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.

Infrared absorption spectra in the C[triple bond]N stretching frequency region were collected for methyl thiocyanate, the simplest model aliphatic thiocyanate, in several common solvents to establish the dependence of the C[triple bond]N spectral band of aliphatic thiocyanate on its local solvation environment. Systematic changes in the C[triple bond]N bandwidth indicate that it reports on fast solvation dynamics. Anomalous asymmetry and temperature dependence of the C[triple bond]N band in fluorinated alcohol solvents indicates that these solvents participate in formation of a discrete hydrogen-bonded complex with the C[triple bond]N end of methyl thiocyanate. These observations indicate that the C[triple bond]N band of thiocyanate could be an effective site-specific probe of both specific hydrogen bonding and local dynamics in more complex systems, such as peptides and proteins.

The vibrational frequency of a chosen normal mode is one of the most accurately measurable spectroscopic properties of molecules in condensed phases. Accordingly, infrared absorption and Raman scattering spectroscopy have provided valuable information on both distributions and ensemble-average values of molecular vibrational frequencies, and these frequencies are now routinely used to investigate structure, conformation, and even absolute configuration of chemical and biological molecules of interest. Recent advancements in coherent time-domain nonlinear vibrational spectroscopy have allowed the study of heterogeneous distributions of local structures and thermally driven ultrafast fluctuations of vibrational frequencies. To fully utilize IR probe functional groups for quantitative bioassays, a variety of biological and chemical techniques have been developed to site-specifically introduce vibrational probe groups into proteins and nucleic acids. These IR-probe-labeled biomolecules and chemically reactive systems are subject to linear and nonlinear vibrational spectroscopic investigations and provide information on the local electric field, conformational changes, site-site protein contacts, and/or function-defining features of biomolecules. A rapidly expanding library of data from such experiments requires an interpretive method with atom-level chemical accuracy. However, despite prolonged efforts to develop an all-encompassing theory for describing vibrational solvatochromism and electrochromism as well as dynamic fluctuations of instantaneous vibrational frequencies, purely empirical and highly approximate theoretical models have often been used to interpret experimental results. They are, in many cases, based on the simple assumption that the vibrational frequency of an IR reporter is solely dictated by electric potential or field distribution around the vibrational chromophore. Such simplified description of vibrational solvatochromism generally referred to as vibrational Stark effect theory has been considered to be quite appealing and, even in some cases, e.g., carbonyl stretch modes in amide, ester, ketone, and carbonate compounds or proteins, it works quantitatively well, which makes it highly useful in determining the strength of local electric field around the IR chromophore. However, noting that the vibrational frequency shift results from changes of solute-solvent intermolecular interaction potential along its normal coordinate, Pauli exclusion repulsion, polarization, charge transfer, and dispersion interactions, in addition to the electrostatic interaction between distributed charges of both vibrational chromophore and solvent molecules, are to be properly included in the theoretical description of vibrational solvatochromism. Since the electrostatic and nonelectrostatic intermolecular interaction components have distinctively different distance and orientation dependences, they affect the solvatochromic vibrational properties in a completely different manner. Over the past few years, we have devel...

We relate the solvent and temperature dependence of the rates of intramolecular electron transfer (ET) of mixed valence complexes of the type {[Ru3O(OAc)6(CO)(L)]2-BL}-1, where L = pyridyl ligand and BL = pyrazine. Complexes were reduced chemically or electrochemically to obtain the mixed valence anions in seven solvents: acetonitrile, methylene chloride, dimethylformamide, tetrahydrofuran, dimethylsulfoxide, chloroform, and hexamethylphosphoramide. Rate constants for intramolecular ET were estimated by simulating the observed degree of nu(CO) IR band shape coalescence in the mixed valence state. Correlations between rate constants for ET and solvent properties including static dielectric constant, optical dielectric constant, the quantity 1/epsilonop - 1/epsilonS, microscopic solvent polarity, viscosity, cardinal rotational moments of inertia, and solvent relaxation times were examined. In the temperature study, the complexes displayed a sharp increase in the ket as the freezing points of the solvents methylene chloride and acetonitrile were approached. The solvent phase transition causes a localized-to-delocalized transition in the mixed valence ions and an acceleration in the rate of ET. This is explained in terms of decoupling the slower solvent motions involved in the frequency factor nuN which increases the value of nuN. The observed solvent and temperature dependence of the ket for these complexes is used in order to formulate a new definition for Robin-Day class II-III mixed valence compounds. Specifically, it is proposed that class II-III compounds are those for which thermodynamic properties of the solvent exert no control over ket, but the dynamic properties of the solvent still influence ket.

Covalently bound azido groups are found in many commercially available biomolecular precursors and substrates, and the NNN asymmetric stretching band of these groups is a strong infrared absorber that appears in a spectral region clear of other signals. In order to evaluate comprehensively the solvatochromism of the asymmetric azido NNN stretching band for site-specific use in biomolecular contexts, infrared spectra of the model compounds 5-azido,1-pentanoic acid and 3-(p-azidophenyl),1-propanoic acid were acquired in a large variety of nonpolar, polar, and hydrogen-bond-donating solvents, as well as mixed aqueous-organic solvents. Spectra in pure solvents indicated that the aliphatic NNN stretching frequency maximum does not depend on solvent polarity, while the aromatic NNN frequency displays a weak but nonzero sensitivity to polarity. In both cases, the NNN frequency exhibits a blue-shift in H-bond-donating solvents, but the frequency in water is higher than in any other H-bond-donating solvent including solvents that are stronger H-bond donors. In nonfluorinated H-bond donor solvents, the frequency blue shift scales with the density of H-bond donors. This sensitivity to the presence of water was further explored in several mixed solvent environments, with the conclusion that this vibrational mode is a highly specific sensor of hydration, even in environments containing other H-bond donors like amides and alcohols, due to the very high local density of H-bond donors in water. The relatively uncomplicated (compared to nitriles, for example), water-specific response of this vibrational mode should lead to its adoption as a site-specific probe of hydration in many different possible systems in which the presence and role of molecular water is of primary interest.