  Electrides are an emerging class of materials with excess electrons localized
in interstices and acting as anionic interstitial quasi-atoms (ISQs). The
spatial ion-electron separation means that electrides can be treated physically
as ionic crystals, and this unusual behavior leads to extraordinary physical
and chemical phenomena. Here, a completely different effect in electrides is
predicted. By recognizing the long-range Coulomb interactions between matrix
atoms and ISQs that are unique in electrides, a nonanalytic correction to the
forces exerted on matrix atoms is proposed. This correction gives rise to an
LA-TA splitting in the acoustic branch of lattice phonons near the zone center,
similar to the well-known LO-TO splitting in the phonon spectra of ionic
compounds. The factors that govern this splitting are investigated, with
isotropic fcc-Li and anisotropic hP4-Na as the typical examples. It is found
that not all electrides can induce a detectable splitting, and criteria are
given for this type of splitting. The present prediction unveils the rich
phenomena in electrides and could lead to unprecedented applications.
