New Evidence of the Existence of Associative Elements of Water (Clusters)

In this review it is reported about new data on the structure of intermolecular water cyclic associates (clusters) with general formula (Н2О)n and their charged ionic clusters [H(Н2О)n] and [OH(Н2О)n] by means of computer modeling and spectroscopy methods as Н-NMR, IR-spectroscopy, NES, DNES, EXAFS-spectroscopy, X-Ray and neurons diffraction. The computer calculation of polyhedral nanoclusters (Н2О)n, where n = 3–20 are carried out. Based on this data the main structural mathematical models describing water structure (quasi-crystalline, continuous, fractal, fractal-clathrate) have been examined and some important physical characteristics were obtained.

and shortage of inner electron shells, which enables the neighboring H2O molecule to approach the hydrogen atom of another molecule at very close distance without experiencing any strong electrostatic repulsion.
The Н2О molecule has, therefore, four sites of hydrogen bonding -two uncompensated positive charges at hydrogen atoms and two negative charges at the oxygen atom. Their mutual disposition is characterized by direction from the centre of regular tetrahedron (nucleus of oxygen atom) towards its vertexes. This allows to one Н2О molecule in condensed state to form up to 4 classical hydrogen bonds, two of which are donor bonds and the other two -acceptor ones (taking into consideration bifurkate ("two-forked") hydrogen bond -5) (Pasichnyk et al., 2008). A hydrogen bond according to Bernal-Fowler rules (Bernal & Fowler, 1933) is characterized by the following parameters: а) an oxygen atom of each Н2О molecule is bound with four neighboring hydrogen atoms: by covalent bonding with two own hydrogen atoms, and by hydrogen bonding -with two neighboring hydrogen atoms (as in the crystalline structure of ice); each hydrogen atom in its turn is bound with oxygen atom of neighbour Н2О molecule. b) on the line of oxygen atom -there can be disposed only one proton Н + ; c) the proton, which takes part in hydrogen bonding situated between two oxygen atoms, therefore has two equilibrium positions: it can be located near its oxygen atom at approximate distance of 1 Å, and near the neighboring oxygen atom at the distance of 1.7 Å as well, hence both a usual dimer HO-H...OH2 and an ion pair HO...H-OH2 may be formed during hydrogen bonding, i.e. the hydrogen bond is part electrostatic (∼90%) and part (∼10%) covalent (Isaacs et al., 2000). The state of "a proton near the neighboring oxygen" is typical for the interphase boundary, i.e. near water-solid body or water-gas surfaces. d) the hydrogen bonding of a triad О-Н...О possess direction of the shorter O-H (→) covalent bond; the donor hydrogen bond tends to point directly at the acceptor electron pair (this direction means that the hydrogen atom being donated to the oxygen atom acceptor on another H2O molecule).
The most remarkable peculiarity of hydrogen bond consists in its relatively low strength; it is 5-10 times weaker than chemical covalent bond (Pimentel & McClellan, 1960). In respect of energy hydrogen bond has an intermediate position between covalent bonds and intermolecular van der Waals forces, based on dipole-dipole interactions, holding the neutral molecules together in gasses or liquefied or solidified gasses. Hydrogen bonding produces interatomic distances shorter than the sum of van der Waals radii, and usually involves a limited number of interaction partners. These characteristics become more substantial when acceptors bind H-atoms from more electronegative donors. Hydrogen bonds hold H2O molecules on 15% closer than if water was a simple liquid with van der Waals interactions. The hydrogen bond energy compiles 5-10 kcal/mole, while the energy of О-Н covalent bonds in H2O molecule -109 kcal/mole (Arunan et al., 2011). The values of the average energy (∆EH...O) of hydrogen Н…О-bonds between H2O molecules make up 0.1067 ± 0.0011 eV (Antonov & Galabova, 1992). With fluctuations of water temperature the average energy of hydrogen H...O-bonds in of water molecule associates changes. That is why hydrogen bonds in liquid state are relatively weak and unstable: it is thought that they can easily form and disappear as the result of temperature fluctuations (Ignatov & Mosin, 2013a).
Another key feature of hydrogen bond consists in its cooperativity coupling. Hydrogen bonding leads to the formation of the next hydrogen bond and redistribution of electrons, which in its turn promotes the formation of the following hydrogen bond, which length increasing with distance. Cooperative hydrogen bonding increases the O-H bond length, at the same time causing a reduction in the H…O and O…O distances (Goryainov, 2012). The protons held by individual H2O molecules may switch partners in an ordered manner within hydrogen networks (Bartha et al., 2003). As the result, aqueous solutions may undergo autoprotolysis, i.e. the H + proton is released from Н2О molecule and then transferred and accepted by the neighboring Н2О molecule resulting in formation of hydronium ions as Н3О + , Н5О2 + , Н7О3 + , Н9О4 + , etc. This leads to the fact, that water should be considered as associated liquid composed from a set of individual H2O molecules, linked together by hydrogen bonds and weak intermolecular van der Waals forces (Liu et al., 1996). The simplest example of such associate can be a dimmer of water: (H2O)2 = H2O … HOH The energy of the hydrogen bonding in the water dimer is 0.2 eV (∼5 kcal/mol), which is larger than the energy of thermal motion of the molecules at the temperature of 300 K. Hydrogen bonds are easily disintegrated and re-formed through an interval of time, which makes water structure quite unstable and changeable (George, 1997). This process leads to structural inhomogeneity of water characterizing it as an associated heterogeneous two-phase liquid with short-range ordering, i.e. with regularity in mutual positioning of atoms and molecules, which reoccurs only at distances comparable to distances between initial atoms, i.e. the first H2O layer. As it is known, a liquid in contrast to a solid body, is a dynamic system: its atoms, ions or molecules, keeping short-range order in mutual disposition, participate in thermal motion, the character of which is much more complicated than that of crystals. For example H2O molecules in liquid state under normal conditions (1 atm, 22 0 С) are quiet mobile and can oscillate around their rotation axes, as well as to perform the random and directed shifts. This enabled for some individual molecules due to cooperative interactions to "jump up" from one place to another in an elementary Journal of Medicine, Physiology andBiophysics www.iiste.org ISSN 2422-8427 An International Peer-reviewed Journal Vol.25, 2016 66 volume of water. Random motion of molecules in liquids causes continuous changes in the distances between them. The statistical character of ordered arrangement of molecules in liquids results in fluctuations -continuously occurring deviations not only from average density, but from average orientation as well, because molecules in liquids are capable to form groups, in which a particular orientation prevails. Thus, the smaller these deviations are, the more frequently they occur in liquids. Figure 1: The formation of a hydrogen bond between the four molecules of H2O (red spheres indicate the central atoms of oxygen, white balls -hydrogen atoms). It is shown the value of the angle between the covalent H-O-H bond in Н2О molecule and the length of the hydrogen bond The further important feature is that the hydrogen bonds are spatially oriented. As each Н2О molecule has four sites of hydrogen bond formation (two non-shared electron pairs at an oxygen atom and two uncompensated positive charges at a hydrogen atom), one Н2О molecule in a condensed state is capable to form hydrogen bonds with four Н2О molecules (two donor and two acceptor) (Figure 1), which results in forming a tetrahedron crystal structure clearly observed in ice crystals.
