise and reconstruct the line shapes present in the noisy input spectrum. We present a general approach for training the cGANN using matched pairs of noisy and clean synthetic 2D IR spectra based on the Kubo-line shape model for a three-level system. Experimental shot-to-shot laser noise is added to synthetic spectra to recreate the noise profile present in measured experimental spectra. The cGANNs can recover line shapes from synthetic 2D IR spectra with signal-to-noise ratios as low as 2:1, while largely preserving the key features such as center frequencies, line widths, and diagonal elongation. In addition, we benchmark the performance of the cGANN using experimental 2D IR spectra of an ester carbonyl vibrational probe and demonstrate that, by applying the cGANN denoising approach, we can extract the frequency-frequency time correlation function (FFCF) from reconstructed spectra using a nodal-line slope analysis. Finally, we provide a set of practical guidelines for extending the denoising method to other coherent multidimensional spectroscopies.

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.

2D-Raman-THz spectroscopy with single-shot THz detection

We present a 2D-Raman-terahertz (THz) setup with multichannel (single-shot) THz detection, utilizing two crossed echelons, in order to reduce the acquisition time of typical 2D-Raman-THz experiments from days to a few hours. This speed-up is obtained in combination with a high repetition rate (100 kHz) Yb-based femtosecond laser system and a correspondingly fast array detector. The wavelength of the Yb-laser (1030 nm) is advantageous, since it assures almost perfect phase matching in GaP for THz generation and detection and since the dispersion in the transmissive echelons is minimal. 2D-Raman-THz test measurements on liquid bromoform (CHBr₃) are reported. An enhancement of a factor ∼5.8 in signal-to-noise ratio is obtained for single-shot detection when compared to conventional step-scanning measurements in the THz time domain, corresponding to a speed-up of acquisition time of ∼34.

Two-dimensional terahertz spectroscopy of condensed-phase molecular systems

Nonlinear terahertz (THz) spectroscopy relies on the interaction of matter with few-cycle THz pulses of electric field amplitudes up to megavolts/centimeter (MV/cm). In condensed-phase molecular systems, both resonant interactions with elementary excitations at low frequencies such as intra- and intermolecular vibrations and nonresonant field-driven processes are relevant. Two-dimensional THz (2D-THz) spectroscopy is a key method for following nonequilibrium processes and dynamics of excitations to decipher the underlying interactions and molecular couplings. This article addresses the state of the art in 2D-THz spectroscopy by discussing the main concepts and illustrating them with recent results. The latter include the response of vibrational excitations in molecular crystals up to the nonperturbative regime of light-matter interaction and field-driven ionization processes and electron transport in liquid water.

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.

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.