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.

CH Mode Mixing Determines the Band Shape of the Carboxylate Symmetric Stretch in Apo-EDTA, Ca2+-EDTA, and Mg2+-EDTA.

The infrared spectra of EDTA complexed with Ca2+ and Mg2+ contain, to date, unidentified vibrational bands. This study assigns the peaks in the linear and two-dimensional infrared spectra of EDTA, with and without either Ca2+ or Mg2+ ions. Two-dimensional infrared spectroscopy and DFT calculations reveal that, in both the presence and absence of ions, the carboxylate symmetric stretch and the terminal CH bending vibrations mix. We introduce a method to calculate participation coefficients that quantify the contribution of the carboxylate symmetric stretch, CH wag, CH twist, and CH scissor in the 1400-1550 cm-1 region. With the help of participation coefficients, we assign the 1400-1430 cm-1 region to the carboxylate symmetric stretch, which can mix with CH modes. We assign the 1000-1380 cm-1 region to CH twist modes, the 1380-1430 cm-1 region to wag modes, and the 1420-1650 cm-1 region to scissor modes. The difference in binding geometry between the carboxylate-Ca2+ and carboxylate-Mg2+ complex manifests as new diagonal and cross-peaks between the mixed modes in the two complexes. The small Mg2+ ion binds EDTA tighter than the Ca2+ ion, which causes a redshift of the COO symmetric stretches of the sagittal carboxylates. Energy decomposition analysis further characterizes the importance of electrostatics and deformation energy in the bound complexes.

An ultrafast vibrational study of dynamical heterogeneity in the protic ionic liquid ethyl-ammonium nitrate. I. Room temperature dynamics.

Using ultrafast two-dimensional infrared spectroscopy (2D-IR), a vibrational probe (thiocyanate, SCN-) was used to investigate the hydrogen bonding network of the protic ionic liquid ethyl-ammonium nitrate (EAN) in comparison to H2O. The 2D-IR experiments were performed in both parallel (⟨ZZZZ⟩) and perpendicular (⟨ZZXX⟩) polarizations at room temperature. In EAN, the non-Gaussian lineshape in the FTIR spectrum of SCN- suggests two sub-ensembles. Vibrational relaxation rates extracted from the 2D-IR spectra provide evidence of the dynamical differences between the two sub-ensembles. We support the interpretation of two sub-ensembles with response function simulations of two overlapping bands with different vibrational relaxation rates and, otherwise, similar dynamics. The measured rates for spectral diffusion depend on polarization, indicating reorientation-induced spectral diffusion (RISD). A model of restricted molecular rotation (wobbling in a cone) fully describes the observed spectral diffusion in EAN. In H2O, both RISD and structural spectral diffusion contribute with similar timescales. This complete characterization of the dynamics at room temperature provides the basis for the temperature-dependent measurements in Paper II of this series.

Ultrafast dynamics of ionic liquids in colloidal dispersion.

Ionic liquid (IL)-surfactant complexes have significance both in applications and fundamental research, but their underlying dynamics are not well understood. We apply polarization-controlled two-dimensional infrared spectroscopy (2D-IR) to study the dynamics of [BMIM][SCN]/surfactant/solvent model systems. We examine the effect of the choice of surfactants and solvent, and the IL-to-surfactant ratio (W-value), with a detailed analysis of the orientation and structural dynamics of each system. Different surfactants create very different environments for the entrapped ILs, ranging from a semi-static micro-environment to a fluxional environment that evolves even faster than the bulk IL. The oil-phase also clearly affects the microscopic dynamics. The anisotropy decay for entrapped ILs completes within 10 ps, which is similar to free thiocyanate ion in water, while a significant reorientation-induced spectral diffusion (RISD) effect is observed. The entrapped ionic liquid are highly dynamic for all W-values, and no core-shell structure is observed. We hypothesize that, instead of an ionic liquid-reverse micelle (IL-RM), the microscopic structure of this system is small colloidal dispersions or pairs of IL and surfactants. A detailed analysis of the polarization-controlled 2D-IR spectra of AOT system reveals a potential ion-exchange mechanism.

