DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors
Abstract
Hubbard-corrected density-functional theory (DFT+U) is a popular tool for first-principles modeling of materials with localized d or f electrons, but its on-site corrections tend to over-localize charge and break covalent bonds. Inter-site +V corrections were introduced to counter this and are now widely used, but a formal justification has been lacking. 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-matrix-dependent redefinition of the Hubbard projectors, hybridized with those of neighboring sites, providing insight into the explicit mechanism by which V affects covalency. If the projectors are held frozen, as is common practice, the equivalence partially breaks down. Beyond reinterpreting the formalism, these results sharpen the questions of how V should be computed and what the Hubbard subspaces fundamentally are.
Versions
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BibTeX
@misc{linscott2026dftuv,
title = {{DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors}},
author = {Edward Linscott and Alberto Carta and Nicola Marzari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.18071},
eprint = {2607.18071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18071},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors
AU - Edward Linscott
AU - Alberto Carta
AU - Nicola Marzari
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2607.18071
UR - https://arxiv.org/abs/2607.18071
AB - Hubbard-corrected density-functional theory (DFT+U) is a popular tool for first-principles modeling of materials with localized d or f electrons, but its on-site corrections tend to over-localize charge and break covalent bonds. Inter-site +V corrections were introduced to counter this and are now widely used, but a formal justification has been lacking. 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-matrix-dependent redefinition of the Hubbard projectors, hybridized with those of neighboring sites, providing insight into the explicit mechanism by which V affects covalency. If the projectors are held frozen, as is common practice, the equivalence partially breaks down. Beyond reinterpreting the formalism, these results sharpen the questions of how V should be computed and what the Hubbard subspaces fundamentally are.
ER -