Strength of the Hubbard potential and its modification by breathing distortion in BaBiO3

BaBiO3 compound is known as an archetype example of a three-dimensional Holstein model with the realization of the charge-density wave state at half filling and the superconducting state when doped. Although many works are devoted to the study the electron-phonon interaction in BaBiO3, the influence of the electron-electron Hubbard interaction on the electronic structure in this system is still under investigation. In our work, we obtain analytical expression for the screened Coulomb potential, and along with the basis of ab initio-computed maximally localized Wannier orbitals, we quantitatively estimate the magnitude of the effective on-site Hubbard potential scrutinizing the effects of distortion of the crystal lattice. We show that a proper inclusion of the electron-electron interactions into the Holstein model significantly lowers the value of the underlying electron-phonon coupling. Finally, we find that the amplitudes of the repulsive electron-electron potential and its attractive counterpart mediated by the electron-phonon coupling are rather comparable. This may open a way for a realization of the intermediate phase of BaBiO3 in terms of the Holstein-Hubbard model.