Category:DFT+U: Difference between revisions
No edit summary |
No edit summary |
||
| Line 2: | Line 2: | ||
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>): | 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 | :<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 commonly known as the DFT+U method{{cite|anisimov:prb:91|}} (traditionally called LSDA+U). | where <math>\hat{n}</math>is the on-site occupancy matrix of the <math>d</math> or <math>f</math> electrons. This approach is commonly known as the DFT+U method{{cite|anisimov:prb:91|}} (traditionally called LSDA+U). | ||
Revision as of 19:22, 6 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 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.