Mitigating the Projection-Size Dependence in the DFT+U Method

The DFT+U method improves the description of correlated electron systems, but its accuracy depends sensitively on the size of the local projection sphere used to apply the Hubbard correction. This dependence can lead to inconsistent results across calculations. In this work, we systematically investigate how the effective Hubbard parameter varies with projection size using constrained DFT calculations for rutile and anatase TiO₂ and β-MnO₂. We find that decreases by up to 44% as the projection radius increases, primarily due to the relaxation of the local orbitals. When the renormalized is applied consistently for each projection size, the calculated lattice parameters, electronic structure, and relative stability become quantitatively consistent across all cases. Our results demonstrate a practical strategy to mitigate the projection-size dependence of DFT+U and enhance its transferability in first-principles studies of correlated oxides.