N. N. Medvedev

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...

An algorithm for three‐dimensional Voronoi S‐network

The paper presents an algorithm for calculating the three‐dimensional Voronoi–Delaunay tessellation for an ensemble of spheres of different radii (additively‐weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S‐network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).

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.

Volumetric Properties of Hydrated Peptides: Voronoi–Delaunay Analysis of Molecular Simulation Runs

The study of hydration, folding, and interaction of proteins by volumetric measurements has been promoted by recent advances in the development of highly sensitive instrumentations. However, the separation of the measured apparent volumes into contributions from the protein and the hydration water, V(app) = V(int) + ΔV, is still challenging, even with the detailed microscopic structural information from molecular simulations. By the examples of the amyloidogenic polypeptides hIAPP and Aβ42 in aqueous solution, we analyze molecular dynamics simulation runs for different temperatures, using the Voronoi-Delaunay tessellation method. This method allows a parameter free determination of the intrinsic volume V(int) of complex solute molecules without any additional assumptions. For comparison, we also use fused sphere calculations, which deliver van der Waals and solute accessible surface volumes as special cases. The apparent volume V(app) of the solute molecules is calculated by different approaches, using either a traditional distance based selection of hydration water or the construction of sequential Voronoi shells. We find an astonishing coincidence with the predictions of a simple empirical approach, which is based on experimentally determined amino acid side chain contributions (Biophys. Chem.1999, 82, 35). The intrinsic volumes of the polypeptides are larger than their apparent volumes and also increase with temperature. This is due to a negative contribution of the hydration water ΔV to the apparent volume. The absolute value of this contribution is less than 10% of the intrinsic volume for both molecules and decreases with temperature. Essential volumetric differences between hydration water and bulk water are observed in the nearest neighborhood of the solute only, practically in the first two Delaunay sublayers of the first Voronoi shell. This also helps to understand the pressure dependence of the partial molar volumes of proteins.

Calculation of the volumetric characteristics of biomacromolecules in solution by the Voronoi-Delaunay technique

Recently a simple formalism was proposed for a quantitative analysis of interatomic voids inside a solute molecule and in the surrounding solvent. It is based on the Voronoi-Delaunay tessellation of structures, obtained in molecular simulations: successive Voronoi shells are constructed, starting from the interface between the solute molecule and the solvent, and continuing to the outside (into the solvent) as well as into the interior of the molecule. Similarly, successive Delaunay shells, consisting of Delaunay simplexes, can also be constructed. This technique can be applied to interpret volumetric data, obtained, for example, in studies of proteins in aqueous solution. In particular, it allows replacing qualitatively and descriptively introduced properties by strictly defined quantities, such as the thermal volume, by the boundary voids. The extension and the temperature behavior of the boundary region, its structure and composition are discussed in detail, using the example of a molecular dynamics model of an aqueous solution of the human amyloid polypeptide, hIAPP. We show that the impact of the solute on the local density of the solvent is short ranged, limited to the first Delaunay and the first Voronoi shell around the solute. The extra void volume, created in the boundary region between solute and solvent, determines the magnitude and the temperature dependence of the apparent volume of the solute molecule.

Can Various Classes of Atomic Configurations (Delaunay Simplices) be Distinguished in Random Dense Packings of Spherical Particles

Abstract One-dimensional and two-dimensional distributions of the characteristics introduced previously for the forms of Delaunay simplices - tetrahedricity and octahedricity - have been investigated in computer models of a crystal, a liquid and an amorphous solid. It has been established that in the absence of thermal perturbations (in the proper structure of the liquid and in an amorphous substance) there exists a distinguishable class of simplices with five almost equal edges and the sixth being longer. This class of simplices named isopentacmons, in turn includes the types of good tetrahedra and good quartoctahedra (a quarter of octahedron). In disordered systems the fraction of tetrahedra relative to quartoctahedra exceeds substantially that in the FCC crystal.

Water adsorption isotherms on porous onionlike carbonaceous particles. Simulations with the grand canonical Monte Carlo method.