At present time 14 crystalline modifications of ice are known, each of them has its own structure and a character of disposition of hydrogen atoms (Table 1). Crystals of all ice modifications are made up from H2O molecules, linked by hydrogen bonds into a 3D carcass, consisting of individual tetrahedrons, formed by four H2O molecules (Fig 2). In the crystalline structure of natural ice Ih hydrogen bonds are oriented towards the tetrahedron apexes at strictly defined angles equal to 109°5 (in liquid water this angle is 104 0 5) (Мosin & Ignatov, 2013a). In ice structures Ic, VII and VIII this tetrahedron is nearly the same as a regular 4 triangular tetrahedron. In ice structures II, III, V and VI the tetrahedrons are noticeably distorted. In ice structures VI, VII and VIII two intercrossing systems of hydrogen bonds are distinguished. In the centre of the tetrahedron is located an oxygen atom, at each of the two vertices -H-atom, which electron take part in formation of covalent bond with an electron pair of O-atom. The rest two vertices of the tetrahedron are occupied by two pairs of non -shared electrons of Oatom not participating in formation of molecular bonds.  Increases linearly at 0.0361 kcal/(mol .0 C) from 0 to 273.16 K Notes: 1 cal/(g .0 C) = 4.186 kJ/(kg . K); 1 Ohm -1. cm -1 = 100 Sim/m; 1 dyn = 10 -5 N; 1 N = 1 kg . m/s²; 1 dyn/сm=10 -7 Н/м; 1 cal/(сm·s .0 С) = 418.68 W/(м·К); 1 Poise = g/cm·s = 10 -1 N . s/м 2 .
High pressure ice of trigonal II and tetragonal III modifications is formed by hollow combs, formed by the hexagonal corrugated elements shifted from each other by 1/3 (Fig. 2 b,c ). These ice structures are stabilized in the presence of the noble gases as helium and argon. In the monoclinic structure of ice V the angles between the neighboring O-atoms are varied from 86 0 to 132 0 , which is very different from the valence angle in the H2O molecule makes up 105 0 47'. Ice of VI tetragonal modification consists of two inserted into each other scaffolds, between which there are no H-bonds, resulting in a body-centered crystal lattice (Fig. 2 e). The basis of the structure of ice VI constitutes the hexamers -blocks of six H2O molecules. Their configuration is exactly the same as the structure of a stable cluster of water, which gave computer calculations. A similar structure with frames of ice I, inserted into each other, have ice of cubic modification of VII and VIII, which are low temperature ordered forms of ice VII. Upon the pressure increasing the distance between O-atoms in the crystal lattice of ice VII and ice VIII will decreases, as a result is formed the ice structure X, in which O-atoms are arranged in a regular grid with arranged protons.
Ice XI is formed by deep freezing of ice Ih with addition of alkali below 72 K at normal pressure. Under these conditions, the hydroxyl defects of the crystal are formed, allowing to the growing ice crystals change their structure. Ice XI has a rhombic crystal lattice with an ordered arrangement of protons and is formed simultaneously in many centers of crystallization around the hydroxyl crystal defects.
Among the ice there and metastable forms of IV and XII, which lifetimes are seconds ( Fig. 2 d,f). For obtaining the structures of the metastable ice, the ice Ih is to be compressed to a pressure of 1.8 GPa at a temperature of liquid N2. These ice structures are formed much easier and especially stable if supercooled heavy water is subjected to pressure. Another modification of the metastable ice IX is formed by supercooling of ice III and, therefore, is its low temperature form.
The last two modifications of ice -the monoclinic XIII and rhombic XIV configuration were discovered by scientists from Oxford (UK) in 2006. On Earth, such modifications of ice cannot be formed, but they can exist on the cooled frozen planets and comets. The calculation of density and the heat flows from the surface of the moons of Jupiter and Saturn suggests that Ganymede and Callisto has to be the ice shells, in which alternate ice I, III, V and VI. At the Titan's the ice does not form a crust shell, but the mantle, the inner layer of which consists of ice VI and other high-pressure ice modifications and clathrate hydrates, on the top of which is located hexagonal ice Ih.
In ice Ih the carcasses of hydrogen bonds allocate H2O molecules in form of a spatial hexagon network with internal hollow hexagonal channels. In the nodes of this network O-atoms are orderly organized (crystalline state), forming regular hexagons, while H-atoms have various positions along the bonds (amorphous state). When ice melts, its network structure is destroyed: H2O molecules begin to fall down into the network hollows, resulting in a denser structure of the liquid -this explains why water is heavier than ice. The hydrogen bonding explains other anomalies of water (anomality of temperature, pressure, density, viscosity, fluidity etc. According to theoretical calculations, at the melting of the ice breaks about 15% of all hydrogen bonds (Mosin & Ignatov, 2011); Journal of Medicine, Physiology and Biophysics www.iiste.org ISSN 2422-8427 An International Peer-reviewed Journal Vol.25, 2016 68 by further heating up to +40 0 C breaks down about half of hydrogen bonds in water associates. In the water vapor hydrogen bonds are absent. The physical properties of ice Ih are shown in Table 2.
