  The effect of Non-centrosymmetricity on electronic and optical properties has
been investigated using grid based projector augmented wave method code GPAW.
The calculation of band gap using GLLB-SC which improves on the exchange
potential and explicitly estimates the derivative discontinuity is similar to
experimental result. Ferro-electricity of BaHfO$_{3}$ is increased as lattice
distortion kept on increasing. Static dielectric constant, index of refraction
only show slight change and in good agreement with experimental and other
results. Absorption reaches highest peaks in visible frequency range, and
absorption coefficient decreased as light goes through BaHfO$_{3}$ bulk, this
in turn enhance excitonic property. Exciton binding energy increased over
lattice distortion sites. The presented results are important in connection
with development of typical perovskite optoelectronic device properties.
