Machine learning energies of 2M elpasolite (ABC$_2$D$_6$) crystals

Elpasolite is one of the most predominant quaternary crystal structures (AlNaK$_2$F$_6$ prototype) reported in the Inorganic Crystal Structure Database. We present a machine learning model to calculate density functional theory quality formation energies for all 2M possible ABC$_2$D$_6$ elpasolite crystals one can make up from all main-group elements up to Bi. The model's accuracy can be improved systematically, reaching a mean-absolute out of sample error of 0.1 eV/atom after training on 10k crystals. Out of the 2M crystals, we have identified 128 new structures which we predict to be on the convex hull---among which NFAl$_2$Ca$_6$, a metallic elpasolite with unusual stoichiometry and negative atomic oxidation state of Al.