The bond valence method (or bond valence sum) (not to be mistaken with the valence bond theory in quantum chemistry) is a technique used in coordination chemistry to estimate the oxidation/valence states of atoms.
The basic idea is that the valence Vi of an atom i is the sum of the individual bond valences vij of the Ni surrounding atoms:

Vi  =  $\displaystyle \sum_{{j=1}}^{{N_i}}$ vij (1)

The individual bond valences vij are calculated using:

vij  =  exp$\displaystyle \left(\vphantom{ \frac{R_0 - R_{ij}}{b} }\right.$$\displaystyle {\frac{{R_0 - R_{ij}}}{{b}}}$$\displaystyle \left.\vphantom{ \frac{R_0 - R_{ij}}{B} }\right)$ (2)


vij  =  $\displaystyle \left(\vphantom{ \frac{R_{ij}}{R_0} }\right.$$\displaystyle {\frac{{R_{ij}}}{{R_0}}}$$\displaystyle \left.\vphantom{ \frac{R_{ij}}{R_0} }\right)^{-N}_{}$ (3)

Rij is the computed bond length between atoms i and j, R0, B and N are tabulated [a, b, c].
I.S.A.A.C.S. may compute bond valence sums for atomic species/coordination spheres selected by the users.

I.D. Brown and D. Altermatt
Acta. Cryst., B41:244-247 (1985).
I.D. Brown and R.D. Shannon
Acta. Cryst., A29:266-282 (1973).

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