Search for negative U in the Ba1-xKxBi1-yPbyO3 system using constrained density-functional theory

Calculations using constrained density-functional theory have been carried out for the Ba1-xKxBi1-yPbyO3 system, using a full-potential linearized-augmented-plane-wave method and employing fee supercell geometries with two formula units. The results have been mapped onto Hubbard-type models in order to extract values of interaction parameters U at the Bi sites. Two different mapping procedures have been utilized. The first one is the standard method, based on the comparison of total-energy curvatures. The second method, proposed in the present work, relies on the analysis of single particle energies and yields much smaller numerical errors. For BaBiO3 interaction parameters are obtained for the following models: (i) s and p orbitals at Bi and p orbitals at O sites. Here, U-s = 3.1 +/- 0.4 eV, U-sp = 1.4 +/- 0.2 eV, U-p = 2.2 +/- 0.4 eV are found, (ii) s(Bi) and p(O) orbitals, yielding U-s = 1.9 +/- 0.7 eV, and (iii) an effective one-band model, leading to U-s = 0.6 +/- 0.4 eV. Further studies have been performed for breathing distorted BaBiO3 and for various Ba1-xKxBi1-yPbyO3 alloys using virtual crystal approximations. The resulting U values are somewhat larger than for pure BaBiO3. Thus, in all cases, the values of Bi U parameters are found to be positive. There is no indication of a negative U of electronic origin.