  Using first-principles calculations, we investigate the band structures of a
series of quaternary LiMgPdSn-type Heusler compounds. Our calculation results
show that five compounds CoFeMnSi, CoFeCrAl, CoMnCrSi, CoFeVSi and FeMnCrSb
possess unique electronic structures characterized by a half-metallic gap in
one spin direction while a zero-width gap in the other spin direction showing
spin gapless semiconducting behavior. We further analysis the electronic and
magnetic properties of all quaternary Heusler alloys involved, and reveal a
semi-empirical general rule (total valence electrons number being 26 or 28) for
indentifying spin gapless semiconductors in Heusler compounds. The influences
of lattice distortion and main-group element change have also been discussed.
