  The ``14-1-11'' phase compounds based on magnetic Mn ions and typified by
Ca14MnBi11 and Ba14MnBi11 show unusual magnetic behavior, but the large number
(104) of atoms in the primitive cell has precluded any previous full electronic
structure study. Using an efficient, local orbital based method within the
local spin density approximation to study the electronic structure, we find a
gap between a bonding valence band complex and an antibonding conduction band
continuum. The bonding bands lack one electron per formula unit of being
filled, making them low carrier density p-type metals. The hole resides in the
MnBi4 tetrahedral unit and partially compensates the high spin d^5 Mn moment,
leaving a net spin near 4 \mu_B that is consistent with experiment. These
manganites are composed of two disjoint but interpenetrating `jungle gym'
networks of spin 4/2 MnBi4^{9-} units with ferromagnetic interactions within
the same network, and weaker couplings between the networks whose sign and
magnitude is sensitive to materials parameters. Ca14MnBi11 is calculated to be
ferromagnetic as observed, while for Ba14MnBi11 (which is antiferromagnetic)
the ferro- and antiferromagnetic states are calculated to be essentially
degenerate. The band structure of the ferromagnetic states is very close to
half metallic.
