Structural, vibrational and quasiparticle properties of the Peierls semiconductor $\mathrm{B}\mathrm{a}\mathrm{B}\mathrm{i}{\mathrm{O}}_3$: a hybrid functional and self-consistent GW+vertex-corrections study

$\mathrm{B}\mathrm{a}\mathrm{B}\mathrm{i}{\mathrm{O}}_3$ is characterized by a charge disproportionation with half of the Bi atoms possessing a valence 3+ and half a valence 5+. Because of selfinteraction errors, local and semi-local density functionals fail to describe the charge disproportionation quantitatively, yielding a too small structural distortion and no band gap. Using hybrid functionals we obtain a satisfactory description of the structural, electronic, optical, and vibrational properties of $\mathrm{B}\mathrm{a}\mathrm{B}\mathrm{i}{\mathrm{O}}_3$. The results obtained using GW (Green’s function G and screened Coulomb potential W) based schemes on top of hybrid functionals, including fully selfconsistent GW calculations with vertex corrections in the dielectric screening, qualitatively confirm the HSE picture but a systematic overestimation of the bandgap by about 0.4 eV is observed.