Intricacies of DFT+U, Not Only in a Numeric Atom Centered Orbital Framework.

We implemented the popular Hubbard density-functional theory + U (DFT+U) method in its spherically averaged form in the all-electron, full-potential DFT code FHI-aims. There, electronic states are expressed on a basis of highly localized numeric atomic orbitals (NAO), which straightforwardly lend themselves as projector functions for the DFT+U correction, yielding the necessary occupations of the correlated Hubbard subspace at no additional cost. We establish the efficacy of our implementation on the prototypical bulk NiO and obtain the well-known band gap opening effect of DFT+U. As a more stringent, real world test system, we then study polaron formation at the rutile TiO2(110) surface, where our results are in line with both experimental data as well as hybrid functional calculations. At this TiO2 test system, yet in the bulk, we analyze some of the intricacies of using the DFT+U correction in a localized, numeric atomic orbital basis set. Specifically, we find that multiple localized radial basis functions of the same angular momentum can lead to highly erroneous predictions of ground-state properties. We also demonstrate a number of remedies to this problem. Finally, we highlight the critical influence of the exact choice of projector functions on DFT+U results using a number of projector functions of different spatial extent and composed of linear combinations of NAO basis functions. All of our efforts serve to highlight that, contrary to its deceptive ease of use, the DFT+U is far from the "black-box" approach it is sometimes made out to be.