The main difference between the structure of ice and water is more diffuse arrangement of the atoms in the lattice and disturbance of long-range order. Thermal oscillations (fluctuations) lead to bending and breaking of hydrogen bonds. Those out of the equilibrium positions H2O molecules fall into the adjacent structural voids and for a time held up there, as cavities correspond to the relative minimum of potential energy. This leads to an increase in the coordination number, and the formation of lattice defects. The coordination number (the number of nearest neighbors) varies from 4.4 at +1.5 0 С to 4.9 at +80 0 С. Figure 2: Ice crystalline modifications: a) -natural hexagonal ice Ih; b) -ice of II configuration; c) -ice of III configuration; d) -ice of IV configuration; e) -ice of VI configuration; f) -ice of XII configuration. a) b) Figure 3: Structures of water crystals in carbon nanotubes according to computer simulations (Bai et al., 2006) (diameter of nanotubes 1.35-1.90 nm; preassure 10-40000 atm; temperature -23°C): a) -a general view of the crystal structure of water in nanotubes, b) -the inner wall of the structure of water. Figure 4: Image of hexamer nanocrystal of ice water (average size ∼1 nm) by a scanning tunneling microscope after freezing water to 17 K on the hydrophobic metallic plates of Cu and Ag (Michaelides & Morgenstern, 2007). Reports about evidence of existence of crystal-like structures in water have become more frequent in scientific literature nowadays (Michaelides & Morgenstern, 2007). As computer modeling showed, H2O molecules being placed in carbon nanotubes under high pressure and low temperatures formed crystalline nanostructures like DNA double helix (Bai et al., 2006). In modeling experiment water got frozen inside carbon nanotubes with diameter 1.35-1.90 nm with pressure 10-40000 atm and temperature -23°C. Hydrogen bonds in an ice crystal got distorted leading to the formation of a double-walled helix. The inner wall of this structure represents a four-fold twisted helix, while the outer consists of four double helixes, resembling a helix of DNA molecule ( Figure 3). While being frozen at 17 К on hydrophobic surfaces of Cu, Ag and their salts, water became crystallized into twodimensional ice hexamer nanocrystal, consisting of six attached together H2O molecules ( Figure 4).

Structural Mathematical Models of Water
There are several groups of models, describing structure of liquids -microcrystalline, quasicrystalline, continious, fractal and fractal-clathrate models. The microcrystalline model of J. Bernal and P. Fowler suggests that water is a nonequilibrium 2-phase liquid containing groups of oriented molecules -microcrystals with several dozens or hundreds of molecules (Bernal & Fowler, 1933;Timothy & Zwier, 2004). Within each microcrystal in liquid a solid body ordering (long-range order) is strictly kept. As water is denser than ice, it is assumed that its molecules are allocated in a different way than in ice: like the аtoms of silicon in mineral tridymite or in its more solid modification of quarz. The intermittent increase in water density from 0 to 3.98°C and other anomalous properties of water was explained by the existence of tridymite component at low temperatures (Pople, 1951).
Quasicrystalline model by analogy with a quasicrystal, e.g. a structure that is ordered but not periodic (Nemukhin, 1996), suggests that relative disposition of particles in liquids is nearly the same as in crystals; deviation from regularity increases with the distance from the initial H2O molecule; far apart at longer distances there is no regularity in the disposition of H2O molecules. Each H2O molecule is surrounded by the four neighbouring ones, which are arranged around it in quite the same way, as they are in an ice crystal. However, in the second layer there appear deviations from regularity rapidly increasing with distance from the initial H2O molecule. Studies of X-ray scattering in liquids consisting of polyatomic molecules, revealed not only some regular arrangement of H2O molecules, but consistent pattern in mutual orientation of the molecules (Petkov et al., 2012). This orientation becomes even more expressed for the polar molecules because of the hydrogen bonding effect.
Kinetic theory of liquids proposed by Y.I. Frenkel, also called a "jump-wait" model, explains the structural properties of liquids by peculiarities of thermal motion of their molecules (Frenkel, 1975). The thermal motion of H2O molecules is characterized by two parameters: a period of oscillation of H2O molecule around an equilibrium position and a period of "settled life", i.e. period of oscillation around one particular equilibrium position. Average time of "settled life" of a H2O molecule, within which H2O molecules keep unchanged equilibrium orientation is called relaxation time τ: τ = τ0 × e W/RT , (1) where τ0 is an average period of oscillations of a H2O molecule around an equilibrium position (sec), W -a value of potential energy barrier, separating two neighboring equilibrium positions from each other (J), R -Boltzmann constant (J/К), T -absolute temperature (К).
