Counting Electrons in Electrides.

The selection and design of charge integration methods remain an outstanding challenge in materials chemistry. In complex materials like electrides, this challenge is amplified by the small charge and complex shape of electride wave functions. For these reasons, popular integration methods, such as the Bader method, usually fail to assign any charge to the bare electrons in an electride. To address this challenge, we developed an algorithm that instead partitions the charge based on the electron localization function (ELF), a popular scheme for visualizing chemically important features in molecules and solids. The algorithm uses Bader segmentation of the ELF to find the electride electrons and Voronoi segmentation of the ELF to identify atoms. We apply this method, "BadELF", to the quantification of atomic radii and oxidation states in both ionic compounds and electrides. For ionic compounds, we find that the BadELF method yields radii that agree closely with Shannon crystal radii, while the oxidation states agree closely with the Bader method. When they are applied to electrides, however, only the BadELF algorithm yields chemically meaningful charges. We argue that the BadELF method provides a useful strategy to identify electrides and obtain new insight into their most essential property: the quantity of electrons within them.

Sc2C, a 2D Semiconducting Electride.

Electrides are exotic materials that typically have electrons present in well-defined lattice sites rather than within atoms. Although all known electrides have an electropositive metal cation adjacent to the electride site, the effect of cation electronegativity on the properties of electrides is not yet known. Here, we examine trivalent metal carbides with varying degrees of electronegativity and experimentally synthesize Sc2C. Our studies identify the material as a two-dimensional (2D) electride, even though Sc is more electronegative than any metal previously found adjacent to an electride site. Further, by exploring Sc2C and Al2C computationally, we find that higher electronegativity of the cation drives greater hybridization between metal and electride orbitals, which opens a band gap in these materials. Sc2C is the first 2D electride semiconductor, and we propose a design rule that cation electronegativity drives the change in its band structure.