  The electronic structure and energetic stability of A$_2$BX$_6$ halide
compounds with the cubic and tetragonal variants of the perovskite-derived
K$_2$PtCl$_6$ prototype structure are investigated computationally within the
frameworks of density-functional-theory (DFT) and hybrid (HSE06) functionals.
The HSE06 calculations are undertaken for seven known A$_2$BX$_6$ compounds
with A = K, Rb and Cs, and B = Sn, Pd, Pt, Te, and X = I. Trends in band gaps
and energetic stability are identified, which are explored further employing
DFT calculations over a larger range of chemistries, characterized by A = K,
Rb, Cs, B = Si, Ge, Sn, Pb, Ni, Pd, Pt, Se and Te and X = Cl, Br, I. For the
systems investigated in this work, the band gap increases from iodide to
bromide to chloride. Further, variations in the A site cation influences the
band gap as well as the preferred degree of tetragonal distortion. Smaller A
site cations such as K and Rb favor tetragonal structural distortions,
resulting in a slightly larger band gap. For variations in the B site in the
(Ni, Pd, Pt) group and the (Se, Te) group, the band gap increases with
increasing cation size. However, no observed chemical trend with respect to
cation size for band gap was found for the (Si, Sn, Ge, Pb) group. The findings
in this work provide guidelines for the design of halide A$_2$BX$_6$ compounds
for potential photovoltaic applications.
