The structure of water

© Ignat Ignatov, Oleg Mosin

Ignat Ignatov, DSc., Professor
Oleg Mosin, PhD

Contact E-mail: mosin-oleg@yandex.ru

Abstract

In this review it is reported about the research on the structure of intermolecular water cyclic associates (clusters) with general formula (Н₂О)_n and their charged ionic clusters [(Н₂О)_n]⁺ and [(Н₂О)_n]^- by means of computer modeling and spectroscopy methods as ¹Н-NMR, IR-spectroscopy, 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 (quasicrystalline, continious, fractal, fractal-clathrate) have been examined and some important physical characteristics were obtained. The average energy of hydrogen bonding (DE_H…O) between Н₂О molecules in the process of cluster formation was measured by the DNES method compiles –0,1067±0,0011 eV. It was also shown that water clusters formed from ²H2О were more stable, than those ones from Н₂О due to isotopic effects of deuterium.

Keywords: hydrogen bond, water, structure, clusters.

Introduction

Water with its anomalous physical and chemical properties outranks all other natural substances on the Earth. The ancient philosophers considered water as the most important component of the matter. It performs a vital role in numerous biochemical and metabolic processes occurring in cells with participation of water, being a universal polar solvent for hydrophilic molecules having an affinity for water. Hydroxyl groups (-OH) in H₂O molecule, are polar and therefore hydrophilic. Moreover water act as a reagent for a big number of chemical reactions (hydrolysis, oxidation-reduction reactions). In chemical processes water due to its high ionizing ability possesses strong amphoteric properties, and can act both as an acid and a base in reactions of chemical exchange.

Modern science has confirmed the role of water as a universal life sustaining component, which defines the structure and properties of inorganic and organic objects, consisted from water.. The recent development of molecular and structural-chemical concepts has enabled to clarify an explanation of ability of water molecules to form the short-lived hydrogen bonds with neighboring molecules and many other chemical substances to bond them into intermolecular associates. It has also become clear the role of bounded water in forming hydrated substances and their physicochemical conduct in aqueous solutions.

The great scientific and practical interest have the studies of a variety of specific supramolecular structures – cyclic water clusters described by general formula (H₂O)_n, which may be calculated and studied with the help of modern numerical computing methods. The clusters are also important for studying the structure of water and hydration phenomena at molecular level since they form the basic building blocks of the hydrated substances. This paper deals with the mathematical modeling of the water structure and water associates.

Results and Discussion

Nature of Hydrogen Bond in Liquids and Crystals

The peculiarities of chemical structure of Н₂О molecule and weak bonds caused by electrostatic forces and donor-acceptor interaction between hydrogen and oxygen atoms in Н₂О molecules create favorable conditions for formation of directed intermolecular hydrogen bonds (О–Н…О) with neighboring Н₂О molecules, binding them into complex intermolecular associates which composition represented by general formula (H₂O)_n, where n can vary from 3 to 50 units [1]. The hydrogen bond – a form of association between the electronegative O oxyden atom and a H hydrogen atom, covalently bound to another electronegative O oxyden atom, is of vital importance in the chemistry of intermolecular interactions, based on weak electrostatic forces and donor-acceptor interactions with charge-transfer [2]. It results from interaction between electron-deficient H-atom of one Н₂О molecule (hydrogen donor) and unshared electron pair of an electronegative O-atom (hydrogen acceptor) on the neighboring Н₂О molecule; the structure of hydrogen bonding, therefore may be defined as О^...Н^d+–О^d-. As the result, the electron of the H-atom due to its relatively weak bond with the proton easily shifts to the electronegative O-atom. The O-atom with increased electronegativity becomes partly negatively charged – d^-, while the Н-atom on the opposite side of the molecule becomes positively charged – d⁺, that leads to the polarization of О^d-–Н^d+ of the covalent bond. In this process the proton becomes almost bared, and due to the electrostatic attraction forces are provided good conditions for convergence of O…O or О…Н atoms, leading to the chemical exchange of a proton in the reaction O–H...O « O...H–O. Although this interaction is essentially compensated by mutual repulsion of the molecules’ nuclei and electrons, the effect of the electrostatic forces and donor-acceptor interactions for Н₂О molecule compiles 5–10 kcal per 1 mole of substance. It is explained by negligible small atomic radius of hydrogen 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 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) [3].

A hydrogen bond according to Bernal–Fowler rules [4] is characterized by the following parameters:

• 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;
• 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 1,0 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 [5]. 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.
• 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, however, consists in its relatively low strength; it is 5–10 times weaker than chemical covalent bond [6]. 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 [7]. The values of the average energy (∆E_H...O) of hydrogen Н…О-bonds between H₂O molecules make up 0,1067 ± 0,0011 eV [8]. 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 [9].

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. The protons held by individual H₂O molecules may switch partners in an ordered manner within hydrogen networks [10]. 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 [11].  The simplest example of such associate can be a dimer 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. 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 ⁰С) 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 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.

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.

Figure 1. Hydrogen bonding between four individual Н₂О molecules. It is shown the value of the angle between the covalent H–O–H bond in Н₂О molecule.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 (Figure 2). In the crystalline structure of natural ice I_h hydrogen bonds are oriented towards the tetrahedron apexes at strictly defined angles equal to 109°5’ (in liquid water this angle is 104⁰5’). In ice structures I_c, 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 O-atom not participating in formation of molecular bonds.

Table 1

Ice Crystal modifications and their physical characteristics

• Modification; Crystal structure; Hydrogen bond lengths, Å; Angles H–O–H in tetragonals, 0
• Ih; Hexagonal; 2,76; 109,5
• Ic; Cubic; 2,76; 109,5
• II; Trigonal; 2,75–2,84; 80,0–128,0
• III; Tetragonal; 2,76–2,8; 87,0–141,0
• IV; Rhombic; 2,78–2,88; 70,1–109,0
• V; Monoclinic; 2,76–2,87; 84,0–135,0
• VI; Tetragonal; 2,79–2,82; 76,0–128,0
• VII; Cubic; 2,86; 109,5
• VIII; Cubic; 2,86; 109,5
• IX; Tetragonal; 2,76–2,8; 87,0–141,0
• X; Cubic; 2,78; 109,5
• XI; Hexagonal; 4,50; 90,0
• XII; Tetragonal; 4,01; 90,0
• XIII; Monoclinic; 7,47; 90,0–109,7
• XIV; rhombic; 4,08; 90,0

Notes:

 I_h – natural hexagonal ice; I_c – cubic ice.

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, presuure, density, viscosity, fluidity etc. According to theoretical calculations, at the melting of the ice breaks about 15 % of all hydrogen bonds [12]; by further heating to 40 ⁰C breaks down about half of hydrogen bonds in water associates. In the water vapor hydrogen bonds are absent.

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 t = 1,5 ⁰С to 4,9 at t = 80 ⁰С.

Figure 4. Structures of water crystals in carbon nanotubes according to computer simulations [14] (diameter of nano