Yu. I. Naberukhin

Geometrical analysis of the structure of simple liquids: percolation approach

The problem of searching for quantitative laws governing the structure of simple liquids is formulated as a site percolation problem on the Voronoi network. The sites of this four-coordinated network correspond to the figures formed by the four neighbouring atoms (Delaunay simplices). Three quantitative characteristics of the form of the Delaunay simplices are introduced to enable one to colour the sites of the Voronoi network corresponding to the simplices of a specific form and to study the percolation of colouring through the network sites. The clusters of contiguous Delaunay simplices of the specific form have been studied and the percolation thresholds for various colouring types have been obtained for instantaneous configurations of the Lennard-Jones liquid (obtained by the Monte Carlo procedure) as well as for the configurations with removed thermal excitations (F structure). Percolation of all the types of colouring introduced turns out to be correlated, i.e., the Delaunay simplices of a given for...

Shape of the delaunay simplices in dense random packings of hard and soft spheres

Two novel shape parameters for Delaunay simplices are proposed which allow one to recognize slightly distorted tetrahedral and octahedral simplices. These simplex types are found to be the basic building units in dense packings of hard and soft spheres.

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.

Spatial localization and dynamics of water molecules with good tetrahedral surroundings

The local structure of the molecular- dynamic model of water (729 particles at 300 K) is analyzed by isolating molecules whose surroundings differ slightly in configuration from a regular tetrahedron. These molecules are not randomly distributed in space but form nanometer clusters having a fractal structure. In these clusters, molecules are less mobile than the model molecules in general;their self- correlation function of rate and the density of vibrational states also differ from the average characteristics of the system.

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.

An analytical method of computation of radial distribution functions at large distances for liquids and amorphous substances

An analytical method is proposed to obtain quantitatively the radial distribution function (RDF) at large distances for liquids and amorphous materials from the structure factor [S(q)] data in the region of its main peak only. The RDFs obtained prove to be unaffected by the random spread of the experimental points at the tail of S(q). The method is illustrated for a number of simple liquids and for liquid and amorphous solid water. The application of the method to the S(q) extrapolation to the low-q region and the problem of the experimental determination of the direct correlation function are discussed.