  First principles study of structural, elastic, and electronic properties of
the cubic perovskitetype BaHfO$_3$ has been performed using the plane wave
ultrasoft pseudo-potential method based on density functional theory with
revised Perdew-Burke-Ernzerhof exchange-correlation functional of the
generalized gradient approximation (GGA-RPBE). The calculated equilibrium
lattice constant of this compound is in good agreement with the available
experimental and theoretical data reported in the literatures. The independent
elastic constants (\emph{C}$_{11}$, \emph{C}$_{12}$, and \emph{C}$_{44}$), bulk
modules \emph{B} and its pressure derivatives $B^{\prime}$, compressibility
$\beta$, shear modulus \emph{G}, Young's modulus \emph{Y}, Poisson's ratio
$\nu$, and Lam\'{e} constants ($\mu, \lambda$) are obtained and analyzed in
comparison with the available theoretical and experimental data for both the
singlecrystalline and polycrystalline BaHfO$_3$. The band structure
calculations show that BaHfO$_3$ is a indirect bandgap material (R-$\Gamma$ =
3.11 eV) derived basically from the occupied O 2\emph{p} and unoccupied Hf
5\emph{d} states, and it still awaits experimental confirmation. The density of
states (total, site-projected, and \emph{l}-decomposed) and the bonding charge
density calculations make it clear that the covalent bonds exist between the Hf
and O atoms and the ionic bonds exist between the Ba atoms and HfO$_3$ ionic
groups in BaHfO$_3$. From our calculations, it is shown that BaHfO$_3$ should
be promising as a candidate for synthesis and design of superhard materials due
to the covalent bonding between the transition metal Hf 5\emph{d} and O
2\emph{p} states.
