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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 semilocal functional (double-counting term <math>E_{\text{dc}}(\hat{n})</math>):
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>
:<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>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 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).
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).


More detail about the formalism of the DFT+U method can be found [[DFT+U: formalism|here]].
For more details, read the article about the [[DFT+U: formalism|formalism of the DFT+U method]].


==How to==
==How to==
DFT+U can be switched on with the {{TAG|LDAU}} tag and 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.
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 ==

Latest revision as of 20:56, 29 January 2024

The LDA and semilocal 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 or 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 LDA/GGA functional:

where is the double-counting term and 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).

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 -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.