Controlling Projection-Space Artifacts in DFT+U via Projection-Consistent U_{eff}

TL;DR

This paper investigates how the choice of local projection space affects DFT+U predictions and proposes a projection-consistent method to eliminate artifacts, improving the robustness of computational results for correlated materials.

Contribution

It introduces a systematic approach to determine a projection-space consistent U_{eff} in DFT+U, reducing artifacts and enhancing prediction reliability across different projection choices.

Findings

Artificial errors arise when using a fixed U_{eff} across different projection spaces.

Applying a projection-consistent U_{eff} eliminates artifacts and yields stable predictions.

The reduction of U_{eff} with larger projection spaces is linked to orbital relaxation and screening.

Abstract

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 work, we systematically investigate how the effective on-site Coulomb interaction $U_{\mathrm{eff}}$, determined \textit{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 TiO$_2$ and $\beta$-MnO$_2$ as representative test cases, we show that applying a single fixed $U_{\mathrm{eff}}$ 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 $U_{\mathrm{eff}}$ 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 $U_{\mathrm{eff}}$ 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.