  The molybdate oxides SrMoO$_3$, PbMoO$_3$, and LaMoO$_3$ are a class of
metallic perovskites that exhibit interesting properties including high
mobility, and unusual resistivity behavior. We use first-principles methods
based on density functional theory to explore the electronic, crystal, and
magnetic structure of these materials. In order to account for the electron
correlations in the partially-filled Mo $4d$ shell, a local Hubbard $U$
interaction is included. The value of $U$ is estimated via the constrained
random-phase approximation approach, and the dependence of the results on the
choice of $U$ are explored. For all materials, GGA+$U$ predicts a metal with an
orthorhombic, antiferromagnetic structure. For LaMoO$_3$, the $Pnma$ space
group is the most stable, while for SrMoO$_3$ and PbMoO$_3$, the $Imma$ and
$Pnma$ structures are close in energy. The $R_4^+$ octahedral rotations for
SrMoO$_3$ and PbMoO$_3$ are found to be overestimated compared to the
experimental low-temperature structure.
