Category:DFT+U: Difference between revisions
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== Theoretical background == | == Theoretical background == | ||
The semilocal LDA and GGA functionals often fail to describe systems with localized (strongly correlated) <math>d</math> or <math>f</math> | The semilocal LDA and GGA functionals often fail to describe systems with localized (strongly correlated) <math>d</math> or <math>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>d</math> or <math>f</math> atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (<math>E_{\text{HF}}(\hat{n})</math>), as an on-site replacement of the semilocal functional (double-counting term <math>E_{\text{dc}}(\hat{n})</math>): | ||
:<math>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})</math> | :<math>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})</math> | ||
where <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is known as the DFT+U method (traditionally called LSDA+U{{cite|anisimov:prb:91|}} ). | where <math>\hat{n}</math> is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is known as the DFT+U method (traditionally called LSDA+U{{cite|anisimov:prb:91|}} ). |
Revision as of 08:13, 8 April 2022
Theoretical background
The semilocal LDA and GGA functionals often fail to describe systems with localized (strongly correlated) or 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 or atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner (), as an on-site replacement of the semilocal functional (double-counting term ):
where is the on-site occupancy matrix of the or 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 switched on with the tag LDAU in the INCAR file, while the tag LDAUTYPE determines the DFT+U flavor that is used.