First-principles treatment of disorder effects in complex alloys: A study of ${\mathrm{Ba}}_{\mathit{x}}$${\mathrm{K}}_{1\mathrm{-}\mathit{x}}$${\mathrm{BiO}}_3$ and ${\mathrm{BaPb}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Bi}}_{\mathit{x}}$${\mathrm{O}}_3$

We have developed a self-consistent Korringa-Kohn-Rostoker coherent-potential-approximation (KKR-CPA) approach to treat multiatom-per-unit-cell systems in order to study disorder effects in complex materials on a first-principles basis. Electronic structure of the high-${\mathit{T}}_{\mathit{c}}$ superconducting perovskites ${\mathrm{Ba}}_{\mathit{x}}$ ${\mathrm{K}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{BiO}}_3$ and ${\mathrm{BaPb}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Bi}}_{\mathit{x}}$ ${\mathrm{O}}_3$ is discussed. KKR-CPA results for x=0.1,0.2,...,0.9, as well as for the limiting single-impurity cases x=0.0 and x=1.0 are used to delineate rigid-band and non-rigid-band effects in the spectrum. McMillan-Hopfield parameters over the entire composition range are presented.