Using Topology to Predict Electrides in the Solid State

Electrides are characterized by electron density highly localized in interstitial sites, which do not coincide with direct interatomic contacts. The rigorous quantum mechanical definition of electrides is based upon topological criteria derived from the electron density, and in particular the presence of non-nuclear attractors (NNAs). We employ these topological criteria in combination with crystal structure prediction methods (the XtalOpt evolutionary algorithm), to accelerate the discovery of crystalline electrides at ambient and nonambient pressures. The localization and quantification of NNAs is used as the primary discriminator for the electride character of a solid within a multiobjective evolutionary structure search. We demonstrate the reliability of this approach through a comprehensive crystal structure prediction study of Ca₅Pb₃ at 20 GPa, a system previously theorized to exhibit electride character under compression. Our strategy could predict, and sort on-the-fly, several unknown low-enthalpy phases that possess NNAs in interstitial loci, such as the newly discovered P4/mmm structure. These results demonstrate how evolutionary algorithms, guided by rigorous topological descriptors, can be relied upon to effectively survey complex phases to find new electride candidates.