  All-inorganic halide perovskites have attracted a great interest as a
promising light harvester of perovskite solar cells due to their enhanced
chemical stability. In this work we investigate the material properties of
solid solutions CsPb(I$_{1-x}$Br$_x$)$_3$ in cubic phase by applying the
virtual crystal approximation approach within a density functional theory
framework. First we check the validity of constructed pseudopotentials of the
virtual atoms (X = I$_{1-x}$Br$_x$) by verifying that the lattice constants
follow the linear function of mixing ratio. We then suggest an idea of using
the hybrid HSE functional with linear increasing value of exact exchange term
as increasing the Br content x, which produces the band gaps of CsPbX3 in good
agreement with the available experimental data. The calculated light absorption
coefficients and reflectivity show the systematic varying tendency to the Br
content. We calculate the phonon dispersions of CsPbX3, CsX and PbX2 as
slightly changing their volumes, revealing the phase instability of CsPbX3 and
calculating the thermodynamic potential function differences. By projecting
Gibbs free energy differences onto the plane of G = 0, we determine the P - T
diagram for CsPbX3 to be stable against the chemical decomposition,
highlighting that the area of being stable extends gradually as the Br content
increases.
