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$\rm BaBiO_3$ is characterized by a charge disproportionation with half ofthe Bi atoms possessing a valence 3+ and half a valence 5+. Because ofselfinteraction errors, local and semi-local density functionals fail todescribe the charge disproportionation quantitatively, yielding a too smallstructural distortion and no band gap. Using hybrid functionals we obtain asatisfactory description of the structural, electronic, optical, andvibrational properties of $\rm BaBiO_3$. The results obtained using GW (Green'sfunction G and screened Coulomb potential W) based schemes on top of hybridfunctionals, including fully selfconsistent GW calculations with vertexcorrections in the dielectric screening, qualitatively confirm the HSE picturebut a systematic overestimation of the bandgap by about 0.4 eV is observed.

Structural, vibrational and quasiparticle properties of the Peierls  semiconductor $\rm BaBiO_3$: a hybrid functional and self-consistent  GW+vertex-corrections study