According to calculations the relaxation time at room temperature makes up ∼4.5 . 10 -12 sec, while the period of one oscillation of H2O molecules -10 -12 -10 -13 sec. That is why each H2O molecule performs approximately 100 oscillations relative to the same equilibrium position before changing its place. Due to thermal fluctuations one H2O molecule within its "settled life" period of time oscillates around an equilibrium position, after then jumps up to new location and it continues to fluctuate up to the next jump. Through these abrupt movements of molecules in liquids occurs diffusion, which, in contrast to the continuous diffusion in gases, called diffusion jump. With increase in temperature the period of "settled life" of H2O molecules in a temporary state of equilibrium is reduced that brings the structure of water closer to a gas, in which translational and rotational motions of H2O molecules prevail. Theoretical studies show that, along with the fluctuation of molecules surrounded by his neighbors and activation jumps in liquids occur flowing movement of molecules along with their immediate environment. In other words, being in oscillating state, the molecules in the liquid displaced each time by a certain distance (less than the interatomic distance), causing continuous diffusion. It is believed that in the liquefied inert gases and metals dominates continuous diffusion, while for associated liquids as water is more likely the jump diffusion mechanism. The thermal motion of H2O molecules leads to continuous changes in distances between them, which cause fluctuations -continual deviations not only from the average density, but from the average orientation of the molecules as well, because H2O molecules can form groups in which a certain orientation predominates. An attempt to change the water volume (even by small quantity) triggers the process of deformation of hydrogen bonds that fact may explain low water compressibility. Ice melting also causes weakening and deformation of hydrogen bonds, which makes water denser than ice. At the temperature 3.98°С water acquires anomalous state, in which the quasicrystalline phase is maximally densified by filling up of ice carcass hollows with H2O molecules. Further increase in temperature and energy of thermal motion of H2O molecules leads to the gradual disintegration of associated water structures and to the partial rupture of hydrogen bonds with essential reduce of the "settled life" of each H2O molecule in water associates.  : Schematic representation of the space-filling mixture molecules-elements that may exist in a certain proportion of small, 2-4 molecules H2O, clusters and other larger molecules H2O, up to the calculated H2O molecules composing from 280 H2O molecules-elements. It underlines the key role of heterogeneity in the structure of water. Unfortunately, due to lack of data it is difficult to portray to scale spatial relationships between the molecules of both real and likely present clusters. The forces between the clusters are marked in black. They are much weaker than the forces inside the clusters, however these connections are not allocated (Roy R, 2004) The continuous and "fractal" models consider water as a complex dynamic system with a hydrogen network, forming the empty cavities and non-bonded H2O molecules distributed within the network ( Figure 5-7). The structure is based upon dimensional carcasses of individual H2O molecules, joined together into a multi-molecular associate similar to a clathrate having a configuration of a regular polyhedron (Samoilov, 1963). Analogous structure has clathrate hydrates (gas clathrates) -crystalline water-based solids physically resembling ice, in which small non polar gas molecules are placed inside cavities of hydrogen bonded H2O molecules. In 1957 S. Frank and W. Wen proposed a model, postulating arbitrary formation of cyclic associates in water, which presumably had random groups of water associates -the "flickering clusters" with general formula (Н2О)n, which are in a dynamic equilibrium with free H2O molecules (Henry et al., 1957). The hydrogen bonds between H2O molecules are in dynamic equilibrium; they are constantly broken and re-formed in new configurations within a certain time interval; these processes are occurred cooperatively within short-living associated groups of H2O molecules (clusters), which life spans are estimated from 10 -10 to 10 -11 sec.
Water associates evidently may have polymer structure, because hydrogen bond is on 10% partially covalent bond (Isaacs et al., 2000). In 1990 G.А. Domrachev and D.А. Selivanovsky formulated a model of Н2Оpolimers based on the existence of mechanochemical reactions of ionization and dissociation of water in aqueous solutions (Domrachev & Selivanovsky, 1990). Water was thought as dynamically unstable quazi-polymer, composed of (Н2О)n blocks with partially covalent by 10% hydrogen bonds, permitting at least to 10% of Н2О Journal of Medicine, Physiology and Biophysics www.iiste.org ISSN 2422-8427 An International Peer-reviewed Journal Vol.25, 2016 72 molecules to comby in a sufficiently long-lived polymer associates. Similarly with mechanochemical reactions in polymers, in case of mechanical impact on water, the energy absorbed by water required for splitting up the Н-ОН bond, concentrates in a micro-scale area of the liquid water structure. The splitting up reaction of the Н-ОН bond in water polymer associates is expressed by the following equation: (Н2О)n(Н2О..

.H-|-OH) (Н2О)m + E = (Н2О)n+1 (H · ) + (OH · ) (Н2О)m,
where Е -the energy of the Н-ОН bond, 460 кJ/mole; the dot denotes an unpaired electron. Splitting up of the Н-ОН bond is accompanied by formation of new disordered bonds between "fragments" of the initial molecules, leading to the formation of fluctuation areas with different density fluctuations that can be observed in aqueous solutions.
Another interesting physical phenomenon was discovered by A. Antonov in 2005(Antonov, 2005. It was established experimentally that at evaporation of water droplet the contact angle θ decreases discretely to zero, whereas the diameter of the droplet changes insignificantly. By measuring this angle within a regular time intervals a functional dependence f(θ) can be determined, which is designated by the spectrum of the water state. For practical purposes by registering the spectrum of water state it is possible to obtain information about the averaged energy of hydrogen bonds in an aqueous sample. For this purpose the model of W. Luck is used, which consider water as an associated liquid, consisted of О-Н…О-Н groups (Luck et al., 1980). The major part of these groups is designated by the energy of hydrogen bonds (-E), while the others are free (E = 0). The energy distribution function f(E) is measured in electron-volts (eV -1 ) and may be varied under the influence of various external factors on water as temperature and pressure. For calculation of the function f(E) experimental dependence between the water surface tension (θ) and the energy of hydrogen bonds (E) is established: (2) where b = 14.33 eV -1 The energy of hydrogen bonds (Е) is measured in electron-volts (eV) and is designated by the spectrum of energy distribution. The water spectrum characterized by a non-equilibrium process of water droplets evaporation, thus the term "non-equilibrium energy spectrum of water" (NES) is applied. The difference ∆f(E) = f (samples of water) -f (control sample of water) is called the "differential non-equilibrium energy spectrum of water" (DNES). DNES is a measure of changes in the structure of water as a result of external influences. The cumulative effect of all other factors is the same for the control sample of water and the water sample, which is under the influence of this impact.  (Figure 8) (Saykally, 2005). It was also estimated the possible number of hydrogen bonds (100) depending on the number of H2O molecules (250) in clusters (Sykes, 2007).
O. Loboda and O.V. Goncharuk provided data about the existence of icosahedral water clusters consisting of 280 H2O molecules with the average size up to 3 nm (Loboda & Goncharuk, 2010). The ordering of water molecules into associates corresponds to a decrease in the entropy (randomness), or decrease in the overall Gibbs energy (G = ∆H -T∆S). This means that the change in enthalpy ∆H minus the change in entropy ∆S (multiplied by the absolute temperature T) is a negative value. These results are consistent with our data on research of DNES spectrum of water on which it may make conclusion about the number of H2O molecules in water clusters. DNES spectrum of water has energy ranges from -0.08 to -0.14 eV (Figure 9). The spectral range lies in the middle infrared range from 8 to 14 µm ("window" of the atmosphere transparency to electromagnetic radiation). Under these conditions, the relative stability of water clusters depends on external factors, primarily on the temperature. Figure 9: NES-spectrum of deionized water (chemical purity 99.99%, pH = 6.5-7.5, total mineralization 200 mg/l, electric conductivity 10 µS/cm). On the horizontal axis shows the energy of the H...O hydrogen bonds in the associates -E (eV). The vertical axis -energy distribution function -f (eV -1 ). k -the vibration frequency of the H-O-H atoms (cm -1 ); λ -wavelength (mm). It was shown that the H2O molecules change their position in clusters depending on the energy of intermolecular H…O hydrogen bonds. The values of the average energy (EH...O) of hydrogen bonds between the H2O molecules in the formation of cluster associates with formula (H2O)n compile 0.1067 ± 0.0011 eV. As the energy of hydrogen bonds between H2O molecules increases up to -0.14 eV, the cluster formation of water becomes "destructuring". In this case, the energy redistribution between the individual H2O molecules occures ( Figure 10).
