Counting electrons in electrides

The wave nature of electrons makes the quantification of charge fundamentally challenging. In complex materials like electrides, this challenge is amplified by the small charge and complex shape of electride wavefunctions. For these reasons, popular integration methods such as the Bader method usually fail to assign any charge to the electron in an electride. To address this challenge, we advance an algorithm that, like the Bader method, assigns charge to an atom through the creation of a dividing surface. Unlike Bader, the dividing surface is defined not by a minimum in charge density but by a minimum in the electron localization function (ELF). We apply this method, “BadELF”, to the quantification of oxidation state in both ionic compounds and electrides. For ionic compounds, we observe that Bader and BadELF perform similarly; on electrides only BadELF yields chemically meaningful charges. We conclude that the BadELF method provides a useful strategy to identify electrides and obtain new chemical insight about their most essential property: the quantity of electrons within them.