  Heusler compounds are widely studied due to their variety of magnetic
properties making them ideal candidates for spintronic and magnetoelectronic
applications. V$_3$Al in its metastable D0$_3$-type Heusler structure is a
prototype for a rare antiferromagnetic gapless behavior. We provide an
extensive study on the electronic and magnetic properties of V$_3$Al, V$_3$Ga
and V$_3$In compounds based on state-of-the-art electronic structure
calculations. We show that the ground state for all three is a G-type itinerant
antiferromagnetic gapless semiconductor. The large antiferromagnetic exchange
interactions lead to very high N\'eel temperatures, which are predicted to be
around 1000 K. The coexistence of the gapless and antiferromagnetic behaviors
in these compounds can be explained considering the simultaneous presence of
three V atoms at the unit cell using arguments which have been employed for
usual inverse Heusler compounds. We expect that our study on these compounds to
enhance further the interest on them towards the optimization of their growth
conditions and their eventual incorporation in devices.
