Since each of the terminal atoms contributes equal numbers of electrons to the bond, the bond valence is also equal to the number of valence electrons that each atom contributes.
It is apparent that the closer two atoms approach each other, the larger the overlap region and the more electrons are associated with the bond.
[1] It is this empirical relation that links the formal theorems of the bond valence model to the real world and allows the bond valence model to be used to predict the real structure, geometry, and properties of a compound.
2 is used to derive the distortion theorem which states that the more the individual bond lengths in a coordination sphere deviate from their average, the more the average bond length increases provided the valence sum is kept constant.
Some atoms, such as sulfur(VI), are only found with one coordination number with oxygen, in this case 4, but others, such as sodium, are found with a range of coordination numbers, though most lie close to the average, which for sodium is 6.2.
This results in the atom having a smaller coordination number, hence a higher bonding strength, when the lone pair is stereoactive.
Ions with lone pairs have a greater ability to adapt their bonding strength to match that of the counter-ion.
4 are difficult, if not impossible, to prepare, and chemical reactions tend to favour the compounds that provide the best valence match.
If VE is the charge on the atomic core (which is the same as the valence of the atom when all the electrons in the valence shell are bonding), and NE is the corresponding average coordination number, VE/NE is proportional to the electric field at the surface of the core, represented by SE in Eq.
If these conditions are satisfied, as they are in many ionic and covalent compounds, the electrons forming a bond can all be formally assigned to the anion.
The association of the cation bonding electrons with the anion in the ionic model is purely formal.
If an atom has a valence, V, that is equal to its coordination number, N, its bonding strength according to Eq.
Compounds can be constructed by linking carbon and hydrogen atoms with bonds that are all exactly equivalent.
A chemical structure can be represented by a bond network of the kind familiar in molecular diagrams.
The individual bond capacitors are not initially known, but in the absence of any information to the contrary we assume that they are all equal.
In this case the circuit can be solved using the Kirchhoff equations, yielding the valences of each bond.
Additional constraints include electronic anisotropies (lone pairs and Jahn-Teller distortions) or steric constraints, (bonds stretched or compressed in order to fit them into three-dimensional space).
[10] The bond valence model is an extension of the electron counting rules and its strength lies in its simplicity and robustness.
The empirical parameters of the model are tabulated and are readily transferable between bonds of the same type.
The concepts used are familiar to chemists and provide ready insight into the chemical restraints acting on the structure.
It cannot in principle predict electron density distributions or energies since these require the solution of the Schoedinger equation using the long-range Coulomb potential which is incompatible with the concept of a localized bond.
In 1930, Lawrence Bragg[11] showed that Pauling's electrostatic valence rule could be represented by electrostatic lines of force emanating from cations in proportion to the cation charge and ending on anions.
The lines of force are divided equally between the bonds to the corners of the coordination polyhedron.
These new insights were developed by later workers culminating in the set of rules termed the bond valence model.
Bond valence calculations use parameters which are estimated after examining a large number of crystal structures of uranium oxides (and related uranium compounds); note that the oxidation states which this method provides are only a guide which assists in the understanding of a crystal structure.
[16][17] In 2020 David Brown published a nearly comprehensive set of bond valence parameters on the IuCr web site.