  The recently developed theory of topological quantum chemistry (TQC) has
built a close connection between band representations in momentum space and
orbital characters in real space. It provides an effective way to diagnose
topological materials, leading to the discovery of lots of topological
materials after the screening of all known nonmagnetic compounds. On the other
hand, it can also efficiently reveal spacial orbital characters, including
average charge centers and site-symmetry characters. By using TQC theory with
the computed irreducible representations in the first-principles calculations,
we demonstrate that the electrides with excess electrons serving as anions at
vacancies can be well identified by analyzing band representations (BRs), which
cannot be expressed as a sum of atomic-orbital-induced band representations
(aBRs). In fact, the floating bands (formed by the excess electrons) belong to
the BRs induced from the "pseudo-orbitals" centered at vacancies. In other
words, the electrides are proved to be unconventional ionic crystals, where a
set of occupied bands is not a sum of aBRs but necessarily contains a BR from
vacancies. The TQC theory provides a promising avenue to pursue more electride
candidates in ionic crystals.
