  In the present paper electronic, magnetic, and structural properties of a
novel system FeZnMo$_3$O$_8$ with a polar crystal structure are investigated
using GGA+U calculations. It is shown that Fe ions preferably occupy octahedral
and Zn ions tetrahedral positions. This structural feature is caused by
different ionic radii of these ions and not by the exchange coupling. The
calculated exchange constants naturally explain magnetic structure observed in
this material.
