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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>
:<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 known as the DFT+U method (traditionally called LSDA+U{{cite|anisimov:prb:91|}} ).


==How to==
==How to==

Revision as of 19:23, 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 known as the DFT+U method (traditionally called LSDA+U[1] ).

How to

DFT+U can be used by specifying the tags LDAU and LDAUTYPE in the INCAR file.



Pages in category "DFT+U"

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