Category:DFT+U: Difference between revisions

Latest revision as of 20:56, 29 January 2024

The LDA and semilocal 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 or 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 LDA/GGA functional:

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

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 $l$ -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

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).

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[2]

[3]

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-== Theoretical background ==
+The LDA and semilocal 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 or 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 LDA/GGA functional:
+:<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>E_{\text{dc}}(\hat{n})</math> is the double-counting term and <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}}).
-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 first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. {{cite|rohrbach:jcp:03}} (the original implementation was done by Olivier Bengone {{cite|Bengone:prb:00}} and Georg Kresse).
-:<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|}} ).
-The first VASP DFT+U calculations, including some additional technical details on the VASP implementation, can be found in Ref. {{cite|rohrbach:jcp:03}} (the original implementation was done by Olivier Bengone <ref name="Bengone:prb:00"/> and Georg Kresse).
+For more details, read the article about the [[DFT+U: formalism|formalism of the DFT+U method]].
 ==How to==
-DFT+U can be used by specifying the tags {{TAG|LDAU}} and {{TAG|LDAUTYPE}} in the {{FILE|INCAR}} file.
+DFT+U can be switched on with the {{TAG|LDAU}} tag, while the {{TAG|LDAUTYPE}} tag determines the DFT+U flavor that is used. {{TAG|LDAUL}} specifies the <math>l</math>-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 {{TAG|LDAUU}} and  {{TAG|LDAUJ}} tags, respectively. Note that it is recommended to increase {{TAG|LMAXMIX}} to 4 for ''d''-electrons or 6 for ''f''-elements.
+== References ==
+<references/>
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 [[Category:VASP|LDA+U]][[Category:Exchange-correlation functionals]]