All these data indicate that the water is a complex associated non-equilibrium liquid consisting of associative groups containing according to the present data, from 3 to 20 individual H2O molecules (Tokmachev et al., 2010). Associates can be perceived as unstable groups (dimmers, trimmers, tetramers, pentamers, hexamers etc.) in which H2O molecules are linked by van der Waals forces, dipole-dipole and other charge-transfer interactions, including hydrogen bonding. At room temperature, the degree of association of H2O molecules may vary from 2 to 6. In 1993 K. Jordan (USA) (Tsai & Jordan, 1993) calculated the possible structural modifications of small water clusters consisting of six H2O molecules (Figure 10a-c). Subsequently, it was shown that H2O molecules capable of hydrogen bonding by forming the structures representing topological 1D rings and 2D chains composed from numerous H2O molecules. Interpreting the experimental data, they are considered as pretty stable elements of the structure. According to computer simulations, clusters are able to interact with each other through the exposed protons on the outer surfaces of hydrogen bonds to form new clusters of more complex composition.  Figure 10: Calculation of small water cluster structures (a-c) with general formula (H2O)n, where n = 6 (Tsai & Jordan, 1993). In 2000 it was deciphered the structure of the trimmer water, and in 2003 -tetramer, pentamer and the water hexamer (Wang & Jordan, 2003). Structures of water clusters with formula (H2O)n, where n = 3-5, similar to the cage structure. Hexagonal structure with n = 6, consisting of six H2O molecules at the hexagon vertices, is less stable than the cage structure. In the hexagon structure four H2O molecules can be cross-linked by hydrogen bonds (Figure 11).  It is reasonable that the structure of liquid water should be related to the structure of hexagonal ice, formed from H2O tetrahedrons, which exist under atmospheric pressure. In the computer simulation H2O tetrahedrons grouped together, to form a variety of 3D-spatial and 1D, 2D-planar structures, the most common of which is hexagonal structure where 6 H2O molecules (tetrahedrons) are combined into a ring. A similar type of structure is typical for ice Ih crystals. When ice melts, its hexagonal structure is destroyed, and a mixture of clusters consisting of tri-, tetra-, penta-, and hexamers of water and free H2O molecules is formed. Structural studies of these clusters are significantly impeded, since the water is perceived as a mixture of different clusters that are in dynamic equilibrium with each other.
S. Zenin (Russia) calculated a cluster model based on a minimum "quantum" of water (Zenin, 1999), which is a 4 triangular tetrahedron composed of four 12 pentagonal dodecahedrons (Figure 14). The "quantum" consisted of 57 H2O molecules interacting with each other at the expense of free hydrogen bonds exposed on the surface. Of 57 H2O molecules in the "quantum" 17 H2O molecules compose tetrahedral completely hydrophobic, i.e. saturated with four hydrogen bonds in the central carcass, and four dodecahedra on the surface of each there are 10 centers for the formation of hydrogen bond (O-H or O). 16 "quanta" form a bigger cluster structure consisted from 912 H2O molecules similar to a tetrahedron.
Journal of Medicine, Physiology and Biophysics www.iiste.org ISSN 2422-8427 An International Peer-reviewed Journal Vol.25, 2016 76 а) b) Figure 14: Model of water associates accordung to S.V. Zenin: a) -assosiate of 57 H2O molecules, tetrahedron of four dodecahedron ("quantum"); b) -bulk packaging of "quanta" (Zenin, 1999). M. Chaplin (London South Bank University, UK) (Chaplin, 2011) calculated the water structure based on 20 triangular icosahedron ( Figure 15). The structure is based on minimal tetrahedral water cluster, consisting of 14 H2O molecules. Arrangement of 20 of these 14-molecule structures forms an icosahedral network, consisting from 280 H2O molecules. Each 280-molecule in icosahedral contains several substructures with each H2O molecule involved in four hydrogen bonds; two as donor and two as acceptor. 13 overlapping icosahedra may form more large cluster (tricontahedron) consisting from 1820 H2O molecules, which has twice more H2O molecules than in the previous model.
The clusters, evidently, may be rather stable under a certain conditions, and can be obtained in the isolated state within a very short interval of time. There is also a reason to believe that the charged ions stabilize the clusters. Therefore, the clusters can be divided into positively and negatively charged ionic clusters -[(H2O)n] + , [(H2O)n] -, and not having a charge -neutral clusters with general formula (H2O)n. Clusters, containing 20 individual H2O molecules and a proton in the form of hydronium ion H3O + ("magic" number) form the most stable ionic clusters (H2O)20H3O + or (H2O)21H + (Figure 16) (Cui et al., 2006). It is assumed that the stability of ionic clusters is due to the special clathrate structure in which 20 H2O molecules are formed 12 pentagonal dodecahedron, in which cavities is captured the H3O + ion. It is occurred because of all the clusters only the dodecahedron has large cavities enough to accommodate a bulky H3O + ion. Subsequently, due to cooperative interactions H3O + is further able to move to the surface of the cluster and lose a proton H + leading to the formation of hydronium ions like H5O2 + , H7O3 + , and H9O4 + , fixed on the surface of the cluster. These data show the diversity of supposed water structures and the complexity of molecular interactions between the different water clusters, the nature of which we are only beginning to understand.

