# The Bond Valence Model

On the last page we have seen a relationship between the shortest and second shortest O-H bond in a crystal. The relation may be formulated as

with F being an empirical formula depending on the bond distance R. The function may be improved, if we use more than two bonds:

Now we have a k-dimensional relation. If we set k = coordination number, const. = W (the valence of th atom) and F(R) = s we get:

This is exactly the definition of the Bond Valence Sum Rule in the Bond Valence Model [for example Brown 1978, 1981] used mainly in inorganic chemistry, crystallography and mineralogy.

The bond valence model describes a crystal structure as net with the atoms as nodes and the bond connecting the nodes. The strength of each bond connecting the atoms is the amount which each atom contributes to the valence of the central atom.

When the coordination is symmetrical with bonds of equal lengths, then it is possible to describe the bond valence with the electrostatic bond strength derived from Paulings second rule [Pauling 1929].

In case the coordination is irregular, it is necessary to describe the bond valence s as a function of the bond distance R. Any empirical equation which obeys the bond valence sum rule is allowed. Nevertheless, usually only two equations are in use with the bond valence model:

R0, b and N are empirical constants with R0 as the bond length for a bond with the valence 1. The constants have to be fitted for each pair of atoms.

### Why are bond valences not used in organic chemistry?

So far, the bond valence model seems a simple model to define the strength of a bond. So why is it not used in organic chemistry?

This has mainly two reasons:

1. Bond valences are only valid between atoms of different electronegativity. Pauling [see his famous book about the Nature of the chemical bond, 1960] showed that the function above may be used for C-C bonds describing the bond order, but this concept was never used very much.
2. Single, double and delocalized bonds are sufficient to describe a molecule. Interactions between molecules are mainly ignored as the term non-bonded interactions already describe. Of course this is a simplification, but organic chemistry has other models which work fine, while inorganic chemistry struggles much more describing the properties of bonds.

Last Updated: 26 October 1996