A Case Study in the Molecular Interpretation of Optical Kerr Effect Spectra: Instantaneous-Normal-Mode Analysis of the OKE Spectrum of Liquid Benzene

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.

Exploring the Microscopic Aspects of 1-Methyl-3-octylimidazolium Tetrafluoroborate Mixtures with Formamide, N-Methylformamide, and N,N-Dimethylformamide by Multiple Spectroscopic Techniques and Computations

The microscopic aspects of 1-methyl-3-octylimidazolium tetrafluoroborate ([MOIm][BF₄]) mixtures with formamide (FA), N-methylformamide (NMF), and N,N-dimethylformamide (DMF) were investigated using spectroscopic techniques of femtosecond Raman-induced Kerr effect spectroscopy (fs-RIKES), FT-IR, and NMR. Molecular dynamics simulations and quantum chemistry calculations were also performed. According to fs-RIKES, the first moment of the low-frequency spectrum bands mainly originating from the intermolecular vibrations in the [MOIm][BF₄]/FA and [MOIm][BF₄]/DMF systems changed gradually with the molecular liquid mole fraction X_ML but that in the [MOIm][BF₄]/NMF system was constant up to X_NMF = 0.7 and then gradually increased in the range of X_NMF ≥ 0.7. Excluding the contribution of the 2D hydrogen-bonding network due to the presence of FA in the low-frequency spectrum band, the X_ML dependence of the normalized first moment of the low-frequency band in the [MOIm][BF₄]/FA and [MOIm][BF₄]/NMF systems revealed that the normalized first moment did not remarkably change in the range of X_ML < 0.7 but drastically increased in X_ML ≥ 0.7. FT-IR results indicated that the amide C═O band shifted to the low-frequency side with increasing X_ML for the three mixtures due to the hydrogen bonds. The imidazolium ring C-H band also showed a similar tendency to the amide C═O band. ¹⁹F NMR probed the microenvironment of [BF₄]^- in the mixtures. The [MOIm][BF₄]/NMF and [MOIm][BF₄]/DMF systems showed an up-field shift of the F atoms of the anion with increasing X_ML, and the [MOIm][BF₄]/FA system exhibited a down-field shift. Steep changes in the chemical shifts were confirmed in the region of X_ML > 0.8. On the basis of the quantum chemistry calculations, the observed chemical shifts with increasing X_ML were mainly attributed to the many-body interactions of ions and amides for the [MOIm][BF₄]/FA and [MOIm][BF₄]/DMF systems. Meanwhile, the long distance between the cation and the anion was due to the high dielectric medium for the [MOIm][BF₄]/NMF system, which led to an up-field shift.

Intermolecular Dynamics of Positively and Negatively Charged Aromatics and Their Isoelectronic Neutral Analogs in Aqueous Solutions

In this study, we investigated the temperature dependence of intermolecular vibrations and orientational dynamics in the aqueous solutions of imidazole hydrochloride, imidazole, sodium triazolide, and triazole using femtosecond Raman-induced Kerr effect spectroscopy (fs-RIKES) and steady-state Raman spectroscopy. The difference low-frequency Raman spectra under 250 cm-1 of the aqueous solutions relative to the neat water showed that the spectral shoulder in the high-frequency region at 60-100 cm-1, assigned to the libration of an aromatic ring, was higher in frequency for the imidazolium cation but lower for the triazolide anion than those of the respective neutral aromatics. The results of the ab initio quantum chemistry calculations of the clusters of the aromatics and water molecule(s) were consistent with the experimental spectra of the aqueous solutions. Further, the results of the temperature-dependent experiments showed that the signal intensity in the low-frequency region below 50 cm-1 increased for all solutions with an increase in temperature. In contrast, the spectral density in the high-frequency region above 80 cm-1 exhibited almost no shift for the 1.0 M solutions, while a significant red shift was observed for the 5.0 M solutions. In addition, the temperature-dependent densities, viscosities, and surface tensions were characterized for the aqueous aromatic solutions from 293 to 353 K.

