  Large bandgap insulators are considered promising for applications such as
photocatalysts, dielectric resonators and interference filters. Based on
synchrotron X-ray diffraction, diffuse reflectance measurement and density
functional theory, we report the crystal structure, optical response, and
electronic properties of the synthesized $d^0$ double perovskite
Ba$_2$ScTaO$_6$. In contrast to earlier prediction, the electronic bandgap is
found to be large, $\sim 4.66$ eV. The optical response is characterized by the
presence of multiple exciton modes extending up to the visible range. A
detailed investigation of the direct gap excitons based on the Elliot formula
is presented. Density functional theory based investigation of the electronic
properties within generalized gradient approximation severely underestimates
the electronic gap. To reach a quantitative agreement, we consider different
available flavors of the modified-Becke-Johnson exchange-correlation potential
and discuss their effects on the electronic and optical properties.