Methods of Study Water Clusters
Cluster structures in water calculated theoretically on computer were confirmed by 1 H-NMR, IR, Raman, Compton scattering, EXAFS-spectroscopy and X-ray diffraction (Ignatov, 2005;Мosin & Ignatov, 2011). Information obtained with using the modern detection methods corresponds to femtosecond time, i.e instantaneous dynamics of intermolecular interactions in the molecular scale. The presence of hydrogen bonding causes the noticable effect on vibrational and 1 H-NMR spectra. In 1 H-NMR the chemical shift of the proton involved in the hydrogen bonding shifts about 0.01 ppm reducing strength of hydrofen bonding while the temperature is raised (Yamaguchi et al., 2001). Increased extent of hydrogen bonding within clusters results in a similar effect; the higher chemical shifts with greater cooperativity, the shorter hydrogen bonded O-H…O distances. 1 H peaks shift to greater ppm with increasing hydrogen bonding strength.
In IR-spectroscopy the characteristic vibration frequency bands containing hydrogen are reduced in spectra if hydrogen atom is included in the hydrogen bonding. Infrared absorption bands, such as OH-groups are much expanded when the hydrogen bond is formed, and their intensity increases. The main stretching band in liquid water is shifted to a lower fequency (v3, 3480 cm -1 and v1, 3270 cm -1 ), while the bending frequency (v2, 1640 cm -1 ) increased by hydrogen bonding (Ohno et al., 2005). Increased strength of hydrogen bonding shifts the stretch vibration to lower frequencies with greatly increased intensity in the infrared due to the increased dipoles. With raising the temperature the stretch vibrations shift to higher frequency, while the intramolecular vibrations shift to lower frequencies (Ignatov, 2012;Ignatov & Mosin, 2013b). Hydrogen bond energy lies in the range of 2.3 kcal/mole for the N-H...O-bonds up to 7.0 kcal/mol for the bonds with hydrogen fluoride F-H...F. The strength of the hydrogen bonding depends on the cooperative/anticooperative character of the surrounding hydrogen bonds with the strongest hydrogen bonds giving the lowest vibrational frequencies.
In X-ray absorption spectroscopy (EXAFS-spectroscopy) X-ray radiation excites the electrons of the inner shell of an oxygen atom in H2O molecules and stipulates their transition onto unoccupied upper electronic levels in the molecules (Wernet et al., 2004). Probability of electron transitions and characteristics of the absorption contour depends mostly on the molecular environment. This allows by varying the energy of the X-rays to study the distribution of associations for HOH...OH2 bond judging on lengths and angles of the covalently bonded hydrogen atom in the molecule. EXAFS spectrum near the oxygen atom is also sensitive to hydrogen bonding. This method is used to obtain information about the molecular structure of water in the first coordination sphere. Since the time of excitation of electrons is much smaller than the vibrational motions in liquids, X-ray probe of the electronic structure provides information about the instantaneous changes of configurations of the water structure.
Diffraction techniques (X-ray and neutron diffraction) on liquid water allow to calculate the function of density radial distribution (O or H) and the probability of detection of H2O molecules at a certain distance from a randomly chosen individual H2O molecule (Tokushima et al., 2008). This allows to detect the irregularities in water by constructing the radial distribution function, i.e. the distance between the atoms of O, H, and O-H in H2O molecule and its nearest neighbors. Thus, the distribution of the distances between the oxygen atoms at a room temperature, gives three major peaks measured at 2.8, 4.5 and 6,7 Å. The first maximum corresponds to the distance to the nearest neighbor and its value is approximately equal to the length of the hydrogen bond. The second maximum is close to the average edge length of a tetrahedron, as H2O molecules in the crystalline structure of ice Ih arranged at the vertices of the tetrahedron allocated around the center of the molecule. The third peak, expressed very weakly, corresponds to the distance to the third and more distant neighboring H2O molecules on the hydrogen network. In 1970 I.S. Andrianov and I.Z. Fisher calculated the distance up to the eighth of the neighboring H2O molecule; the distance to the fifth the neighboring H2O molecule turned out to be 3 Å, and to the sixth molecule -3,1 Å. This allowed draw conclusions about the geometry of hydrogen bonds and farther surroundings of H2O molecules.
Another method for structural studies -neutron diffraction is similar to X-ray diffraction. However, because the neutron scattering lengths vary slightly among different atoms, this method is limited in the case of the isomorphous substitution of hydrogen atoms in H2O molecule by deuterium (D). In practice generally operate with a crystal whose molecular structure is approximately defined by other methods. Then, it is measured the intensity of the neutron diffraction of this crystal. From these results, the Fourier transform is carried out; the measured neutron intensity and phase are using for calculation. Then, on the resultant Fourier map hydrogen and deuterium atoms are represented with much greater atomic weight than on the electron density map, as the contribution of these atoms in neutron scattering is essentially big. On the resulting density map is determined the arrangement of hydrogen 1 H (negative density) and deuterium D (positive density) atoms. A variation of the method consists in that the crystal of an ordinary protonated water (H2O) before measurements kept in 99.9 at.% of heavy water (D2O). In this case the neutron diffraction can not only establish the localization of the hydrogen atoms, as well as to identify those protons that can be exchanged by deuterium, that is particularly important for the study of isotopic (H-D) exchange. Such information in some cases may help confirm the correctness of the water structure established by other methods.
The clusters formed of D2O are some more stable and resistant than those ones from H2O due to isotopic effects of deuterium caused by 2-fold increasing nuclear mass of deuterium (molecular mass of D2O is more by 11% than that of H2O). The structure of D2O molecule is the same, as that of Н2O, with small distinction in values of lengths of covalent bonds. D2O crystals have the same structure as a conventional ice Ih, the difference in unit cell size is very insignificant (0.1%). But they are heavy (0.982 g/cm 3 at 0 0 C over 0.917 g/cm 3 for conventional ice). D2O boils at 101.44 0 С, freezes at 3,82 0 С, has density at 20 0 С 1.105 g/cm 3 , and the maximum density occurs not at the 3.89 0 C, as for H2O, but at 11.2 0 C (1.106 g/cm 3 ) ( Table 3). The mobility of D3O + ion on 28.5% lower than that of H3O + ion and ODion -39.8% lower than that of OHion, the constant of ionization of D2O is less than the constant of ionization of H2O, which means that D2O has a bit more hydrophobic properties than H2O. All these effects lead that the hydrogen bonds formed by deuterium atoms differ in strength and energy from ordinary hydrogen bonds (O-H length 1.01 Å, O-D length 0.98 Å, D-O-D angle 106 0 ). Commonly used molecular models use O-H lengths ∼0.955 Å and 1.00 Å and H-O-H angles from ∼105.5 0 to ∼109.4 0 . The substitution of H with D atom affects the stability and geometry of hydrogen bonds in apparently rather complex way and may, through the changes in the hydrogen bond zero-point vibrational energies, alter the conformational dynamics of hydrogen (deuterium)-bonded structures of associates. In general, isotopic effects stabilize hydrogen bond with participation of deuterium, resulting in somewhat greater stability of associates (clusters) formed from D2O molecules (Мosin & Ignatov, 2013b).
