Category:DFT+U

Theoretical background

The semilocal LDA and GGA functionals often fail to describe systems with localized (strongly correlated) ${\displaystyle d}$ or ${\displaystyle f}$-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 ${\displaystyle d}$ or ${\displaystyle f}$ atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (${\displaystyle E_{\text{HF}}({\hat {n}})}$), as an on-site replacement of the semilocal functional (double-counting term ${\displaystyle E_{\text{dc}}({\hat {n}})}$):

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

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

The first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. ^[2] (the original implementation was done by Olivier Bengone ^[3] and Georg Kresse).

How to

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