Intermolecular Dynamics and Structure in Aqueous Lidocaine Hydrochloride Solutions

We investigated the intermolecular dynamics and static structure in the aqueous solutions of lidocaine hydrochloride (LDHCl) in the concentration range of [LDHCl] = 0-2.00 M using femtosecond Raman-induced Kerr effect spectroscopy (fs-RIKES), small- and wide-angle X-ray scattering (SWAXS), and dynamic light scattering (DLS). For the fs-RIKES experiments, the concentration dependence of the difference low-frequency spectra of the aqueous LDHCl solutions relative to the neat water, which was mainly due to the intermolecular vibrations, was characterized using an exponential function with a characteristic concentration of ∼1 M. For the SWAXS experiments, we observed a manifestation of an excess scattering component centered within a range of 8-10 nm^-1 in the aqueous LDHCl solutions. The results of Fourier inversion and further deconvolution analyses unambiguously demonstrated that lidocaines assemble into a nanometer-sized micelle-like structure with the innermost core (∼0.3 nm) and outer shell (∼0.5 nm), respectively. The DLS experiments also found nanometer-sized aggregates and further indicated evidence of the clusters of the aggregates. The results of viscosities, densities, and surface tensions of the solutions and the quantum chemistry calculations supported the unique features of the microscopic intermolecular interaction and the micelle-like aggregation.

Low-Frequency Spectra of 1-Methyl-3-octylimidazolium Tetrafluoroborate Mixtures with Poly(ethylene glycol) by Femtosecond Raman-Induced Kerr Effect Spectroscopy

This is the first report on low-frequency spectra of ionic liquid (IL)/polymer mixtures using femtosecond Raman-induced Kerr effect spectroscopy. We studied mixtures of 1-methyl-3-octylimidazolium tetrafluoroborate ([MOIm][BF₄]) and poly(ethylene glycol) (PEG) with M_n = 400 (PEG400) at various concentrations. To elucidate the unique features of the IL/polymer mixture system, mixtures of PEG400 with a molecular liquid, 1-octhylimidazole (OIm), which is a neutral analog of the cation, were also studied. In addition, mixtures of [MOIm][BF₄] with ethylene glycol (EG) and poly(ethylene glycol) with M_n = 4000 (PEG4000) were also investigated. The first moments of broad low-frequency spectra, mainly due to intermolecular vibrations for the [MOIm][BF₄]/PEG400 and OIm/PEG400, increased slightly with increasing concentration of PEG400, indicating that microscopic intermolecular interactions, in general, are slightly enhanced. We also compared the [MOIm][BF₄] mixtures with EG, PEG400, and PEG4000 at concentrations of 5 and 10 wt % PEG or EG. The low-frequency spectra of samples with the same concentrations were quite similar, but a comparison of the normalized spectra showed that the spectral intensity in the low-frequency region below ∼50 cm^-1 of the [MOIm][BF₄] mixtures with PEG400 and PEG4000 is somewhat lower than that of the [MOIm][BF₄] mixtures with EG. Although the effect of the polymer is small compared to other polymer solution systems, this feature is attributed to a suppression of translational motion in the mixtures of [MOIm][BF₄] with PEG compared to the mixtures of [MOIm][BF₄] with EG due to the greater mass of PEG than EG. Density, surface tension, viscosity, and electrical conductivity were also estimated. From Walden plots, it was found that the [MOIm][BF₄]/PEG4000 system showed more ideal electrical conductive behavior than the [MOIm][BF₄]/PEG400 and [MOIm][BF₄]/EG systems.