According to the international SMOW standard the absolute content of D (isotopic shift, δ, ppm) in sea water: D/H = (155.76±0.05) . 10 -6 (155.76 ppm) (Ignatov & Mosin, 2013d). For SLAP standard isotopic shifts for D in seawater: D/H = 89 . 10 -6 (89 ppm). The content of the lightest isotopologue -H2 16 O in water corresponding to SMOW standard is 997.0325 g/kg (99.73 mol.%), and for SLAP standard -997.3179 g/kg (99.76 mol.%). In surface waters, the ratio D/H = (1.32-1.51) . 10 -4 , while in the coastal seawater -(1.55-1.56) . 10 -4 . .60 Viscosity at +20 0 C, cP 1.002 1.47 As a result of experiments on quasi-elastic neutron scattering was measured the most important parameter -the coefficient of self-diffusion of water at different temperatures and pressures. To analyze the self-diffusion coefficient on quasi-elastic neutron scattering, it is necessary to know the character of moving of molecules. If they move in accordance with the "jump-wait" model, then the "settled" life time (the time between jumps) of H2O molecule compiles 3.2 ps. The newest methods of femtosecond laser spectroscopy allow to estimate the lifetime of the broken hydrogen bonds: a proton needs 200 fs to find a partner.
The studying the full details of the structure of associative elements in water can be made, considering all the parameters by computer simulation or numerical experiment ( Figure 17). For this in a given space is chosen random ensemble of n H2O molecules and are optimal parameters -the energy of interatomic interactions, bond length, the arrangement of atoms and molecules, the most consistent with the diffraction data. Data thus obtained are then extrapolated to the actual water structure, and further used to calculate thermodynamic parameters. Data obtained by computer experiments, show that the nature of the thermal motion of the molecules in the liquids corresponds on the whole to a vibration of the individual H2O molecules near the equilibrium centers, with occasional jumps up to the new position. Journal of Medicine, Physiology andBiophysics www.iiste.org ISSN 2422-8427 An International Peer-reviewed Journal Vol.25, 2016 79 Figure 17: Cluster structure of water in a numerical experiment The comparative analysis of IR-spectra of H2O solutions and its deuterated analogues (D2О, HDO) is of considerable interest for biophysical studies, because at changing of the atomic mass of hydrogen by deuterium atoms in H2O molecule their interaction will also change, although the electronic structure of the molecule and its ability to form H-bonds, however, remains the same. The IR spectra of water usually contain three absorption bands, which can be identified as 1 -absorption band of the stretching vibration of OHgroup; 2 -absorption band of the first overtone of the bending vibration of the molecule HDO; 3 -absorption band of stretching vibration of ODgroup. OHgroup is able to absorb much infrared radiation in the infrared region of the IR-spectrum. Because of its polarity, these groups typically react with each other or with other polar groups to form intra-and intermolecular hydrogen bonds. The hydroxyl groups not involved in formation of hydrogen bonds are usually given the narrow bands in IR spectrum and the associated groups -broad intense absorption bands at lower frequencies. The magnitude of the frequency shift is determined by the strength of the hydrogen bond. Complication of the IR spectrum in the area of OHstretching vibrations can be explained by the existence of different types of associations, a manifestation of overtones and combination frequencies of OHgroups in hydrogen bonding, as well as the proton tunneling effect (on the relay mechanism. Such complexity makes it difficult to interpret the IR spectrum and partly explains the discrepancy in the literature available on this subject. The local maximums in IR-spectra reflect vibrational-rotational transitions in the ground electronic state; the substitution with deuterium changes the vibrational-rotational transitions in H2O molecule that is why it appears other local maximums in IR-spectra. In the water vapor state, the vibrations involve combinations of symmetric stretch (v1), asymmetric stretch (v3) and bending (v2) of the covalent bonds with absorption intensity (H2O) v1;v2;v3 = 2671; 1178.4; 2787.7 cm -1 . For liquid water absorption bands are observed in other regions of the IR-spectrum, the most intense of which are located at 2100, cm -1 and 710-645 cm -1 . For D2О molecule these ratio compiles 2723.7, 1403.5 and 3707.5 cm -1 , while for HDО molecule -2671.6, 1178.4 and 2787.7 cm -1 . HDO (50 mole% H2O + 50 mole% 2 Н2О; ~50 % HDO, ~25 % H2O, ~25 % D2О) has local maxima in IR-spectra at 3415 cm -1 , 2495 cm -1 1850 cm -1 and 1450 cm -1 assigned to OH --stretch, OD --stretch, as well as combination of bending and libration and HDO bending respectively.
In the IR-spectrum of liquid water absorbance band considerably broadened and shifted relative to the corresponding bands in the spectrum of water vapor. Their position depends on the temperature (Ignatov & Mosin, 2013b). The temperature dependence of individual spectral bands of liquid water is very complex (Zelsmann, 1995). Furthermore, the complexity of the IR-spectrum in the area of OHstretching vibration can be explained by the existence of different types of H2O associations, manifestation of overtones and composite frequencies of OHgroups in the hydrogen bonds, and the tunneling effect of the proton (for relay mechanism) (Yukhnevitch, 1973). Such complexity makes it difficult to interpret the spectrum and partly explains the discrepancy in the literature available on this subject.
