Category:DFT+U: Difference between revisions

The LDA and semilocal 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 or 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 LDA/GGA functional:

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

where ${\displaystyle E_{\text{dc}}(\hat{n})}$ is the double-counting term and ${\displaystyle \hat{n}}$ 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).

For more details, read the article about the formalism of the DFT+U method.

How to

DFT+U can be switched on with the LDAU tag, while the LDAUTYPE tag determines the DFT+U flavor that is used. LDAUL specifies the ${\displaystyle l}$-quantum number for which the on-site interaction is added, and the effective on-site Coulomb and exchange interactions are set (in eV) with the LDAUU and LDAUJ tags, respectively. Note that it is recommended to increase LMAXMIX to 4 for d-electrons or 6 for f-elements.

References