sum rule It follows from these definitions, that the valence of an atom is equal to the sum of the valences of all the bonds it forms. This is known as the valence sum rule, Eq. 1, which is central to the bond valence model. (Eq. 1) A bond is formed when the valence shells of two atoms overlap. 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. We therefore expect a correlation between the bond valence and the bond length and find empirically that for most bonds it can be described by Eq. 2: (Eq. 2) where S is the valence and R is the length of the bond, and Ro and b are parameters that are empirically determined for each bond type. For many bond types (but not all), b is found to be close to 0.37 Å. A list of bond valence parameters for different bond types (i.e. for different pairs of cation and anion in given oxidation states) can be found at the web site. 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. If the structure of a compound is known, the empirical bond valence - bond length correlation of Eq. 2 can be used to estimate the bond valences from their observed bond lengths. Eq. 1 can then be used to check that the structure is chemically valid; any deviation between the atomic valence and the bond valence sum needs to be accounted for. The distortion theorem Eq. 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. Alternatively if the average bond length is kept constant, the more the bond valence sum increases The valence matching rule If the structure is not known, the average bond valence, Sa can be calculated from the atomic valence, V, if the coordination number, N, of the atom is known using Eq. 3. (Eq. 3) If the coordination number is not known, a typical coordination number for the atom can be used