On the importance of consistency between Hubbard parameters and projection manifolds in Hubbard-corrected density-functional theory

Density-functional theory with extended Hubbard functionals is a powerful method for studying complex materials containing transition-metal and rare-earth elements, owing to its accuracy in correcting self-interactions and its low computational costs. There are two key elements in these formulations which are closely interconnected: i) the choice of the on-site U and inter-site V Hubbard parameters, and ii) the choice of the Hubbard manifold. Often, these are chosen empirically, disregarding both the goal of DFT functionals (reproducing total energies, not band gaps) and the nature of the Hubbard manifold used in the actual calculations. Having developed automated and reliable approaches for the non-empirical determination of the U and V parameters from density-functional perturbation theory [1], we highlight here the role played by the Hubbard manifold, comparing atomic orbitals (in different oxidation states and orthogonalized or not) and maximally localised Wannier functions. [1] I. Timrov et al., PRB 98, 085127 (2018).