Temperature and chain length dependence of ultrafast vibrational dynamics of thiocyanate in alkylimidazolium ionic liquids: A random walk on a rugged energy landscape.

Ultrafast two-dimensional infrared spectroscopy of a thiocyanate vibrational probe (SCN-) was used to investigate local dynamics in alkylimidazolium bis-[trifluoromethylsulfonyl]imide ionic liquids ([Imn,1][Tf2N], n = 2, 4, 6) at temperatures from 5 to 80 °C. The rate of frequency fluctuations reported by SCN- increases with increasing temperature and decreasing alkyl chain length. Temperature-dependent correlation times scale proportionally to temperature-dependent bulk viscosities of each ionic liquid studied. A multimode Brownian oscillator model demonstrates that very low frequency (<10 cm-1) modes primarily drive the observed spectral diffusion and that these modes broaden and blue shift on average with increasing temperature. An Arrhenius analysis shows activation barriers for local motions around the probe between 5.5 and 6.5 kcal/mol that are very similar to those for translational diffusion of ions. [Im6,1][Tf2N] shows an unexpected decrease in activation energy compared to [Im4,1][Tf2N] that may be related to mesoscopically ordered polar and nonpolar domains. A model of dynamics on a rugged potential energy landscape provides a unifying description of the observed Arrhenius behavior and the Brownian oscillator model of the low frequency modes.

Reorientation-induced spectral diffusion of non-isotropic orientation distributions.

When reorientation of a vibrational chromophore is faster than the relaxation of its local environment, the frequency fluctuation correlation function (FFCF) measured by two-dimensional infrared spectroscopy (2D-IR) spectroscopy is an interplay of scalar structural spectral diffusion and vectorial reorientation-induced spectral diffusion (RISD). Theory has been established to calculate the RISD component of different polarization configurations with the assumption that the molecule orients randomly in a local electric field. We show here that in the [BMIM][SCN]/AOT/chlorobenzene system, where the local electric field is strong, this assumption is incapable of reproducing the experimental results. We modify the current theory by assuming a Boltzmann distribution of transition dipoles of the chromophores in a local electric field and use a Markov chain model to calculate the RISD component of 2D-IR with different polarization configurations. The result reproduces key features of the experiment and suggests a potential ion-exchange in the [BMIM][SCN]/AOT/chlorobenzene system.

Two-dimensional ultrafast vibrational spectroscopy of azides in ionic liquids reveals solute-specific solvation.

The stereochemistry and the reaction rates of bimolecular nucleophilic substitution reactions involving azides in ionic liquids are governed by solute-solvent interactions. Two-dimensional ultrafast vibrational spectroscopy (2D-IR) shows that the picosecond dynamics of inorganic azides are substantially slower than organic azides in a series of homologous imidazolium ionic liquids. In water, both organic and inorganic azides spectrally diffuse with a ∼2 ps time constant. In the aprotic solvent tetrahydrofuran, both kinds of azides spectrally diffuse on a timescale >5 ps. In ionic liquids, like 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), organic azides spectrally diffuse with a 2-4 ps time constant, and inorganic azides spectrally diffuse with a >40 ps time constant. Such a striking difference suggests that neutral (organic) and charged (inorganic) azides are incorporated in the ionic liquids with different solvation structures.

Ultrafast vibrational spectroscopy (2D-IR) of CO2 in ionic liquids: Carbon capture from carbon dioxide's point of view.

