Extended Data Fig. 2. Metal s and oxygen 2p characters of Ba_0.35K_0.65SbO₃ and Ba_0.35K_0.65BiO₃.

The fat-band representations of the band structure of Ba_0.35K_0.65BiO₃ calculated via the hybrid-DFT showing a, Bi 6s, b, O 2p_π, and c, O 2p_σ orbital characters. The black dashed circle in a denotes a band at Γ at which Bi 6s (a_1g symmetry) do not hybridize with any O 2p states in the cubic structure. The energy of this band can be used to estimate the on-site energy of Bi 6s^31,34,35, if one neglects weak Bi 6s–O 2s hybridization. The two black dashed circles in b denote triply degenerate bands at R at which the O 2p_π states have the t_2g and t_1g symmetries, respectively, and do not hybridize with Bi 6s or 6p states. The on-site energy of O 2p_π can be reasonably approximated by averaging the energies of these two bands, which cancels out the effect of O 2p–O 2p hybridization. The fat-band representations of the electronic band structure of Ba_0.35K_0.65SbO₃ calculated via the hybrid-DFT showing d, Sb 5s, e, O 2p_π, and f, O 2p_σ orbital characters. The black dashed circles in d and e denote the bands with Sb 5s (a_1g) and O 2p_π t_2g and t_1g characters as in the case of Ba_0.35K_0.65BiO₃.