Optical Kerr Effect of Liquid Acetonitrile Probed by Femtosecond Time-Resolved X-ray Liquidography

Optical Kerr effect (OKE) spectroscopy is a method that measures the time-dependent change of the birefringence induced by an optical laser pulse using another optical laser pulse and has been used often to study the ultrafast dynamics of molecular liquids. Here we demonstrate an alternative method, femtosecond time-resolved X-ray liquidography (fs-TRXL), where the microscopic structural motions related to the OKE response can be monitored using a different type of probe, i.e., X-ray solution scattering. By applying fs-TRXL to acetonitrile and a dye solution in acetonitrile, we demonstrate that different types of molecular motions around photoaligned molecules can be resolved selectively, even without any theoretical modeling, based on the anisotropy of two-dimensional scattering patterns and extra structural information contained in the q-space scattering data. Specifically, the dynamics of reorientational (libration and orientational diffusion) and translational (interaction-induced motion) motions are captured separately by anisotropic and isotropic scattering signals, respectively. Furthermore, the two different types of reorientational motions are distinguished from each other by their own characteristic scattering patterns and time scales. The measured time-resolved scattering signals are in excellent agreement with the simulated scattering signals based on a molecular dynamics simulation for plausible molecular configurations, providing the detailed structural description of the OKE response in liquid acetonitrile.

Low-Frequency (Gigahertz to Terahertz) Depolarized Raman Scattering Off n-Alkanes, Cycloalkanes, and Six-Membered Rings: A Physical Interpretation

Molecular liquids have long been known to undergo various distinct intermolecular motions, from fast librations and cage-rattling oscillations to slow orientational and translational diffusion. However, their resultant gigahertz to terahertz spectra are far from simple, appearing as broad shapeless bands that span many orders of magnitude of frequency, making meaningful interpretation troublesome. Ad hoc spectral line shape fitting has become a notoriously fine art in the field; a unified approach to handling such spectra is long overdue. Here we apply ultrafast optical Kerr-effect (OKE) spectroscopy to study the intermolecular dynamics of room-temperature n-alkanes, cycloalkanes, and six-carbon rings, as well as liquid methane and propane. This work provides stress tests and converges upon an experimentally robust model across simple molecular series and range of temperatures, providing a blueprint for the interpretation of the dynamics of van der Waals liquids. This will enable the interpretation of low-frequency spectra of more complex liquids.

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.

Low-Frequency Vibrational Motions of Polystyrene in Carbon Tetrachloride: Comparison with Model Monomer and Dependence on Concentration and Molecular Weight

In this study, the low-frequency vibrational dynamics of polystyrene (PS) in CCl₄ was investigated by femtosecond Raman-induced Kerr effect spectroscopy. Ethylbenzene (EBz) was also investigated as a model monomer of the polymer to elucidate the unique dynamical features of PS in solution. The broadened low-frequency spectrum of the PS/CCl₄ in the frequency region below 150 cm^-1 is significantly different from that of the EBz/CCl₄. Difference spectra between the PS or EBz solutions and neat CCl₄, normalized to an internal vibrational mode of CCl₄, clearly show a much lower spectral intensity for the PS/CCl₄ than the EBz/CCl₄ in the low-frequency region below ca. 20 cm^-1. This indicates that translational motions are suppressed in the PS/CCl₄ compared to the EBz/CCl₄. Moreover, the high-frequency motion at ca. 70 cm^-1, mainly due to phenyl ring librations, occurs at higher frequency in PS (78 cm^-1) than EBz (65 cm^-1). In addition, the results of concentration-dependent experiments show that the first moment (M₁) of the low-frequency difference spectra of both PS/CCl₄ and EBz/CCl₄ is almost independent of the concentration. The molecular weight dependence of the low-frequency spectrum in the PS/CCl₄ shows that the M₁ value of the low-frequency spectral band of PS shifts to higher frequencies when the molecular weight of PS increases up to M_w = ∼1000, which corresponds approximately to the decamer, and then remains constant upon further increasing the molecular weight.

