Electrostatic flux

These link regions, which we can identify with chemical bonds, are characterized by the electrostatic flux, defined by eqn (2.6), that links the two ions i and j ... 

Definition of coordination number. The coordination number of an ion is the number of ions to which it is linked by electrostatic flux. 

This chapter shows that the ionic model can not only be presented in terms of chemical bonds characterized by their electrostatic flux, but also that the improbable assumptions of the model are satisfied by the wide range of compounds that conform to the following two conditions ... 

Figure 2 The relation between bond valence and bond length for Ca-0 bonds. The line shows equation (1). The points are electrostatic fluxes calculated using Coulomb s law for several different Ca-bearing crystals. (Figure 3.1 from The Chemical Bond in Inorganic Chemistry by Brown, David (2001)). (Ref. 3. Reproduced by permission of Oxford University Press)...

So far as the mechanism of bistability is concerned in non-reacting system including membrane process, there is general agreement that it is related to the interplay of the hydrodynamics flux and electrostatic flux, which act in opposite directions [32]. 

Figure 21.17 The Gaussian box at the oil/water interface and the electrostatic fluxes normal to the plane.

The second boundary condition comes from the components of the field that are perpendicular to the interface. Make a small Gaussian box that sandwiches the surface (see Figure 21.17). Because the surface is uncharged, the net flux out is zero, so the perpendicular electrostatic flux into the oil phase (DoEo,nX area) must equal the perpendicular electrostatic flux into the water phase (Du Eu, nX area), and... 

This leads to an interesting extension of the core-and-valence-shell picture. Where the valence of a bond was previously defined as the flux linking the cation core to the electrons it contributes to the bond, in the ionic model it is defined by the same flux which now links the cation to the anion. If the positions of the atoms in the array are known from experiment, this flux can be directly calculated. The calculation involves extensive computation, but Preiser et al. [17] have shown that in stmctures in equilibrium, the correlation between the bond flux and bond length is the same as the correlation that had previously been observed between the bond valence and bond length, showing that the electrostatic flux and bond valence are indeed the same. 

It is sometimes assumed that the long range of the Coulomb potential makes it impossible to define a localized bond in the ionic model, but in fact the ionic model is the only model that provides a useful and unambiguous definition of a bond. Since the electrostatic flux that links two ions is equal to the valence of the bond that links them, a bond only exists between ions if they are linked by flux. A simple picture of the electrostatic field in the ionic model is provided by the lines of field that connect a cation to its first shell of anion neighbors as shown in Fig. 5. 

More importantly, we can use the ionic model to predict the electrostatic flux or valence of the individual bonds, and from these we can predict their lengths. If the positions of the atoms are already known, the bond flux can, in principle, be calculated using Coulomb s law, but this is computationally intensive, and as it requires a prior knowledge of the structure, the result is not a prediction. Fortunately there is a simpler approach that requires no prior knowledge of the atomic positions. AU that is required is a knowledge of the bond network, that is, which atoms are linked by bonds. 

The core and valence shell model can be used to examine the effects of lone pairs on the bonding geometiy. Because every atom has a spherically symmetric electron density, the electric field linking the core to the valence shell is also spherically symmetric. If lone pairs are present in the valence shell, some of the electrostatic flux (valence) will link to lone pair electrons and some to bonding electrons. Although the total flux is distributed synunetrically, its function as either bonding flux or lone pair flux need not be. 

Since a localized bond model requires information neither about the distribution of electron density nor about the energy of the molecule, quantum mechanics is not needed. Bond valence theory determines the number of bonding electrons (atomic valence) by counting how many electrons have a small ionization energy, and it develops the bond picture using the electrostatic field rather than the electrostatic potential. In the ionic model representation of bond valence theory, a bond exists between any two atoms linked by lines of electric field and the number of these lines linking two atoms (the electrostatic flux) is a measure of the number of electrons used to form the bond. This is the foundation on which the model is built. 

Figure 2 immediately leads to the definition of a bond any two atoms that are linked by lines of field are connected by a bond. Further, the number of lines (the electrostatic flux) is a direct measure of the strength of the bond. If the charges of the ions are set equal to their atomic valence (the number of electrons the atom uses for bonding), the electrostatic flux that forms the bond is called the bond valence. From this simple construction comes the most important rule of the bond valence theory the valence sum rule (Eq. 2 in [1]), which states that the valence of an atom is equal to the sum of the valences of the bonds it forms. This is Gauss law of electrostatics. 

It should also be apparent that if two atoms are brought closer to each other, the number of lines of field linking them will increase. This leads us to expect a correlation between the valence (electrostatic flux) and the length of the bond (Eq. 4 in [1]). Although the length of a bond is not likely to be of great interest in... 

Although the itMiic model is often thought to apply orfly to compounds composed of ionic bonds. Sect 5 of [1] shows that its application is almost universal only homoionic and delocalized bonds are excluded. The ionic model describes covalent and ionic bonds without distinction because the electrostatic flux depends only on the number of valence electrons and not on whether the bonding electrons lie closer to the anion or cation, or somewhere in between. It has been customary to label strong bmids as covalent, but attempts to define a covalent bond quickly run into problems. 

Bipartite graph The graph of a bond network in which the atoms are of two kinds (e.g., cation or anion) with no bonds occurring between atoms of the same kind Bond The chemical link between two neighboring atoms. In the ionic model, two atoms are bonded if and only if they are linked by electrostatic flux Bond network A topological description of the way in which atoms in a system are linked by bonds... 

Bond strain index Root mean square deviation between the observed and ideal bond valence averaged over all the bonds in the formula unit Bond valence, 5 The number of valence electrons an atom uses to form a given bond. In the ionic model it is equal to the electrostatic flux linking two ions. The... 

Electrostatic flux The electrostatic flux linking two atoms in the ionic model is the bond valence... 

Ionic model A model in which every atom is assigned as either a cation or an anion, each carrying a charge equal to its valence. A bond exists in this model between two atoms if they are linked by electrostatic flux. This model can be applied to any valence compound without regard to whether the bonding is ionic or covalent... 

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