In liquid water and ice the IR-spectra are far more complex than those ones of the vapor due to vibrational overtones and combinations with librations (restricted rotations, e.g. rocking motions). These librations are due to the restrictions imposed by hydrogen bonding (minor L1 band at 395.5 cm -1 ; major L2 band at 686.3 cm -1 ; for liquid water at 0 0 C, the absorbance of L1 increasing with increasing temperature, while L2 absorbance decreases but broadens with reduced wave number with increasing temperature (Brubach et al., 2005). The IR spectra of liquid water usually contain three absorbance bands, which can be identified on absorption band of the stretching vibration of OHgroup; absorption band of the first overtone of the bending vibration of the molecule HDO and absorption band of stretching vibration of ODgroup (Max & Chapados, 2009). Hydroxyl group OHis able to absorb much infrared radiation in the infrared region of the IR-spectrum. Because of its polarity, these groups typically react with each other or with other polar groups to form intra-and intermolecular hydrogen bonds. The hydroxyl groups, which are not involved in formation of hydrogen bonds usually produce the narrow bands in IR spectrum, while the associated groups -broad intense absorbance bands at lower frequencies. The magnitude of the frequency shift is determined by the strength of the hydrogen bond. Complication of the IR spectrum in the area of OHstretching vibrations can be explained by the existence of different types of associations of H2O molecules, a manifestation of overtones and combination frequencies of OHgroups in hydrogen bonding, as well as the proton tunneling effect (on the relay mechanism). Assignment of main absorption bands in the IR-spectrum of liquid water is given in Table 4. The IR spectrum of H2O molecule was examined in detail from the microwave till the middle (4-17500 cm -1 ) visible region and the ultraviolet region -from 200 nm -1 to ionization limit at 98 nm -1 (Walrafen, 1972). In the middle visible region at 4-7500 cm -1 are located rotational spectrum and the bands corresponding to the vibrationalrotational transitions in the ground electronic state. In the ultraviolet region (200 to 98 nm -1 ) are located bands corresponding to transitions from the excited electronic states close to the ionization limit in the electronic ground state. The intermediate region of the IR-spectrum -from 570 nm to 200 nm corresponds to transitions to higher vibrational levels of the ground electronic state.
The results of IR-spectroscopy with device Infra Spec VFA-IR show that at 4.1 µm, even at low concentrations of deuterium of 0.35 and 0.71%, there is observed a decline in the local maximums relative to the local maximum of 100% pure water (the local maximums in IR-spectra reflect vibrational-rotational transitions in the ground electronic state because at changing the atomic mass of hydrogen and deuterium atoms in the water molecule their interaction will also change, although the electronic structure of the molecule and its ability to form H-bonds, however, remains the same; with the substitution with deuterium the vibrational-rotational transitions are changed, that is why it appears other local maximums in IR-spectra. At further transition from H2O monomers to H4O2 dimmer and H6O3 trimmer absorption maximum of valence stretching vibrations of the O-H bond is shifted toward lower frequencies (v3 = 3490 cm -1 and v1 = 3280 cm -1 ) (Eisenberg & Kauzmann, 1969) and the bending frequency increased (v2 = 1644 cm -1 ) because of hydrogen bonding. The increased strength of hydrogen bonding typically shifts the stretch vibration to lower frequencies (red-shift) with greatly increased intensity in the infrared due to the increased dipoles. In contrast, for the deformation vibrations of the H-O-H, it is observed a shift towards higher frequencies. Absorption bands at 3546 and 3691 cm -1 were attributed to the stretching modes of the dimmer [(H2O)2]. These frequencies are significantly lower than the valence modes of ν1 and ν3 vibrations of isolated H2O molecules at 3657 and 3756 cm -1 respectively). The absorption band at 3250 cm -1 represents overtones of deformation vibrations. Among frequencies between 3250 and 3420 cm -1 is possible Fermi resonance (this resonance is a single substitution of intensity of one fluctuation by another fluctuation when they accidentally overlap each other). The absorption band at 1620 cm -1 is attributed to the deformation mode of the dimmer. This frequency is slightly higher than the deformation mode of the isolated H2O molecule (1596 cm -1 ). A shift of the band of deformation vibration of water in the direction of high frequencies at the transition from a liquid to a solid state is attributed by the appearance of additional force, preventing O-H bond bending. Deformation absorption band in IR-spectrum of water has a frequency at 1645 cm -1 and very weak temperature dependence. It changes little in the transition to the individual H2O molecule at a frequency of 1595 cm -1 . This frequency is found to be sufficiently stable, while all other frequencies are greatly affected by temperature changes, the dissolution of the salts and phase transitions. It is believed that the persistence of deformation oscillations is stipulated by processes of intermolecular interactions, e.g. by the change in bond angle as a result of interaction of H2O molecules with each other, as well as with cations and anions.
Thus the study of the characteristics of the IR spectrum of water allows to answer the question not only on the physical parameters of the molecule and the covalent bonds at isotopic substitution with deuterium, but also to make a certain conclusion on associative environment in water. The latter fact is important in the study of structural and functional properties of water associates and its isotopomers at the isotopic substitution with deuterium. The substitution of H with D affects the stability and geometry of hydrogen bonds in an apparently rather complex way and may, through the changes in the hydrogen bond zero-point vibration energies, alter the conformational dynamics of hydrogen (deuterium)-bonded structures of macromolecules as DNA and proteins in Journal of Medicine, Physiology and Biophysics www.iiste.org ISSN 2422-8427 An International Peer-reviewed Journal Vol.25, 2016 D2O (Cleland, 1976).

Conclusion
The experimental data obtained during the last years suggest that water is a complex dynamic associative system, consisting of tens and possibly hundreds individual H2O molecules binding by multiple intermolecular hydrogen bonds, being in a state of dynamic equilibrium. Up till now is scientifically proven the existence of associative water clusters with general formula (H2O)n, where n = 3-20. Although calculated structural models explain pretty well many anomalous properties of water and being in a good agreement with the experimental data on the diffraction of X-rays and neutrons, Raman, Compton scattering and EXAFS-spectroscopy, they are the most difficult to agree with the dynamic properties of water -flow, viscosity and short relaxation times, which are measured by picoseconds.