Determination of the Bonding and Valence Distribution in Inorganic Solids by the Maximum Entropy Method

The distribution of valence among the bonds in the bond graph of an inorganic compound is used to calculate an `entropy'. We show that the distribution of valence that maximizes this entropy (ME) is similar, but not identical, to that obtained using the equal-valence rule (EVR) proposed by Brown [Acta Cryst. (1977), B33, 1305–1310]. Since the ME solutions are maximally non-committal with regard to missing information, they give better predictions of the observed valence distributions than the EVR solutions when lattice constraints or electronic anisotropies are present, but worse predictions when these effects are absent. Since valences calculated using ME are necessarily positive, they give significantly better predictions in cases where EVR predicts a negative bond valence. In the absence of electronic distortions the observed bond graph is either the graph with the highest maximum entropy or it has an entropy within 1% of this value. Since the entropy depends on the oxidation states of the atoms, compounds with the same stoichiometry and cation coordination numbers but different atomic valences may adopt different bond graphs and hence different structures.