Category:DFT+U: Difference between revisions

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) $d$ or $f$ 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 $d$ or $f$ atom a strong intra-atomic interaction in a simplified (screened) Hartree-Fock like manner ( $E_{\text{HF}}({\hat {n}})$ ), as an on-site replacement of the semilocal functional (double-counting term $E_{\text{dc}}({\hat {n}})$ ):

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 ${\hat {n}}$ is the on-site occupancy matrix of the $d$ or $f$ 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 switched on with the tag LDAU in the INCAR file, while the tag LDAUTYPE determines the DFT+U flavor that is used.

Pages in category "DFT+U"

The following 7 pages are in this category, out of 7 total.

D

DFT+U: formalism

L

[anisimov:prb:91-1] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. Rev. B 44, 943 (1991).

[rohrbach:jcp:03-2] A. Rohrbach, J. Hafner, and G. Kresse J. Phys.: Condens. Matter 15, 979 (2003).

[Bengone:prb:00-3] O. Bengone, M. Alouani, P. Blöchl, and J. Hugel, Phys. Rev. B 62, 16392 (2000).

[1]

[2]

[3]

@@ Line 1: / Line 1: @@
 == Theoretical background ==
-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) + 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|}} ).