Yu. Ya. Efimov

The fluctuation hypothesis of hydrogen bonding: I. General discussion

This paper opens a series of articles devoted to the theoretical calculation and physical interpretation of the band shapes in the infra-red and Raman spectra of H-bonded liquids on the basis of the fluctuation model of hydrogen bonding. In the present introductory article general features of the fluctuation model are discussed and the fluctuations of H-bond configurations are classified as dynamical and statistical ones. It is shown that in liquids such as water or alcohols the statistical fluctuations play a dominant role, i.e. the band broadening originates from disorder in equilibrium positions and orientations of the molecules in liquid. This idea does not yet permit us, however, to make the direct calculations of the spectral band shape on the basis of structural data. A semi-empirical approach is proposed instead which allows us to calculate in the frames of the fluctuation model the band shapes in the infra-red and Raman spectra of numerous water complexes with organic bases and of pure H2O and D2...

The fluctuation hypothesis of hydrogen bonding

The paper is devoted to calculations of the contour shapes in the infra-red and Raman spectra of the 1 : 1 and 1 : 2 type complexes of ordinary and heavy water with two organic bases, dioxane and dimethyl sulphoxide, by means of a computer. The calculations have been made using the mathematical formalism developed in the previous papers of this series which takes into account the coupling between two stretching vibrations of the water molecule and the overtone of its bending vibration for a set of the liquid molecules variously perturbed by non-equal H-bonds. The basic parameters of the model are obtained from the spectra of HOD molecules involved in the same complex as the one considered, and from empirical correlations discussed in the previous papers. Starting from a set of parameters determined in this manner we calculate three spectra simultaneously for each of the above-mentioned complexes, namely the infra-red spectrum and the isotropic and anisotropic components of the Raman spectrum. Every spectr...

The fluctuation hypothesis of hydrogen bonding: IV. Calculation of the vibrational spectra of 1:2 complexes of XH2 molecules including Fermi resonance

On the basis of a fluctuation model of hydrogen bonding which takes into account the non-equivalence of H-bonds due to fluctuations of local environments in liquids, a mathematical formalism is developed to calculate the fluctuation spectral contours for the case of coupling of two stretching vibrations and the overtone of the bending mode (Fermi resonance). Computer calculations of the contour shape are performed for the infra-red and Raman spectra of the 1 : 2 complexes formed by an XH2 molecule with two proton-acceptor molecules. The fluctuation model is shown to explain in a quantitative manner some important empirical regularities established for the infra-red spectra of various complexes of water and primary amines with organic bases, namely the convergence of the frequencies of two observed maxima and the equalization of their intensities, both of which accompany the strengthening of H-bonds. The calculations provide the logical connection between numerous empirical correlations inherent in essenti...

The fluctuation hypothesis of hydrogen bonding: III. The calculation of the vibrational spectra of water complexes of the type 1-1

On the basis of the fluctuation hypothesis of hydrogen bonding analytical formulae are obtained for the band shape in the infra-red and Raman spectra of stretching vibrations of H2O molecules with only one OH group involved in H-bonding (so-called complexes of the type 1-1 [1]). The statistical distribution of stretching frequencies ωOH affected by H-bonds of different strengths is derived from the spectrum of HOD molecules in a similar complex using empirical correlation between the half-width of the band and the shift of its maximum relative to monomeric frequency. The coupling of intramolecular vibrations has been taken into account by means of the method of partial oscillators developed in [3], and the frequencies and intensities have been calculated in vibrational spectra of a continuum of water molecules differently perturbed by H-bonding. The series of computations are performed with varying values of basic parameters of the model in order to establish their influence on the spectra. The results of...

Fluctuation theory of hydrogen bonding applied to vibration spectra of HOD molecules in liquid water. I. Raman spectra

Statistical distributions of the frequencies of OH vibrations calculated from the experimental Raman spectra of HOD molecules over the temperature range of 10–200 C using the recently developed deconvolution technique have been analysed in the framework of fluctuation theory of hydrogen bonding. Two temperature independent functions that are the basis of the Zhukovsky theory for describing the temperature transformation of frequency distribution functions of OH vibrations in a statistical ensemble of O—H…O bonds were established and analytically approximated. This made it possible to reconstruct the entire set of initial spectra and to extrapolate their forms to a wider temperature range. These results support the continuum model of liquid water structure.

