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Inorganic Chemistry

Pauling’s rules about crystal structures flunk test

Only 13 % of oxide crystal structures obey 4 of the 5 rules simultaneously

by Celia Henry Arnaud
February 26, 2020

More than 90 years ago, Linus Pauling published a set of five empirical principles explaining why ionic compounds form the crystal structures that they do. Those principles, now known as Pauling’s rules, have become a fixture of textbooks. A new study suggests that these rules may not actually work well.


The percentage of oxide crystal structures that fulfill four of the five Pauling’s rules.

Geoffroy Hautier’s team at the Catholic University of Louvain uses computational methods to design new materials. Pauling’s rules have been among the guiding principles for their work. But it became obvious to them that predictions made using the rules often failed.

“Since their first publication in 1929, Pauling’s rules have been widely used to rationalize the crystal structure of novel compounds—that is, when they work,” says Anubhav Jain, a materials scientist at Lawrence Berkeley National Laboratory who was not involved with the new study. “When they do not, the rules are most typically not commented on at all. Thus, it has generally been unknown what the true predictive power of Pauling’s rules is.”

Looking through the literature, Hautier’s team realized that chemists hadn’t performed a rigorous statistical assessment to determine whether Pauling’s rules were valid. So they decided to undertake one.

They assembled a data set of more than 5,000 oxides with crystal structures in the Inorganic Crystal Structure Database. They focused on oxides because they’re ionic enough for Pauling’s rules to apply and enough oxide crystal structures have been solved to result in a large data set.

Hautier, postdoc Janine George, and coworkers used the data set to test the rules individually and in combination (Angew. Chem., Int. Ed. 2020, DOI: 10.1002/anie.202000829). The hard part was coming up with quantitative definitions for assessing the otherwise qualitative rules. The first rule, which relates to the ratio of the cation and anion radii, turned out to work so poorly on its own that the researchers excluded it from the combined analysis.

The remaining four rules didn’t work much better. A mere 13% of the oxide structures fulfilled all four rules. The percentage improved when the researchers limited the data set to structures with cation coordination numbers no larger than 8. But even then, only 20% of the structures obeyed all four rules.

“The five rules appear to mostly improve as you go down the list, so perhaps Pauling should have listed them backwards,” Jain notes. “In particular, rules that try to minimize the overall electrostatic energy seem to get an overall ‘pass’ as they have a clear correlation to the overall crystal energy.”

Hautier doesn’t want to completely abandon Pauling’s rules. Instead, he wants to update them using artificial intelligence and machine-learning methods. “We still want to start with the way you describe crystal structure by connection of local environments. I think there is interesting intuition there,” he says. “It’s somehow saying that Pauling was right in the way he described crystal structures, but let’s try to extract the rules in a way that’s more modern.”



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