On the equivalence between DFT+U+V and DFT+U with hybridized Hubbard projectors

by Dr Edward Linscott (PSI)

Wednesday 1 Jul 2026, 15:00 → 16:00 Europe/Zurich

OVGA/200

Hubbard-corrected density-functional theory (DFT+U) is a widely-used extension of DFT for predicting the properties of materials and molecules from first principles in the presence of localized d or f electrons. DFT+U adds corrective energy terms to DFT that are constructed from the occupation of Hubbard sites, defined by a set of localized orbitals. Increasingly, inter-site corrections +V are also used, as these additional corrections can address the tendency of on-site corrections to over-localize charge and disrupt orbital hybridization. However, a formal justification for these +V corrections is lacking, and it is unclear what underlying physics leads to DFT+U+V outperforming DFT+U. Here we show that — to first order in V ≪ U — inter-site corrections are exactly equivalent to on-site DFT+U evaluated on a density-dependent redefinition of the Hubbard projectors, hybridized with those of neighboring sites. In the regime used in practice, where projectors are frozen, the equivalence partially breaks down. These observations provide insight into the DFT+U+V formalism but also raise questions about (a) how V is computed and (b) the fundamental meaning of the Hubbard subspaces.