The CO2ν3 asymmetric stretching mode is established as a vibrational chromophore for ultrafast two-dimensional infrared (2D-IR) spectroscopic studies of local structure and dynamics in ionic liquids, which are of interest for carbon capture applications. CO2 is dissolved in a series of 1-butyl-3-methylimidazolium-based ionic liquids ([C4C1im][X], where [X](-) is the anion from the series hexafluorophosphate (PF6 (-)), tetrafluoroborate (BF4 (-)), bis-(trifluoromethyl)sulfonylimide (Tf2N(-)), triflate (TfO(-)), trifluoroacetate (TFA(-)), dicyanamide (DCA(-)), and thiocyanate (SCN(-))). In the ionic liquids studied, the ν3 center frequency is sensitive to the local solvation environment and reports on the timescales for local structural relaxation. Density functional theory calculations predict charge transfer from the anion to the CO2 and from CO2 to the cation. The charge transfer drives geometrical distortion of CO2, which in turn changes the ν3 frequency. The observed structural relaxation timescales vary by up to an order of magnitude between ionic liquids. Shoulders in the 2D-IR spectra arise from anharmonic coupling of the ν2 and ν3 normal modes of CO2. Thermal fluctuations in the ν2 population stochastically modulate the ν3 frequency and generate dynamic cross-peaks. These timescales are attributed to the breakup of ion cages that create a well-defined local environment for CO2. The results suggest that the picosecond dynamics of CO2 are gated by local diffusion of anions and cations.

Azide-water intermolecular coupling measured by two-color two-dimensional infrared spectroscopy.

We utilize two-color two-dimensional infrared spectroscopy to measure the intermolecular coupling between azide ions and their surrounding water molecules in order to gain information about the nature of hydrogen bonding of water to ions. Our findings indicate that the main spectral contribution to the intermolecular cross-peak comes from population transfer between the asymmetric stretch vibration of azide and the OD-stretch vibration of D(2)O. The azide-bound D(2)O bleach/stimulated emission signal, which is spectrally much narrower than its linear absorption spectrum, shows that the experiment is selective to solvation shell water molecules for population times up to ~500 fs. The waters around the ion are present in an electrostatically better defined environment. Afterwards, ~1 ps, the sample thermalizes and selectivity is lost. On the other hand, the excited state absorption signal of the azide-bound D(2)O is much broader. The asymmetry in spectral width between bleach/stimulated emission versus excited absorption has been observed in very much the same way for isotope-diluted ice Ih, where it has been attributed to the anharmonicity of the OD potential.

Rotationally-Resolved Two-Dimensional Infrared Spectroscopy of CO2(g): Rotational Wavepackets and Angular Momentum Transfer.

Angular momentum transfer and wavepacket dynamics of CO2(g) were measured on the picosecond time scale using polarization-resolved two-dimensional infrared (2D-IR) spectroscopy. The dynamics of rotational levels up to Jmax ≈ 50 are observed simultaneously at room temperature. Rotational wavepackets launched by the pump pulses cause oscillations in the intensity of individual peaks and beating patterns in the 2D-IR spectra. The structure of the rotationally resolved 2D-IR spectrum is explained using nonlinear response function theory. Spectral diffusion of the rotationally resolved 2D-IR peaks reveals information about angular momentum transfer. We demonstrate the ability to directly measure inelastic angular momentum dynamics simultaneously across the ∼50 thermally excited rotational levels over several hundred picoseconds.

pH Jumps in a Protic Ionic Liquid Proceed by Vehicular Proton Transport.

The dynamics of excess protons in the protic ionic liquid (PIL) ethylammonium formate (EAF) have been investigated from femtoseconds to microseconds using visible pump mid-infrared probe spectroscopy. The pH jump following the visible photoexcitation of a photoacid (8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt, HPTS) results in proton transfer to the formate of the EAF. The proton transfer predominantly (∼70%) occurs over picoseconds through a preformed hydrogen-bonded tight complex between HPTS and EAF. We investigate the longer-range and longer-time-scale proton-transport processes in the PIL by obtaining the ground-state conjugate base (RO-) dynamics from the congested transient-infrared spectra. The spectral kinetics indicate that the protons diffuse only a few solvent shells from the parent photoacid before recombining with RO-. A kinetic isotope effect of nearly unity (kH/kD ≈ 1) suggests vehicular transfer and the transport of excess protons in this PIL. Our findings provide comprehensive insight into the complete photoprotolytic cycle of excess protons in a PIL.

