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arXiv · 2607.18071

DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors

Edward Linscott·Alberto Carta·Nicola Marzari
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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.

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Edward Linscott, Alberto Carta, Nicola Marzari. 2026-07-20. DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors. https://arxiv.org/abs/2607.18071

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