Modeling of the Hydrogen Bond-Induced Frequency Shifts of the HOH and HOD Bending Modes of Water.

The intramolecular bending mode of water is a possible useful probe of the hydrogen-bond situations in aqueous systems, but the behavior of its frequency and intensity should be further elucidated for better understanding on its nature and, hence, for its better utilization as a probe. Here, an analysis toward this goal is conducted by doing theoretical calculations on molecular clusters of normal isotopic and deuterated species of water and examining the correlations among the vibrational, structural, and electrostatic properties. It is shown that electrostatic interactions, particularly both of the in-plane components of the electric field along the OH bond and perpendicular to it, play a major role in controlling the hydrogen bond-induced shifts of the force constant, but additional factors, including the intermolecular structural and/or charge-transfer properties, are also important. Models of the hydrogen bond-induced shifts of the force constant are presented in a form that may be combined with classical molecular dynamics. With regard to the infrared intensity changes, it is shown on the basis of the electron density analysis that the intermolecular charge flux and polarization effect play an important role, depending on the angular characteristics of the hydrogen bond.

Asymmetry of the Electrostatic Environment as the Origin of the Symmetry Breaking Effect of the Nitrate Ion in Aqueous Solution.

Elucidating the mechanism of how vibrational modes are affected by intermolecular interactions is important for a better understanding of the nature of the former as probes of the latter. Here, such an analysis is carried out for the N-O stretching modes of the nitrate ion interacting with water, with an emphasis on the symmetry breaking effect. On the basis of theoretical calculations on the structural, vibrational, and electrostatic properties of molecular clusters and spectral simulations for an aqueous solution, a transparent view is demonstrated on the mechanism that modulations of spatially local electrostatic environment give rise to structural and spectroscopic symmetry breaking effect. The electrostatic interaction model constructed here is a seven-parameter model; the use of a single electrostatic parameter, such as the electric field on a single atomic site, is found to be insufficient for quantitative evaluation. It is also shown that the frequency modulations of the N-O stretching modes in aqueous solution occur on a time scale much shorter than 0.1 ps.

Substituent Effect and Its Halogen-Atom Dependence of Halogen Bonding Viewed through Electron Density Changes.

Elucidating how the halogen-bonding ability and strength are controlled by the substituent effect and how this control depends on halogen atom will be essential for finely-tuned design of functionally important molecules. Here, this problem is tackled by analyzing the electron density differences/changes for variously substituted halobenzenes. It is shown that the anisotropy of the electron distribution around the halogen atom, which is an important factor for halogen-bonding ability, is not much affected by the substituent effect and rather simply depends on the halogen atom, while the partial charge on the halogen atom, which is related to the bond dipole of the C-X bond, is significantly modulated by the substituent effect and gives rise to enhancement of the electrostatic potential on the line extended from the C-X bond. The properties related to the polarization effect are also discussed.

Nature of hydrogen-bond-enhanced halogen bonding viewed through electron density changes.

Elucidating the mechanism of how we can achieve fine tuning of intermolecular interaction strength will be helpful for designing functionally important molecules. In the present study, a theoretical analysis is conducted, by examining the electron density changes, for two halogen-bonding iodinated systems whose halogen-bond strengths have been considered to be enhanced by the presence of a hydrogen-bond donating group (termed hydrogen-bond-enhanced halogen bonding). It is shown that, contrary to the expectation obtained from the enhancement of electrostatic potential along the line extended from the C-I bond, the anisotropy of electron distribution on the iodine atom remains nearly the same. This means that the hydrogen bond and halogen bond contribute almost independently and additively to the enhancement of electrostatic potential, indicating the nature of this enhancement and, in a more general sense, the relationship between the strength and the extent of directionality of halogen bonding.

Infrared Spectra and Hydrogen-Bond Configurations of Water Molecules at the Interface of Water-Insoluble Polymers under Humidified Conditions.

Elucidating the state of interfacial water, especially the hydrogen-bond configurations, is considered to be key for a better understanding of the functions of polymers that are exhibited in the presence of water. Here, an analysis in this direction is conducted for two water-insoluble biocompatible polymers, poly(2-methoxyethyl acrylate) and cyclic(poly(2-methoxyethyl acrylate)), and a non-biocompatible polymer, poly(n-butyl acrylate), by measuring their IR spectra under humidified conditions and by carrying out theoretical calculations on model complex systems. It is found that the OH stretching bands of water are decomposed into four components, and while the higher-frequency components (with peaks at ∼3610 and ∼3540 cm-1) behave in parallel with the C═O and C-O-C stretching and CH deformation bands of the polymers, the lower-frequency components (with peaks at ∼3430 and ∼3260 cm-1) become pronounced to a greater extent with increasing humidity. From the theoretical calculations, it is shown that the OH stretching frequency that is distributed from ∼3650 to ∼3200 cm-1 is correlated to the hydrogen-bond configurations and is mainly controlled by the electric field that is sensed by the vibrating H atom. By combining these observed and calculated results, the configurations of water at the interface of the polymers are discussed.