Fluctuation theory of hydrogen bonding applied to vibration spectra of HOD molecules in liquid water. II. Infrared spectra: contour shape, integrated intensity, temperature dependence

The infrared spectra of HOD molecules in liquid water are calculated at constant density over the temperature range of 10 to 400°C from the statistical distributions of the vibration frequencies of water OH-groups determined previously from the experimental Raman spectra. Their shape and position are extrapolated over a wider temperature range. The dependence of contour shape and integrated intensity of the IR band on the frequency of its maximum, the first moment of a statistical contour and temperature are described numerically and analytically. Calculations are in qualitative agreement with all available experimental material and fitted quantitatively at a density of water of ∼1 g cm−3. The success of the proposed model applied to infrared spectra supports once more the continuum treatment of liquid water structure.

Stretching frequency distribution and hydrogen bond thermodynamics in water as calculated from ir spectra using the fluctuation model

This paper analyzes recent data on statistical distribution of OH vibration frequencies of liquid water calculated from the IR spectra of HOD molecules. The data are analyzed in terms of the hydrogen bond fluctuation concept. Two temperature invariant functions providing a reconstruction of the whole set of initial data and the statistical integral permitting one to calculate the configuration contributions to the internal energy, entropy, and heat capacity of liquid water over a wide temperature range are found and approximated analytically. The calculated heat capacity is in good agreement with thermophysical experimental data.

Correlations between bond lengths and stretching frequencies in the O—D...O hydrogen bridge and their consequences

Based on modern neutron diffraction data and the known empirical correlations between the geometric and spectroscopic parameters of hydrogen bonds, the analytical expression describing the relation between the O—D covalent and D...O hydrogen bond lengths in the O—D...O hydrogen bridge was obtained. The distribution functions of the interatomic and nearest intermolecular distances in heavy water were calculated from the Raman band shapes in the 10 to 90 °C temperature interval in the framework of the fluctuation theory of hydrogen bonding.

Asymmetry of H2O Molecules in the Liquid State and Its Consequences

The correlations between the geometrical parameters of the O–H...O hydrogen bridge and the stretching frequency νOH are refined by using neutron diffraction and vibrational spectroscopy data. The distribution functions of the interatomic distances rOH and intermolecular distances RO...O in water in the range from –40 to 100°C were calculated from the Raman spectra of HOD. The extent of asymmetry of H2O molecules in the liquid state, caused by fluctuations of the local environment of two OH groups, and its manifestations in the structure and vibrational spectra of water are analyzed.

Nature of the broadening, the form of the spectral bands, and thevAH − RA...B correlation in liquids with hydrogen bonds

ConclusionThe experimentally established correlation for crystals between the frequency of the OH (or OD) stretching vibrations and the interatomic separation RO·O can also be used for each hydrogen bond in the liquid phase taken in isolation, if the equilibrium length Re is used for RO·O. The empirical correlation between the low-frequency shift of the band and its broadening results from the exponentialvOH(Re) relationship, while the distribution function of the frequencies in the vibrational spectrum P(ν) corresponds to the distribution of the energies of the hydrogen bonds P(E). When the deflection of the equilibrium configurations of the H bonds can be neglected, P(ν) is expressed unambiguously through the distribution of the lengths of the hydrogen bonds P(Re) and makes it possible to determine their variance. Otherwise (the continuous network of strongly deflected H bonds in liquid water) the complex form of the spectral band and its temperature dependence can be described quantitatively by a simple equation of the Boltzmann type, in which the exponential part is the energy of the hydrogen bond (the depth of the potential well) making a contribution to the spectrum at the investigated frequency. The agreement between calculation and experiment reveals an important fact, i.e., the equality of the energies for the various configurations of the hydrogen bond producing one and the same frequencyvOH.