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 inter-protein 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 allencompassing 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 semi-empirical 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 website (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-theart 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.

The Ca-sensing protein calmodulin (CaM) is a popular model of biological ion binding since it is both experimentally tractable and essential to survival in all eukaryotic cells. CaM modulates hundreds of target proteins and is sensitive to complex patterns of Ca exposure, indicating that it functions as a sophisticated dynamic transducer rather than a simple on/off switch. Many details of this transduction function are not well understood. Fourier transform infrared (FTIR) spectroscopy, ultrafast 2D infrared (2D IR) spectroscopy, and electronic structure calculations were used to probe interactions between bound metal ions (Ca and several trivalent lanthanide ions) and the carboxylate groups in CaM's EF-hand ion-coordinating sites. Since Tb is commonly used as a luminescent Ca analog in studies of protein-ion binding, it is important to characterize distinctions between the coordination of Ca and the lanthanides in CaM. Although functional assays indicate that Tb fully activates many Ca-dependent proteins, our FTIR spectra indicate that Tb, La, and Lu disrupt the bidentate coordination geometry characteristic of the CaM binding sites' strongly conserved position 12 glutamate residue. The 2D IR spectra indicate that, relative to the Ca-bound form, lanthanide-bound CaM exhibits greater conformational flexibility and larger structural fluctuations within its binding sites. Time-dependent 2D IR lineshapes indicate that binding sites in Ca-CaM occupy well-defined configurations, whereas binding sites in lanthanide-bound-CaM are more disordered. Overall, the results show that binding to lanthanide ions significantly alters the conformation and dynamics of CaM's binding sites.

Dimethyl sulfoxide (DMSO) disrupts the hydrogen-bond networks in water. The widespread use of DMSO as a cosolvent, along with its unusual attributes, have inspired numerous studies. Herein, infrared absorption spectroscopy of the S=O stretching mode combined with molecular dynamics and quantum chemistry models were used to directly quantify DMSO/water hydrogen-bond populations in binary mixtures. Singly H-bonded species are dominant at 10 mol %, due to strong DMSO-water interactions. We found an unexpected increase in non-hydrogen-bonded DMSO near the eutectic point (ca. 35 mol %) which also correlates with several abnormalities in the bulk solution properties. We find evidence for three distinct regimes: 1) strong DMSO-water interactions (<30 mol %), 2) ideal-solution-like (30-90 mol %), and 3) self-interaction, or aggregation, regime (>90 mol %). We propose a "step in" mechanism, which involves hydrogen bonding between water and the DMSO aggregate species.

Metal carbonyl complexes offer both rich chemistry and complex vibrational spectroscopy due to strong coupling among the carbonyl stretches. Using two-dimensional infrared (2DIR) spectroscopy, it is possible to resolve the underlying transitions between vibrational energy levels, determine the orientations and relative magnitude of the corresponding transition dipole moments, measure the coupling between modes due to the anharmonicity of the potential, and probe energy redistribution among the modes as well as energy relaxation to other degrees of freedom. Measurements on metal carbonyl complexes have played, and continue to play, a crucial role in facilitating the development of 2DIR spectroscopy. These compounds have provided powerful demonstrations of the unique ability of 2DIR spectroscopy to resolve vibrational structure and dynamics in multimode systems. In addition, invaluable new information has been obtained on metal-to-ligand charge transfer processes, solvent-solute interactions and fluxionality. Since transition metal complexes play important roles in catalysis and as dye sensitizers for semiconductor nanoparticle photocatalysis, detailed probes of equilibrium and phototriggered dynamics should aid our understanding of these key catalytic systems. The richness and level of detail provided by the 2DIR spectra of metal carbonyl complexes turn them into extremely useful model systems for testing the accuracy of ab initio quantum chemical calculations. Accurate modeling of the 2DIR spectra of solvated metal carbonyl complexes requires the development of new theoretical and computational tools beyond those employed in the standard analysis of one-dimensional IR spectra, and represents an ongoing challenge to currently available computational methodologies. These challenges are further compounded by the increasing interest in triggered 2DIR experiments that involve nonequilibrium vibrational dynamics on multiple electronic potential surfaces. In this Account, we review the various metal carbonyl complexes studied via 2DIR spectroscopy and outline the theoretical approaches used in order to model the spectra. The capabilities of 2DIR spectroscopy and its interplay with modern ab initio calculations are demonstrated in the context of the metal carbonyl complex Mn(2)(CO)(10) recently studied in our lab. Continued progress in experimental implementation and theoretical analysis will enable transient 2D spectroscopy to provide structurally sensitive details of complex, highly interacting nonequilibrium processes that are central to diverse chemical transformations.

Multidimensional infrared (MDIR) spectroscopy of a strongly coupled multilevel vibrational system Mn(2)(CO)(10) (dimanganese decacarbonyl) in cyclohexane solution reveals fully resolved excited vibrational state coherences that exhibit slow 0.25-0.50 ps(-1) decay constants. Detailed analysis of the waiting-time dependence of certain cross-peak amplitudes shows modulation at multiple frequencies, providing a direct signature of excited vibrational coherences resulting from coherence transfer. A new signature of coherence transfer is observed as temporally modulated cross-peak amplitudes with more than one modulation frequency. The relative importance of different coherence transfer paths is considered in the context of the orientational response of a system which includes two vibrational modes with parallel dipole moments. Since MDIR spectroscopy enables spectral isolation of individual excited vibrational coherences (i.e., coherences between fundamental excitations), these experiments report directly on the frequency-frequency correlation functions of the excited states relative to each other as well as relative to the ground state. These results highlight the rich information contained in fully exploring three-dimensional third-order spectroscopy, particularly regarding chemically relevant slower dynamics and the importance of intramolecular interactions leading to dephasing by optically dark or low-frequency modes of the molecule.