Singular value decomposition analysis of the electron density changes occurring upon electrostatic polarization of water.

In-depth elucidation of how molecules are electrically polarized would be one key factor for understanding the properties of those molecules under various thermodynamic and/or spatial conditions. Here this problem is tackled for the case of hydrogen-bonded water by conducting singular value decomposition of the electron density changes that occur upon electrostatic polarization. It is shown that all those electron density changes are approximately described as linear combinations of ten orthonormal basis "vectors". One main component is the interatomic charge transfer through each OH bond, while some others are characterized as the atomic dipolar polarizations, meaning that both of these components are important for the electrostatic polarization of water. The interaction parameters that reasonably well reproduce the induced dipole moments are derived, which indicate the extent of mixing of the two components in electrostatic polarization.

Hidden Halogen-Bonding Ability of Fluorine Manifesting in the Hydrogen-Bond Configurations of Hydrogen Fluoride.

Elucidating how the intermolecular interactions of a covalently bonded fluorine atom are similar to and different from those of the other halogen atoms will be helpful for a better unified understanding of them. In the present study, the case of hydrogen fluoride is theoretically studied from this viewpoint by using the techniques of electron density analysis, molecular dynamics of liquid, and others. It is shown that the extra-point model, which locates an additional charge site on the line extended from (not within) the covalent bond and has been adopted for halogen-bonding systems as a key to the generation of proper stability and directionality, works well also in this case. A significantly bent hydrogen-bond configuration, which is characteristic of the intermolecular interactions of hydrogen fluoride, is reasonably well reproduced, meaning that it is a manifestation of the latent halogen-bonding ability, which is hidden by the strongly electronegative nature.

Role of Intermolecular Charge Fluxes in the Hydrogen-Bond-Induced Frequency Shifts of the OH Stretching Mode of Water.

The relation between the vibrational properties and the electrostatic situations of the vibrating functional group is useful to predict vibrational spectroscopic features based on, for example, classical molecular dynamics of liquids or biomolecular systems, but to pursue its generality or the extent of applicability, it is required to understand the mechanisms giving rise to it. Here such an analysis is carried out for the OH stretching mode of water. By examining the correlations among various (structural, vibrational, and electrostatic) properties and by analyzing the spatial characteristics of the behavior of electrons occurring upon the vibration, it is shown that the dependence of the vibrational frequency and the dipole derivative of the OH stretching mode on the electric field is not of purely electrostatic origin, and the delocalized electronic motions occurring with this mode, called intermolecular charge fluxes, related to both the dipole first and second derivatives play important roles.

Dissecting the electric quadrupolar and polarization effects operating in halogen bonding through electron density analysis with a focus on bromine.

The form of the electron density change (or difference) is usable as a kind of fingerprint of the electronic structural origin or mechanism that gives rise to intermolecular interactions. Here, this method is applied to halogen-bonding brominated systems to dissect the electric quadrupolar effect (arising from the anisotropic distribution of the valence electrons and intrinsic to the s2px 2py 2pz electronic configuration) and the polarization effect (induced by a partial negative charge of the halogen-bond accepting atom). It is shown that a suitable location of the "extra point" for placing a partial positive charge to represent the former is crucial and is clearly found from the electron density difference from the spherically isotropic Br- ion, while the latter consists of the dipolar polarization of the Br atom and the delocalized polarization of the whole molecule. A practical way for application to molecular dynamics simulations, etc., to represent these two factors is discussed.

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.

Hydrogen order at the surface of ice Ih revealed by vibrational spectroscopy.

Among numerous crystalline phases of ice, the Ih phase is the most stable above 72 K at atmospheric pressure. It is well established that the orientations of water molecules in the bulk of ice Ih are statistical without long-range order. However, the orientational order of water at the surface of ice Ih has been enigmatic. Here we show that the surface of ice Ih at 100 K has hydrogen order with the OH group pointing upward to the air ("H-up" orientation). We applied nonlinear optical spectroscopy and theoretical modeling to the surface of isotopically pure and diluted ice Ih and observed OH stretch vibrational signatures attributed to H-up ordering. Furthermore, we found that this hydrogen order takes place despite a more inhomogeneous microenvironment at the surface than in the bulk. Our results suggest the prominent role of the surface to allow the reorientation of water molecules for hydrogen ordering that is virtually prohibited in the bulk.

Correlation of the partial charge-transfer and covalent nature of halogen bonding with the THz and IR spectral changes.

