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. A good agreement with results from piecewise linear hybrid functionals is found for the electronic and structural properties of polarons, including the formation energies. The values of U determined in this way are found to give a robust description of the polaron energetics upon variation of the considered state. In particular, we also address a polaron hopping pathway, finding that the determined value of U leads to accurate energetics without requiring a configurational-dependent U. 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 and band widths. 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.

自 Anisimov 及其同事的初步工作以来，哈伯德校正 DFT+ U 泛函已被用于通过将现场有效库仑相互作用应用于特定轨道来预测相关材料的特性。然而，尽管提出了多种方法，但哈伯德U参数的确定仍在激烈讨论中。在这里，我们定义了一个基于使用极化子缺陷态的选择标准，用于在电子占据时强制执行总能量的分段线性。发现极化子的电子和结构特性（包括形成能）与分段线性混合泛函的结果非常吻合。U的值发现以这种方式确定的对所考虑状态变化时的极化子能量学给出了有力的描述。特别是，我们还解决了极化子跳跃路径，发现确定的U值导致准确的能量学，而不需要依赖于构型的U。需要强调的是，U的选择应基于与U所应用的轨道直接相关的物理特性，而不是基于更全局的特性，例如带隙和带宽。为了进行比较，我们还通过完善的线性响应方案确定U ，发现明显不同的U值从而产生不同的形成能量。讨论了这些差异的可能来源。作为案例研究，我们考虑了 BiVO ₄中的自陷电子、MgO 中的自陷空穴、MgO 中的锂陷空和α -SiO ₂中的铝陷空。