Hubbard U through polaronic defect states

Since the preliminary work of Anisimov and co-workers, the Hubbard corrected DFT+U functional has been used for predicting properties of correlated materials by applying on-site effective Coulomb interactions to specific orbitals. However, the determination of the Hubbard U parameter has remained under intense discussion despite the multitude of approaches proposed. Here, we define a selection criterion based on the use of polaronic defect states for the enforcement of the piecewise linearity of the total energy upon electron occupation. The values of U determined in this way are found to be robust upon variation of the considered state. The corresponding electronic and structural properties are in good agreement with results from piecewise linear hybrid functionals. In particular, defect formation energies are well reproduced, thereby validating the energetics achieved with our selection criterion. It is emphasized that the selection of U should be based on physical properties directly associated with the orbitals to which U is applied, rather than on more global properties such as band gaps. For comparison, we also determine U through a well-established linear response scheme finding noticeably different values of U and consequently different formation energies. Possible origins of these discrepancies are discussed. As case studies, we consider the self-trapped electron in BiVO₄, the self-trapped hole in MgO, the Li-trapped hole in MgO, and the Al-trapped hole in α-SiO₂.