The electronic structural origin of the THz and IR spectral changes occurring upon halogen-bond formation is examined by employing the technique of electron density analysis. Theoretical calculations and analyses are conducted for the complexes of pentafluoroiodobenzene (C6F5I) and nitryl chloride (O2NCl) formed with other (halogen-bond accepting) molecules taken as typical examples. It is shown that, in the case of the C-I stretching mode of C6F5I appearing in the THz spectral region, the intensity enhancement occurring upon halogen-bond formation arises from the intermolecular charge flux and (together with the vibrational frequency) is correlated to the partial charge-transfer and covalent nature of the halogen bond. For the N-Cl stretching vibration of O2NCl, it is shown that the high-frequency shift occurring upon complex formation with NH3 arises mainly from the electrostatic effect, while the reduction of its IR intensity arises from the polarization effect and, to a larger extent, from the intermolecular charge flux. These results indicate, therefore, that there are some observable spectroscopic properties in the THz and IR region that are mainly controlled by (and, hence, shed light on) the partial charge-transfer and covalent nature of halogen bonding.

Intermediate length-scale chirality related to the vibrational circular dichroism intensity enhancement upon fibril formation in a gelation process.

Chiro-optical spectroscopic methods, such as vibrational circular dichroism (VCD) spectroscopy, are regarded as useful measures that provide us information on the structural properties of chiral species, but for correct interpretation of the measured spectra, appropriate modeling that can be compared with the observed spectra is essential. In the present study, the origin of the VCD intensity enhancement observed upon fibril formation in a gelation process is examined theoretically. Comparing with the observed spectroscopic feature and also with the observed scanning electron microscope (SEM) image, it is derived that there are at least three hierarchical tiers of chirality in the gel. The VCD intensity enhancement originates from one of them on the ∼50 nm length scale, which consists of a co-axial antiparallel right-handed double helical structure that persistently continues over ∼100 molecules, indicating that the intermediate length-scale fibril formation plays a crucial role in the VCD intensity enhancement, in a way similar to some fibril-forming peptides examined previously. The time course of the gelation process observed by the time dependence of the VCD intensity is also shown and discussed.

Strategy for Modeling the Electrostatic Responses of the Spectroscopic Properties of Proteins.

For better understanding and more efficient use of the spectroscopic probes (vibrational and NMR) of the local electrostatic situations inside proteins, appropriate modeling of the properties of those probes is essential. The present study is devoted to examining the strategy for constructing such models. A more well-founded derivation than the ones in previous studies is given in constructing the models. Theoretical analyses are conducted on two representative example cases related to proteins, i.e., the peptide group of the main chains and the CO and NO ligands to the Fe2+ ion of heme, with careful treatment of the behavior of electrons in the electrostatic responses and with verification of consistency with observable quantities. It is shown that, for the stretching frequencies and NMR chemical shifts, it is possible to construct reasonable electrostatic interaction models that encompass the situations of hydration and uniform electric field environment and thus are applicable also to the cases of nonuniform electrostatic situations, which are highly expected for inside of proteins.

Intermolecular charge fluxes and far-infrared spectral intensities of liquid formamide.

The intensity generation mechanisms of the far-infrared (far-IR) [or terahertz (THz)] spectrum of liquid formamide, particularly with regard to the behavior of electrons induced by modulations of the hydrogen-bonding conditions of the molecules, are examined theoretically. The theoretical analysis is done in the following two steps. First, density functional theory (DFT) calculations are carried out for the dimers and larger clusters of formamide to analyze the change in the dipole derivative (the square of which is proportional to the IR intensity) induced by hydrogen-bond formation. Then, by using the information derived in the first step, molecular dynamics-based spectral simulations are carried out. It is shown that, upon formation of a hydrogen bond, a change in the dipole derivative is induced along the direction of the hydrogen bond, and is reasonably modeled by the intermolecular charge flux mechanism, where a certain amount of electron density is transferred between molecules according to the modulation of the hydrogen-bond length, similarly to the case of liquid water. This model is in a form that is suitable for use in molecular dynamics-based spectral simulations. From these spectral simulations, it is found that the observed spectral features of the far-IR spectrum of liquid formamide are reasonably reproduced, and that the inclusion of the effect of intermolecular charge flux is essential for it. Contrary to the case of liquid water, the molecular libration band (rather than the molecular translation band) is significantly enhanced by the intermolecular charge flux. It is discussed that this difference is related to the geometrical relation between the hydrogen bonds and the atomic displacements in the molecular translations and librations (rotations). It is considered that, in general, in hydrogen-bonding liquids, modulations of hydrogen-bond lengths occurring upon dynamics of molecules give rise to intermolecular charge fluxes, significantly affecting the dipole derivatives, and hence, the IR intensity distributions in the spectra.

Unified Electrostatic Understanding on the Solvation-Induced Changes in the CN Stretching Frequency and the NMR Chemical Shifts of a Nitrile.

