  $\text{BaBiO}_{3}$ 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 of the electron-phonon interaction in
$\text{BaBiO}_{3}$, the influence of the electron-electron Hubbard interaction
on the electronic structure in this system is still under quest. In our work,
we obtain an analytical expression for the screened Coulomb potential, and
along with the basis of \textit{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 $\text{BaBiO}_{3}$ in terms of the
Holstein-Hubbard model.
