Bond valence method

The bond valence method (or bond valence sum) (not to be mistaken for the valence bond theory in quantum chemistry) is a popular method in coordination chemistry to estimate the oxidation states of atoms.

The basic idea is that the valence V of an atom is the sum of the individual bond valences vi surrounding the atom:
 * $$ V = \sum(v_i) $$

The individual bond valences in turn are calculated from the observed bond lengths.
 * $$ v_i=\exp \left( \frac {R_0-R_i} {b} \right) $$

Ri is the observed bond length, R0 is tabulated, and b is a constant, typically 0.37 Å.

Also, :$$ v_i= \left( \frac {R_i} {R_0}\right)^{-6} $$ see

Actinide oxides
It is possible by bond valence calculations to estimate how great a contribution a given oxygen atom is making to the assumed valence of uranium. Zachariasen Lists the parameters to allow such calculations to be done for many of the actinides. 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.

For uranium binding to oxygen the constants Ro and B are tabulated in the table below. For each oxidation state use the parameters from the table shown below.

What level of accuracy do we have?
In applying the bond valence sum on PMo12O40V2$$^{-5}$$ of the symmetry P-1, The following table was obtained However, according to bond valence method the Molybdenum on this molecule would have the valence 7, which is chemically impossible.

Doing the calculations
It is possible to do these calculations on paper or software. A program which does it can be obtained free of charge.