Crystal chemical rules are widely applied to understand and rationalize inorganic crystal structures. Examples of such include Pauling rules and Beck's extended coordination number rule. For the latter no large-scale benchmark has been performed yet. A rigorous analysis of the validity of the extended coordination number rule was performed on a dataset consisting of 1044 ternary fluorides. 59.9% of the examined crystal structures agree with Beck's rule. An additional 22.3% of structures the deviations can be explained by a more or equally homogenous distribution of charges, thus yielding a total rationalization power of 82.2%. The structural complexity of the crystal structures was identified as a main reason for disagreement with Beck's rule.
Langer et al. (Tue,) studied this question.