What is Hubbard U correction (DFT+U)?

The Hubbard U correction (DFT+U or GGA+U) adds an on-site Coulomb interaction term to specific atomic orbitals (usually transition metal d or rare earth f orbitals) to correct for the self-interaction error in standard DFT.

Why It Is Needed

Standard GGA/PBE functionals tend to over-delocalize d and f electrons, leading to:

• Incorrect ground states for transition metal oxides
• Wrong magnetic ordering
• Metallic predictions for known insulators (e.g., FeO, NiO)

How It Works

A Hubbard U parameter (typically 2-6 eV) is added to penalize fractional occupation of the targeted orbitals. This favors integer occupation and localizes the electrons, improving the description of:

• Transition metal oxides (Fe, Co, Ni, Mn, V, Cr compounds)
• Rare earth compounds
• Materials with strong electron correlation

Materials Project U Values

Materials Project uses empirically fitted U values for specific elements:

• V: 3.25 eV, Cr: 3.7 eV, Mn: 3.9 eV, Fe: 5.3 eV
• Co: 3.32 eV, Ni: 6.2 eV, Cu: 4.0 eV, Mo: 4.38 eV, W: 6.2 eV

These values were calibrated to reproduce experimental formation enthalpies of binary oxides.

Implications for Users

When comparing materials containing transition metals across databases, be aware that different U values or no U correction will give different results. Filter by data source for consistent comparisons.