Two-dimensional vibrational spectroscopy. III. Theoretical description of the coherent two-dimensional IR-Raman spectroscopy for the investigation of the coupling between both IR- and Raman-active vibrational modes

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopies provides access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, Centroid Molecular Dynamics (CMD) and Ring Polymer Molecular Dynamics (RPMD) naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

Distinguishing different excitation pathways in two-dimensional terahertz-infrared-visible spectroscopy

In condensed molecular matter, low-frequency modes (LFMs) associated with specific molecular motions are excited at room temperature and determine essential physical and chemical properties of materials. LFMs, with typical mode energies of up to ∼500 cm^-1 (62 meV), contribute significantly to thermodynamic parameters and functions (e.g., heat capacity and entropy) and constitute the basis for room temperature molecular dynamics (e.g., conformational fluctuations and change). LFMs are often analyzed indirectly by the measurement of their effect on specific high-frequency modes (HFMs); the LFM-HFM coupling is reflected in the lineshape, as well as in the spectral and angular diffusion of the HFM. Two-dimensional terahertz-infrared-visible (2D TIRV) spectroscopy allows measuring the LFM-HFM coupling directly and can thereby provide new insights into the strength and nature of the coupling and the character of LFMs. However, the interference between the different signals generated by different excitation pathways can complicate 2D TIRV spectra, preventing a straightforward analysis. Here, we develop an experimental method to distinguish different excitation pathways in 2D TIRV spectroscopy and plot them separately in different quadrants of a 2D spectrum. We validate this method by measuring the spectra of CaF₂ and nitrogen gas. For CaF₂, only sum-frequency mixing between infrared and terahertz fields generates the signal. In contrast, for N₂, only difference-frequency mixing is observed. We then use this method to separate sum- and difference-frequency pathways in the 2D TIRV spectrum of liquid water, verifying the previous interpretation of the lineshape of the 2D TIRV spectrum of water.

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.

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.

Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy

The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.

Coherent two-dimensional terahertz-terahertz-Raman spectroscopy

We present 2D terahertz-terahertz-Raman (2D TTR) spectroscopy, the first technique, to our knowledge, to interrogate a liquid with multiple pulses of terahertz (THz) light. This hybrid approach isolates nonlinear signatures in isotropic media, and is sensitive to the coupling and anharmonicity of thermally activated THz modes that play a central role in liquid-phase chemistry. Specifically, by varying the timing between two intense THz pulses, we control the orientational alignment of molecules in a liquid, and nonlinearly excite vibrational coherences. A comparison of experimental and simulated 2D TTR spectra of bromoform (CHBr3), carbon tetrachloride (CCl4), and dibromodichloromethane (CBr2Cl2) shows previously unobserved off-diagonal anharmonic coupling between thermally populated vibrational modes.

Notes on simulating two-dimensional Raman and terahertz-Raman signals with a full molecular dynamics simulation approach

Recent developments in two-dimensional (2D) THz-Raman and 2D Raman spectroscopies have created the possibility for quantitatively investigating the role of many dynamic and structural aspects of the molecular system. We explain the significant points for properly simulating 2D vibrational spectroscopic studies of intermolecular modes using the full molecular dynamics approach, in particular, regarding the system size, the treatment of the thermostat, and inclusion of an Ewald summation for the induced polarizability. Moreover, using the simulation results for water employing various polarization functions, we elucidate the roles of permanent and induced optical properties in determining the 2D profiles of the signal.

Calculating fifth-order Raman signals for various molecular liquids by equilibrium and nonequilibrium hybrid molecular dynamics simulation algorithms

The fifth-order two-dimensional (2D) Raman signals have been calculated from the equilibrium and nonequilibrium (finite field) molecular dynamics simulations. The equilibrium method evaluates response functions with equilibrium trajectories, while the nonequilibrium method calculates a molecular polarizability from nonequilibrium trajectories for different pulse configurations and sequences. In this paper, we introduce an efficient algorithm which hybridizes the existing two methods to avoid the time-consuming calculations of the stability matrices which are inherent in the equilibrium method. Using nonequilibrium trajectories for a single laser excitation, we are able to dramatically simplify the sampling process. With this approach, the 2D Raman signals for liquid xenon, carbon disulfide, water, acetonitrile, and formamide are calculated and discussed. Intensities of 2D Raman signals are also estimated and the peak strength of formamide is found to be only five times smaller than that of carbon disulfide.

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.

Higher-order optical correlation spectroscopy in liquids

Linear optical spectroscopies have long been used to study the behavior of liquids. Laser technology has progressed to the point that it has become possible to perform nonlinear optical experiments that probe higher-order correlation functions in liquids, opening a new window into our understanding of the microscopic details of solution-phase processes. Here we review advances that have been made in recent years in employing higher-order electronic and vibrational spectroscopies to study liquid-state dynamics and structure.