title: Machine Learning Energies of 2 Million Elpasolite (ABC_{2}D_{6}) Crystals.
abstract: Elpasolite is the predominant quaternary crystal structure (AlNaK_{2}F_{6} prototype) reported in the Inorganic Crystal Structure Database. We develop a machine learning model to calculate density functional theory quality formation energies of all ∼2×10^{6} pristine ABC_{2}D_{6} elpasolite crystals that can be made up from main-group elements (up to bismuth). Our model's accuracy can be improved systematically, reaching a mean absolute error of 0.1  eV/atom for a training set consisting of 10×10^{3} crystals. Important bonding trends are revealed: fluoride is best suited to fit the coordination of the D site, which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of the elements A and B is very small on average. Low formation energies result from A and B being late elements from group II, C being a late (group I) element, and D being fluoride. Out of 2×10^{6} crystals, 90 unique structures are predicted to be on the convex hull-among which is NFAl_{2}Ca_{6}, with a peculiar stoichiometry and a negative atomic oxidation state for Al.
authors.affiliation: Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, 4056 Basel, Switzerland.
authors.forename: Felix A
authors.initials: FA
authors.lastname: Faber
authors.affiliation: Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden.
authors.forename: Alexander
authors.initials: A
authors.lastname: Lindmaa
authors.affiliation: Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials, Department of Chemistry, University of Basel, 4056 Basel, Switzerland.|General Chemistry, Free University of Brussels, Pleinlaan 2, 1050 Brussels, Belgium.
authors.forename: O Anatole
authors.initials: OA
authors.lastname: von Lilienfeld
authors.affiliation: Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden.
authors.forename: Rickard
authors.initials: R
authors.lastname: Armiento