Intramolecular Vibrational Energy Relaxation of CO2 in Cross-Linked Poly(ethylene glycol) Diacrylate-Based Ion Gels.

Ultrafast two-dimensional infrared spectroscopy (2D-IR) and Fourier transform infrared spectroscopy (FTIR) were used to measure carbon dioxide (CO2) in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf2N]), cross-linked low-molecular-weight poly(ethylene glycol) diacrylate (PEGDA), and an ion gel composed of a 50 vol % blend of the two. The center frequency of the antisymmetric stretch, ν3, of CO2 shifts monotonically to lower wavenumbers with increasing polymer content, with the largest line width in the ion gel (6 cm-1). Increasing polymer content slows both spectral diffusion and vibrational energy relaxation (VER) rates. An unexpected excited-state absorbance peak appears in the 2D-IR of cross-linked PEGDA due to VER from the antisymmetric stretch into the bending mode, ν2. Thirty-two response functions are necessary to describe the observed features in the 2D-IR spectra. Nonlinear least-squares fitting extracts both spectral diffusion and VER rates. In the ion gel, CO2 exhibits spectral diffusion dynamics that lie between that of the pure compounds. The kinetics of VER reflect both fast excitation and de-excitation of the bending mode, similar to the ionic liquid (IL), and slow overall vibrational population relaxation, similar to the cross-linked polymer. The IL-like and polymer-like dynamics suggest that the CO2 resides at the interface of the two components in the ion gel.

What can we learn from three-dimensional infrared spectroscopy?

The low-frequency part of the vibrational spectrum of a liquid is dominated by intermolecular degrees of freedom. Hence, it reports on the motion of solvent molecules with respect to each other rather than on the intramolecular details of individual molecules. In hydrogen-bonded liquids, in particular water, a detailed understanding of the low-frequency spectrum is enormously complicated because of the complex hydrogen-bond network, which constantly rearranges on an ultrafast femtosecond to picosecond time scale. Many of the peculiar properties of water have their origin in these processes. Conventional far-infrared (far-IR) or Raman spectroscopy, as well as two-dimensional IR (2D-IR) spectroscopy, are all linear with respect to the intermolecular (solvent) degrees of freedom. These spectroscopies tell us much about the density of states in the low-frequency range but little about the dynamics of the hydrogen-bond making and breaking. In this Account, we propose three-dimensional IR (3D-IR) spectroscopy as a novel tool that is nonlinear with respect to these low-frequency degrees of freedom; hence, it may provide much more detailed insights into intermolecular dynamics. The first experimental realizations of 3D-IR spectroscopy have been demonstrated in the literature; the information it affords is similar to that of 2D-Raman spectroscopy. Three-dimensional IR spectroscopy will, for the first time, reveal whether the low-frequency part of the vibrational spectrum of liquids has to be considered mostly homogeneously or inhomogeneously broadened. Alternately, we may find that either of these classifications is completely wrong because the normal mode picture fails when thermal energy is of the same order of magnitude as the ruggedness of the intramolecular potential energy surface. We briefly introduce the theoretical background of 3D-IR spectroscopy and discuss two of its most promising applications: (a) the more thorough characterization of non-Gaussian stochastic processes such as the hydrogen-bond dynamics of water and (b) non-Markovian ultrafast exchange processes. In the ultrafast regime, many of the otherwise valid simplifying assumptions of nonequilibrium statistical mechanics (for example, linear response and Markovian dynamics) are likely to fail; 3D-IR spectroscopy will allow us for the first time to experimentally explore their range of validity.

Enhancing signal detection and completely eliminating scattering using quasi-phase-cycling in 2D IR experiments.

