Correlation effects in charge-density wave insulator BaBiO$_3$

The negative-U nature of $\rm BaBiO_3$ leads to a charge-ordered insulating state in which pentavalent $\rm Bi^{5+}$ coexists with trivalent $\rm Bi^{3+}$. Despite the apparent absence of strong-correlation effects in $\rm BaBiO_3$ standard density functional (DFT) theory yields a much too small band gap of 0.14 eV. By means of an hybrid-DFT approach combined with self-consistent GW including vertex corrections we investigate the electronic, vibrational and dielectric properties of $\rm BaBiO_3$. We show that the inclusion of strong-correlation effects increases the band gap up to 1.2 eV, shifts the oxygen breathing modes upwards by $\approx$ 2 THz and reduces the dielectric constant by a factor of 3. The overall agreement with available experimental data is significantly improved.