Controlling projection-space artifacts in DFT+U via projection-consistent U eff

Density functional theory augmented with a Hubbard correction (DFT+U) is widely used to treat localized electronic states, but its predictions are often sensitive to the choice of the local projection space defining the correlated subspace. This sensitivity poses a practical challenge for computational reproducibility, particularly when projection parameters vary across codes, basis sets, or materials. In this study, we systematically investigate how the effective on-site Coulomb interaction Ueff, determined ab initio using constrained density functional theory, depends on the size of the local projection space in all-electron APW+lo calculations. Using rutile and anatase TiO2 and β-MnO2 as representative test cases, we show that applying a single fixed Ueff across different projection choices introduces artificial projection-driven errors in total energies, including spurious magnetic ordering transitions and unphysical sensitivity of phase stability. These artifacts are eliminated when Ueff is determined in an internally consistent manner for each projection space, yielding projection-consistent DFT+U predictions for lattice parameters, phase energetics, and magnetic ground states. By analyzing total-energy trends alongside the spatial characteristics of the localized d orbitals, we demonstrate that the systematic reduction of Ueff with increasing projection size originates from orbital relaxation and enhanced electronic screening associated with orbital spatial extension. These results provide a physically motivated framework for controlling projection-space artifacts in DFT+U calculations and for obtaining energetically robust predictions across diverse correlated materials and computational setups.