We demonstrate how quasi-phase-cycling achieved by sub-cycle delay modulation can be used to replace optical chopping in a box-CARS 2D IR experiment in order to enhance the signal size, and, at the same time, completely eliminate any scattering contamination. Two optical devices are described that can be used for this purpose, a wobbling Brewster window and a photoelastic modulator. They are simple to construct, easy to incorporate into any existing 2D IR setup, and have attractive features such as a high optical throughput and a fast modulation frequency needed to phase cycle on a shot-to-shot basis.

The OH stretch vibration of liquid water reveals hydrogen-bond clusters.

Using molecular dynamics simulations, we investigate the fluctuations of the hydrogen-bond network in liquid water and its relation to vibrational spectroscopy. We show that the high-frequency shoulder, which is most evidently found in Raman spectra of the OH stretch vibration of isotope diluted water, is (at least to a certain extent) related to a three-fold hydrogen-bonded ring. This suggests that it is not always sufficient to classify individual water molecules when studying some aspects of hydrogen-bond dynamics, rather, one should consider the topology of the local structure around a given water molecule.

Purely absorptive three-dimensional infrared spectroscopy.

We demonstrate a method to collect purely absorptive three-dimensional (3D) fifth-order vibrational spectra on the model system CO(2) in H(2)O. The six beam interferometer is described, as well as a method to experimentally determine the phase of the 3D spectrum. The measured spectra agree very well with simulations of the data based on the cumulant expansion. There are five peaks corresponding to different paths up and down the vibrational ladder. The positions, signs, and amplitudes of the peaks agree with theoretical predictions, and the intensities of the peaks scale linearly with concentration. Based on the concentration dependence and agreement between the simulations and measurements, we conclude that cascaded lower order signals contribute negligibly to the observed signal.

Modeling Carbon Dioxide Vibrational Frequencies in Ionic Liquids: III. Dynamics and Spectroscopy.

In recent years, interest in carbon capture and sequestration has led to numerous investigations of the ability of ionic liquids to act as recyclable CO2-sorbent materials. Herein, we investigate the structure and dynamics of a model physisorbing ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate ([C4C1Im][PF6]), from the perspective of CO2 using two-dimensional (2D) IR spectroscopy and molecular dynamics simulations. A direct comparison of experimentally measured and calculated 2D IR line shapes confirms the validity of the simulations and spectroscopic calculations. Taken together, the simulations and experiments reveal new insights into the interactions of a CO2 solute with the surrounding ionic liquid and how these interactions manifest in the 2D IR spectra. In particular, higher CO2 asymmetric stretch vibrational frequencies are associated with softer, less populated solvent cages and lower frequencies are associated with tighter, more highly populated solvent cages. The CO2 interacts most strongly with the anions, and these interactions persist for more than 1 ns. The second strongest interactions are with the imidazolium cation ring that last 100 ps, and the weakest interactions are with the cation butyl tail that persist for 10 ps. The principal contributors to spectral diffusion of the CO2 asymmetric stretch vibrational frequency due to the dynamical evolution of the solvent are through Lennard-Jones interactions at short times and electrostatics at long times.

Enthalpic Driving Force for the Selective Absorption of CO2 by an Ionic Liquid.

Molecular dynamics (MD) simulations validated against two-dimensional infrared (2D-IR) measurements of CO2 in an imidazolium-based ionic liquid have revealed new insights into the mechanism of CO2 solvation. The first solvation shell around CO2 has a distinctly quadrupolar structure, with strong negative charge density around the CO2 carbon atom and positive charge density near the CO2 oxygen atoms. When CO2 is modeled without atomic charges (thus removing its strong quadrupole moment), its solvation shell weakens and changes significantly into a structure that is similar to that of N2 in the same liquid. The solvation shell of CO2 evolves more quickly when its quadrupole is removed, and we find evidence that solvent cage dynamics is measured by 2D-IR spectroscopy. We also find that the solvent cage evolution of N2 is similar to that of CO2 with no atomic charges, implying that the weaker quadrupole of N2 is responsible for its higher diffusion and lower absorption in ionic liquids.