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  • Letter
  • Open Access

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

Edward Linscott* and Alberto Carta

Nicola Marzari

  • *Contact author: edward.linscott@psi.ch
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Phys. Rev. Research 8, L042015 – Published 30 October, 2026

DOI: https://doi.org/10.1103/qghb-78nd

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. Intersite +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—intersite 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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Phys. Rev. Research 8, L042015– Published 30 October, 2026
  • Received 21 July 2026
  • Accepted 11 September 2026
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