  Intermetallic compounds with sizable band gaps are attractive for their
unusual properties but rare. Here, we present a new family of stable
semiconducting quaternary Heusler compounds, designed and discovered by means
of high-throughput \textit{ab initio} calculations based on the 18-electron
rule. The 99 new semiconductors reported here adopt the ordered quaternary
Heusler structure with the prototype of LiMgSnPd (F$\bar{\mathbf{4}}$3m,
No.\,216) and contain 18 valence electrons per formula unit. They are realized
by filling the void in the half Heusler structure with a small and
electropositive atom, i.e., lithium. These new stable quaternary Heusler
semiconductors possess a range of band gaps from 0.3 to 2.5\,eV, and exhibit
some unusual properties different from conventional semiconductors, such as
strong optical absorption, giant dielectric screening, and high Seebeck
coefficient, which suggest these semiconductors have potential applications as
photovoltaic and thermoelectric materials. While this study opens up avenues
for further exploration of this novel class of semiconducting quaternary
Heuslers, the design strategy used herein is broadly applicable across a
potentially wide array of chemistries to discover new stable materials.
