  In the present work, we report a detailed density functional theory
calculation on polymorphic InVO$_4$ phases by means of projector augmented wave
method. The computed first-order structural phase transformation from
orthorhombic \emph{(Cmcm)} to monoclinic \emph{(P2/c)} structure is found to
occur around 5.6 GPa along with a large volume collapse of 16.6$\%$, which is
consistent with previously reported experimental data. This transformation also
leads to an increase in the coordination number of vanadium atom from 4 to 6.
The computed equilibrium and high pressure structural properties of both
InVO$_4$ phases, including unit cell parameters, equation of state, and bulk
moduli, are in good agreement with the available experimental data. In
addition, compressibility is found to be highly anisotropic and the
\emph{b}-axis being more compressible than the other for both the structures.
Electronic band structures for both the phases were calculated, and the band
gap for orthorhombic and monoclinic InVO$_4$ are found to be 4.02 and 1.67 eV,
respectively, within the Tran-Blaha Modified Becke-Johnson potential as
implemented in linearized augmented planewave method. We further examined the
optical properties such as dielectric function, refractive index, and
absorption spectra for both the structures. From the implications of these
results, it can be proposed that the high pressure InVO$_4$ phase can be more
useful than orthorhombic phase for photo catalytic applications.