Understanding on the spectroscopic properties of a functional group is essential to use it to detect changes in the structural and/or dynamical properties through the situations of intermolecular interactions. The present study is devoted to elucidating the factors that control the solvation-induced changes in the C≡N stretching frequency and the (13)C and (15)N NMR chemical shifts of the nitrile group. It is shown that the nonelectrostatic contribution of the hydration-induced changes in the C≡N stretching frequency as previously thought, as well as the specific effect of hydrogen bonding on the (13)C and (15)N chemical shifts, actually originate from the spatially inhomogeneous nature of the electrostatic situation generated by the hydrogen-bond donating water molecule, especially by the OH bond dipole. On this basis, a unified electrostatic interaction model that encompasses the cases of both hydration and dipolar solvation is constructed. The responses of electrons in these two cases are also discussed.

Roles of the scalar and vector components of the solvation effects on the vibrational properties of hydrogen- or halogen-bond accepting stretching modes.

Solvation-induced vibrational frequency shifts and infrared (IR) intensity changes of the hydrogen- or halogen-bond accepting stretching modes, especially their dependence on the angular position of the hydrogen- or halogen-bond donating molecule, are examined theoretically. Calculations are carried out for some modes of hydrogen- or halogen-bonding molecular complexes, including the S[double bond, length as m-dash]O stretch of dimethyl sulfoxide-(13)C2H2O, the C[triple bond, length as m-dash]N stretch of acetonitrileH2O, and the amide I' mode of the N-methylacetamide-d1BrNC 1 : 1 complex. It is shown that, in all the example cases dealt with in this study, the frequency shift depends rather strongly on the hydrogen- or halogen-bond angle (e.g., S[double bond, length as m-dash]OH angle), with a larger low-frequency shift as the hydrogen or halogen bond becomes more bent, indicating the generality of the results obtained for the amide I' mode of the N-methylacetamide-d1(2)H2O 1 : 1 complex in a previous study. Contrary to our vague expectation, the frequency shift is not well correlated to the hydrogen- or halogen-bond distance or strength, but nevertheless, it is well reproduced by an electrostatic interaction model if it is carefully constructed by considering the scalar and vector components separately in a reasonable way. On the basis of this electrostatic interaction model, the reason why our vague expectation is not realized is clarified, and a unified understanding is achieved on the hydration-induced high-frequency shift of the C[triple bond, length as m-dash]N stretch and the low-frequency shifts of the S[double bond, length as m-dash]O stretch and amide I'. With regard to the IR intensity, it is shown that, in some of the example cases, it also has rather strong angular position dependence. The mechanism of the IR intensity changes is estimated by analyzing the dipole derivative vector, especially its angular relation with the hydrogen or halogen bond.

Secondary Structure Dependence and Hydration Effect of the Infrared Intensity of the Amide II Mode of Peptide Chains.

Every vibrational mode to be used as a marker of the structural, dynamical, and/or interaction properties demands our good understanding of the relations between those properties and the spectral features. The present study is devoted to elucidating the effects of secondary structure variations and hydration on the infrared (IR) intensity of the amide II mode of peptide chains. It is shown that the IR intensity is significantly enhanced for the C5 (fully extended planar ß-strand) conformation because of the interpeptide charge flux through the H···O interaction of the C5 ring, and there is a small cooperative effect giving rise to a larger enhancement for a consecutive C5 conformation. In contrast, the IR intensity is reduced for the α-helix conformation because of the partially canceling polarization effect of the hydrogen-bond accepting O atom in the N-H···O═C hydrogen bond and the absence of the interpeptide charge flux. With regard to the hydration effect, it is found that the IR intensity enhancement/reduction depends critically on the angular position of the hydrating water molecule, and is related to the presence/absence of the intermolecular charge flux and the polarization effect. It is suggested that, both for the secondary structure dependence and for the hydration effect, the geometrical relation between the vibrating N-H bond and the H···O interaction (of the C5 ring and/or the hydrogen bond) is an essential factor determining the enhancement/reduction of the IR intensity of the amide II mode.

Amide I Vibrational Properties Affected by Hydrogen Bonding Out-of-Plane of the Peptide Group.

The amide I vibrational properties of a peptide-water complex in various intermolecular configurations are analyzed theoretically to see whether a water molecule with a weak out-of-plane hydrogen bond really induces a large low-frequency shift. It is shown that the frequency shift strongly depends on the C═O···H angle, with a larger low-frequency shift as the C═O···H becomes more bent, suggesting that the so-called hydrated helix with a rather low amide I frequency has an additional water molecule located out-of-plane of the peptide group as compared with a typical α-helix. The infrared intensity also depends on the angular position of water. A new model parameter set (that can be combined with molecular dynamics) is developed for a more correct representation of the hydration-induced frequency shift. The question regarding the scalar and vectorial nature of the molecular properties related to the frequency shift is also discussed.