  Doubling the perovskite cell (double perovskite) has been found to open new
possibilities for engineering functional materials, magnetic materials in
particular. This route should be applicable to the antiperovskite (aPV) class.
In the pnictide based double aPV (2aPV) class introduced here magnetism is very
rare, and we address them as new topological materials, possibly with
thermoelectric interest. We have found that the 2aPV supercell provides a
systematically larger band gap that can serve to inhibit bulk conductivity, and
also large spin-orbit coupling (SOC) for band inversion. We present examples
from a broad study of double antiperovskites focusing on the X$_6$AA$'$B$_2$
configuration, where X is the alkaline earth element and A and B are the group
5A pnictogens. We find that an "extended s" state at the valence band minimum,
described alternatively as a cation valence state or a modulated interstitial
planewave state, plays a crucial role in both topological and thermoelectric
properties. Several of these compounds may house topological phases, while
transport calculations indicate they may also find themselves useful in
thermoelectric applications.
