Fig. 4. Computed band structures of 80-atom supercells of (A) 1, (B) 1:Sn (1.25 atom% Sn) with Sn²⁺ substitution at the Ag⁺ site and a vacancy at another Ag⁺ site, and (C) 1:Sn (1.25 atom% Sn) with Sn⁴⁺ substitution at the Bi³⁺ site and a vacancy at a Ag⁺ site. Projections of the Sn orbital character of the bands are shown in color. (D) The magnitude of the transition dipole matrix elements of direct transitions between the highest lying valence and lowest lying conduction band in the vicinity of Γ for 1, 1:Sn (alloying Cases 1 & 4, which are predicted to give direct gaps; see Section 5), and for CsPbBr₃, a direct-bandgap perovskite. Equivalent k points are denoted; (1/2, 1/2, 1/2) corresponds to L and R in the double perovskites and in CsPbBr₃, respectively. The range of k-points plotted is from (0, 0, 0) to (0.1, 0.1, 0.1), corresponding to the direction from Γ towards L or R, and from (0, 0, 0) to (0.1, 0.0, 0.1), corresponding to the direction from Γ towards X.