  We investigate the structural, electronic and optical properties of mixed
bromide-iodide lead perovskite solar cell CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$
by means of the virtual crystal approximation (VCA) within density functional
theory (DFT). Optimizing the atomic positions and lattice parameters increasing
the bromide content $x$ from 0.0 to 1.0, we fit the calculated lattice
parameter and energy band gap to the linear and quadratic function of Br
content, respectively, which are in good agreement with the experiment,
respecting the Vegard's law. With the calculated exciton binding energy and
light absorption coefficient, we make sure that VCA gives consistent results
with the experiment, and the mixed halide perovskites are suitable for
generating the charge carriers by light absorption and conducting the carriers
easily due to their strong photon absorption coefficient, low exciton bindign
energy, and high carrier mobility at low Br contents. Furthermore analyzing the
bonding lengths between Pb and X (I$_{1-x}$Br$_x$: virtual atom) as well as C
and N, we stress that the stability of perovskite solar cell is definitely
improved at $x$=0.2.
