The rule of four: anomalous distributions in the stoichiometries of inorganic compounds

This paper investigates the unexpectedly high abundance of inorganic compounds whose primitive unit cells contain a number of atoms that is a multiple of four. This phenomenon, termed the 'rule of four,' is analyzed using two large databases of inorganic crystal structures: the Materials Project and the Materials Cloud 3D source database. The study explores the relationship between the rule of four and established descriptors of crystal structures, including symmetries and energies. Surprisingly, the overabundance is not correlated with low-energy or high-symmetry structures but rather with low symmetries and loosely packed arrangements. Machine learning techniques, specifically Principal Covariates Regression and Random Forest classification, are employed to further investigate the connection between local atomic environments and the rule of four.

Elena Gazzarrini, Rose K. Cersonsky, Marnik Bercx, Carl S. Adorf, Nicola Marzari