  Ternary perovskites have long featured prominently in solid-state chemistry
and in condensed matter physics, but the joint understanding of their two main
subgroups -- halides and oxides -- has not been fully developed. Indeed, unlike
the case in simpler compounds having a single, robust, repeated bonding motif,
certain cubic perovskite can manifest a non-thermal distribution of local
motifs, such as positional degrees of freedom. Unlike thermal motion, such
static distortions do not time-average to zero. The present study compares
electronic structure features of oxide and halide perovskites starting from the
static motif distribution described by DFT minimization of the T=0 internal
energy, continuing to finite temperature thermal disorder modeled via finite
temperature DFT MD simulations. We find that (i) Different oxide vs halide
compounds adopt different energy lowering symmetry breaking modes. The
calculated pair distribution function of SrTiO$_3$ agrees with recently
measured PDF; (ii) In both oxides and halides, such static distortions lead to
band gap blueshifts with respect to undistorted cubic Pm-3m structure (iii) For
ABO$_3$ perovskites, thermal-induced distortions revealed by AIMD simulation
can lead to a band gap redshift. (iv) In contrast, for cubic halide perovskite
CsPbI$_3$, both the intrinsic distortions and the thermal distortions
contribute in tandem to band gap blueshift, the former, intrinsic effect being
dominant. (v) In the oxide SrTiO$_3$ and CaTiO$_3$, (but not in halide)
perovskites octahedral tilting leads to the emergence of a distinct
$\Gamma$-$\Gamma$ direct band gap component as a secondary valley minimum to
the well-known indirect R-$\Gamma$ gap. The understanding of such static vs
thermal effects on oxide vs halide perovskites holds the potential for
designing target electronic properties.