Optical Kerr effect spectroscopy of CS2 in monocationic and dicationic ionic liquids: insights into the intermolecular interactions in ionic liquids

A comparative study of the intermolecular dynamics of CS₂ in monocationic and dicationic ionic liquids (ILs) was performed using optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES). The reduced spectral densities (RSDs) of mixtures of CS₂ in 1-alkyl-3-methylimidazolium bis[(trifluoromethane)sulfonyl]amide ([C_nC₁im][NTf₂] for n = 3-5) and 1,2n-bis(3-methylimidazolium-1-yl) alkane bis[(trifluoromethane)sulfonyl]amide ([(C₁im)₂C_2n][NTf₂]₂ for n = 3-5) were investigated as a function of concentration at 295 K. An additivity model was used to obtain the CS₂ contribution to the RSD of a mixture in the 0-200 cm^-1 region. One of the aims of this study is to show how CS₂ can be used as a probe of intermolecular/interionic interactions in ILs. The concentrations were chosen such that the CS₂-to-imidazolium ring mole fraction of a mixture with [(C₁im)₂C_2n][NTf₂]₂ (DIL(2n)) is the same as that of a mixture with [C_nC₁im][NTf₂] (MIL(n)). As found previously for CS₂ in monocationic ILs, the intermolecular spectrum of CS₂ in dicationic ILs is lower in frequency and narrower than that of neat CS₂. The new result is that the intermolecular spectrum of CS₂ is higher in frequency in DIL(2n) than in the corresponding MIL(n), indicating that CS₂ molecules experience a stiffer potential in dicationic ILs than in monocationic ILs. The intermolecular dynamics of CS₂ being higher in frequency in DIL(2n) than in MIL(n) is consistent with recent molecular dynamics simulations (Lynden-Bell and Quitevis, J. Chem. Phys., 2018, 148, 193844) that show the stiffer potential is the result of greater confinement of CS₂ in DIL(2n) than in MIL(n). We also show in this study how effects due to dilution and the intermolecular potential seen by a solute molecule in solution are unraveled.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

Empirical Analysis of Optical Kerr Effect Spectra: A Case for Constraint

Ultrafast optical Kerr effect (OKE) spectroscopy is a widely used method for studying the depolarized, Raman-active intermolecular dynamics of liquids. Through appropriate manipulation of OKE data, it is possible to determine the reduced spectral density (RSD), which is the Bose-Einstein-corrected, low-frequency Raman spectrum with the contribution of diffusive reorientation removed. OKE RSDs for van der Waals liquids can often be fit well to an empirical function that is the sum of a Bucaro-Litovitz function and an antisymmetrized Gaussian (AG). Although these functions are not directly representative of specific intermolecular dynamics, the AG fit parameters can provide useful insights into the microscopic properties of liquids. Here we show that fits using the AG function are typically not well-determined, and that equally good results can be obtained with a wide range of fitting parameters. We propose the use of a physically motivated constraint on the amplitude of the AG function, and demonstrate that this constraint leads to more intuitive trends in the fit parameters for temperature-dependent RSDs in 1,3,5-trifluorobenzene and hexafluorobenzene.

Comparative study of the intermolecular dynamics of imidazolium-based ionic liquids with linear and branched alkyl chains: OHD-RIKES measurements

This article describes a comparative study of the low-frequency (0-450 cm^-1) Kerr spectra of the branched 1-(iso-alkyl)-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([(N - 2)mC_N-1C₁im][NTf₂] with N = 3-7) ionic liquids (ILs) and that of the linear 1-(n-alkyl)-3-methylimidazolium bis(trifluoromethylsulfonyl)amide ([C_NC₁im][NTf₂] with N = 2-7) ILs. The spectra were obtained by use of femtosecond optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES). The intermolecular spectrum of a branched IL is similar to that of a linear IL that is of the same alkyl chain length rather than of the same number of carbon atoms in the alkyl chain. This similarity and the lack of a correlation of the first spectral moments and widths of the intermolecular spectra with chain length is mainly attributed to the increase in the dispersion contribution to the total molar cohesive energy being compensated by stretching of the ionic network due to the increasing size of the nonpolar domains, which is dependent only on the length of the alkyl chain.

