  Halide perovskites, with prototype cubic phase ABX3, undergo various phase
transitions accompanied by rigid rotations of corner-sharing BX6 octahedra.
Using first-principles density functional theory calculations, we have
performed a comprehensive investigation of all the possible octahedral tilting
in eighteen halide perovskites ABX3 (A = Cs, Rb, K; B= Pb, Sn; X= I, Br, Cl)
and found that the stabilization energies i.e. energy differences between cubic
and the most stable tilted phases, are linearly correlated with tolerance
factor t. Moreover, the tilt energies i.e. energy differences between cubic and
various tilted phases, are linearly correlated with the change of atomic
packing fractions ({\Delta}{\eta}), confirming the importance of atomic packing
fraction as part of stability descriptor (t+{\mu}){\eta}, proposed in our
previous work [JACS 139, 14905 (2017)]. We further demonstrate that
(t+{\mu}){\eta}remains the best stability descriptor for tilted perovskites
among descriptor candidates of {\eta}, {\mu}, t, and t+{\mu},extending
previously proposed stability trend from cubic phases to tilted phases in
general perovskites.
