  We report evidence that the experimentally found antiferromagnetic structure
as well as the semiconducting ground state of BaMn$_2$As$_2$ are caused by
optimally-localized Wannier states of special symmetry existing at the Fermi
level of BaMn$_2$As$_2$. In addition, we find that a (small) tetragonal
distortion of the crystal is required to stabilize the antiferromagnetic
semiconducting state. To our knowledge, this distortion has not yet been
established experimentally.
