Category:DFT+U

Theoretical background

The semilocal LDA and GGA functionals often fail to describe systems with localized (strongly correlated) [math]\displaystyle{ d }[/math] and [math]\displaystyle{ f }[/math]-electrons (this manifests itself primarily in the form of unrealistic one-electron energies and too small magnetic moments). In some cases this can be remedied by introducing on the [math]\displaystyle{ d }[/math] or [math]\displaystyle{ f }[/math] atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner ([math]\displaystyle{ E_{\text{HF}}(\hat{n}) }[/math]), as an on-site replacement of the semilocal functional (double-counting term [math]\displaystyle{ E_{\text{dc}}(\hat{n}) }[/math]):

[math]\displaystyle{ E_{\text{xc}}^{\text{LDA/GGA}+U}(n,\hat{n}) = E_{\text{xc}}^{\text{LDA/GGA}}(n,\hat{n}) + E_{\text{HF}}(\hat{n}) - E_{\text{dc}}(\hat{n}) }[/math]

where [math]\displaystyle{ \hat{n} }[/math]is the on-site occupancy matrix of the [math]\displaystyle{ d }[/math] or [math]\displaystyle{ f }[/math] electrons. This approach is commonly known as the DFT+U method^[1] (traditionally called LSDA+U).

How to

DFT+U can be used by specifying the tags LDAU and LDAUTYPE in the INCAR file.