A memory diffusion model for molecular anisotropic diffusion in siliceous β-zeolite

A memory diffusion model of molecules on β-zeolite is proposed. In the model, molecular diffusion in β-zeolites is treated as jumping from one adsorption site to its neighbors and the jumping probability is a compound probability which includes that provided by the transitional state theory as well as that derived from the information about which direction the target molecule comes from. The proposed approach reveals that the diffusivities along two crystal axes on β-zeolite are correlated. The model is tested by molecular dynamics simulations on diffusion of benzene and other simple molecules in β-zeolites. The results show that the molecules with larger diameters fit the prediction much better and that the "memory effects" are important in all cases.

The importance of polarizability: comparison of models of carbon disulphide in the ionic liquids [C1C1im][NTf2] and [C4C1im][NTf2]

Three dimensional distribution of CS₂ around a [C₁C₁im]⁺ ion showing the difference in behaviour of polarizable (red) and unpolarizable (blue) models of CS₂.

Applicability of the Caldeira-Leggett Model to Vibrational Spectroscopy in Solution

Formulating a rigorous system-bath partitioning approach remains an open issue. In this context, the famous Caldeira-Leggett model that enables quantum and classical treatment of Brownian motion on equal footing has enjoyed popularity. Although this model is by any means a useful theoretical tool, its ability to describe anharmonic dynamics of real systems is often taken for granted. In this Letter, we show that the mapping between a molecular system under study and the model cannot be established in a self-consistent way, unless the system part of the potential is taken effectively harmonic. Mathematically, this implies that the mapping is not invertible. This "invertibility problem" is not dependent on the peculiarities of particular molecular systems and is rooted in the anharmonicity of the system part of the Caldeira-Leggett model potential.

Optical Kerr effect of liquid and supercooled water: the experimental and data analysis perspective

The time-resolved optical Kerr effect spectroscopy (OKE) is a powerful experimental tool enabling accurate investigations of the dynamic phenomena in molecular liquids. We introduced innovative experimental and fitting procedures, that enable a safe deconvolution of sample response function from the instrumental function. This is a critical issue in order to measure the dynamics of liquid water. We report OKE data on water measuring intermolecular vibrations and the structural relaxation processes in an extended temperature range, inclusive of the supercooled states. The unpreceded data quality makes possible a solid comparison with few theoretical models: the multi-mode Brownian oscillator model, the Kubo's discrete random jump model, and the schematic mode-coupling model. All these models produce reasonable good fits of the OKE data of stable liquid water, i.e., over the freezing point. The features of water dynamics in the OKE data becomes unambiguous only at lower temperatures, i.e., for water in the metastable supercooled phase. We found that the schematic mode-coupling model provides the more rigorous and complete model for water dynamics, even if its intrinsic hydrodynamic approach does not give a direct access to the molecular information.

Two-dimensional measurements of the solvent structural relaxation dynamics in dipolar solvation

Resonant-pump polarizability response spectroscopy (RP-PORS) is based on an optical heterodyne detected transient grating (OHD-TG) method with an additional resonant pump pulse. In RP-PORS, the resonant pump pulse excites the solute-solvent system and the subsequent relaxation of the solute-solvent system is monitored by the OHD-TG spectroscopy. RP-PORS is shown to be an excellent experimental tool to directly measure the solvent responses in solvation. In the present work, we extended our previous RP-PORS (Park et al., Phys. Chem. Chem. Phys., 2011, 13, 214-223) to measure time-dependent transient solvation polarizability (TSP) spectra with Coumarin153 (C153) in acetonitrile. The time-dependent TSP spectra showed how the different solvent intermolecular modes were involved in different stages of the solvation process. Most importantly, the inertial and diffusive components of the solvent intermolecular modes in solvation were found to be spectrally and temporally well-separated. In a dipolar solvation of C153, high-frequency inertial solvent modes were found to be driven instantaneously and decay on a subpicosecond timescale while low-frequency diffusive solvent modes were induced slowly and decayed on a picosecond timescale. Our present result is the first experimental manifestation of frequency-dependent solvent intermolecular response in a dipolar solvation.