Gh. Rao et Id. Brown, DETERMINATION OF THE BONDING AND VALENCE DISTRIBUTION IN INORGANIC SOLIDS BY THE MAXIMUM-ENTROPY METHOD, Acta crystallographica. Section B, Structural science, 54, 1998, pp. 221-230
The distribution of valence among the bonds in the bond graph of an in
organic compound is used to calculate an 'entropy'. We show that the d
istribution of valence that maximizes this entropy (ME) is similar, bu
t not identical, to that obtained using the equal-valence rule (EVR) p
roposed by Brown [Acta Cryst. (1977), B33, 1305-1310]. Since the ME so
lutions are maximally non-committal with regard to missing information
, they give better predictions of the observed valence distributions t
han the EVR solutions when lattice constraints or electronic anisotrop
ies 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 negati
ve 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 stoichiomet
ry and cation coordination numbers but different atomic valences may a
dopt different bond graphs and hence different structures.