  Using first-principles calculations, the electronic and magnetic properties
of orthorhombic BaFeO$_{3}$ (BFO) are investigated with local spin density
approximation (LSDA). The calculations reveal that at the optimized lattice
volume BFO has a lower energy in ferromagnetic state as compared with
antiferromagnetic state. At the equilibrium volume, BFO shows metallic
behavior, however, under a large tensile strain ($\sim25\%$), BFO shows
half-metallic behavior consistent with the integer magnetic moment of
$4.0\mu_{\rm{B}}$/fu mainly caused by the $t_{2g}$ and $e_{g}$ electrons of Fe.
Including a Hubbard-like contribution $U$ (LSDA$+U$) on Fe $d$ states induced
half-metallic bahvior without external strain, which indicates that $U$ can be
used to tune the electronic structure of BFO. The magnetic moments remained
robust against $\sim 10\%$ compressive and tensile strain. At large compressive
(tensile) strain, the half-metallicity of BFO is mainly destroyed by the Fe-$d$
(O-$p$) electrons in agreement with the non-integer value of the magnetic
moments of BFO.