The grand canonical Monte Carlo method is used to simulate the adsorption isotherms of water molecules on different types of model soot particles. These soot models are constructed by first removing atoms from onion-fullerene structures in order to create randomly distributed pores inside the soot, and then performing molecular dynamics simulations, based on the reactive adaptive intermolecular reactive empirical bond order (AIREBO) description of the interaction between carbon atoms, to optimize the resulting structures. The obtained results clearly show that the main driving force of water adsorption on soot is the possibility of the formation of new water-water hydrogen bonds with the already adsorbed water molecules. The shape of the calculated water adsorption isotherms at 298 K strongly depends on the possible confinement of the water molecules in pores of the carbonaceous structure. We found that there are two important factors influencing the adsorption ability of soot. The first of these factors, dominating at low pressures, is the ability of the soot of accommodating the first adsorbed water molecules at strongly hydrophilic sites. The second factor concerns the size and shape of the pores, which should be such that the hydrogen bonding network of the water molecules filling them should be optimal. This second factor determines the adsorption properties at higher pressures.

Computer simulation study of intermolecular voids in unsaturated phosphatidylcholine lipid bilayers

Computer simulation of the liquid crystalline phase of five different hydrated unsaturated phosphadidylcholine (PC) lipid bilayers, i.e., membranes built up by 18:0/18:1omega9cis PC, 18:0/18:2omega6cis PC, 18:0/18:3omega3cis PC, 18:0/20:4omega6cis PC, and 18:0/22:6omega3cis PC molecules have been performed on the isothermal-isobaric ensemble at 1 atm and 303 K. (The notation n:domegapcis specifies the lipid tails: n refers to the total number of carbon atoms in the chain, d is the number of the methylene-interrupted double bonds, p denotes the number of carbons between the chain terminal CH(3) group and the nearest double bond, and cis refers to the conformation around the double bonds.) The characteristics of the free volume in these systems have been analyzed by means of a generalized version of the Voronoi-Delaunay method [M. G. Alinchenko et al., J. Phys. Chem. B 108, 19056 (2004)]. As a reference system, the hydrated bilayer of the saturated 14:014:0 PC molecules (dimyristoylphosphatidylcholine) has also been analyzed. It has been found that the profiles of the fraction of the free volume across the membrane exhibit a rather complex pattern. This fine structure of the free volume fraction profiles can be interpreted by dividing the membrane into three separate major zones (i.e., zones of the aqueous, polar, and apolar parts of the membrane) and defining five subzones within these zones according to the average position of various atomic groups in the membrane. The fraction of the free volume in the middle of the membrane is found to increase with increasing unsaturation of the sn-2 chain of the lipid molecule. This is due to the fact that with increasing number of methylene-interrupted double bonds the lipid tails become more flexible, and hence they do not extend to the middle of the membrane. It is found that there are no broad enough preformed channels in the bilayers through which small penetrants, such as water molecules, can readily go through; however, the existing channels can largely facilitate the permeation of these molecules.

Structural and thermodynamic properties of different phases of supercooled liquid water

Computer simulation results are reported for a realistic polarizable potential model of water in the supercooled region. Three states, corresponding to the low density amorphous ice, high density amorphous ice, and very high density amorphous ice phases are chosen for the analyses. These states are located close to the liquid-liquid coexistence lines already shown to exist for the considered model. Thermodynamic and structural quantities are calculated, in order to characterize the properties of the three phases. The results point out the increasing relevance of the interstitial neighbors, which clearly appear in going from the low to the very high density amorphous phases. The interstitial neighbors are found to be, at the same time, also distant neighbors along the hydrogen bonded network of the molecules. The role of these interstitial neighbors has been discussed in connection with the interpretation of recent neutron scattering measurements. The structural properties of the systems are characterized by looking at the angular distribution of neighboring molecules, volume and face area distribution of the Voronoi polyhedra, and order parameters. The cumulative analysis of all the corresponding results confirms the assumption that a close similarity between the structural arrangement of molecules in the three explored amorphous phases and that of the ice polymorphs I(h), III, and VI exists.

The Voronoi–Delaunay approach for the free volume analysis of a packing of balls in a cylindrical container

Abstract The paper describes an approach for free volume analysis of packing of balls confined in a cylinder. The generalized Voronoi diagram is used as an underlying data structure. Two problems are addresses. One is an efficient construction of the confined Voronoi diagram inside a cylindrical boundary. The second is the analysis of the Voronoi network to study a distribution of empty spaces (voids) in the system. The approach is implemented in three-dimensional space and tested on the models of disordered packed bed of 300 balls in cylinders of different radii. The models were obtained by using the Monte Carlo method. The analysis of bottle-necks of channels between balls (and between balls and the boundary) and spatial distribution of the pores was performed.