LDAUTYPE: Difference between revisions

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{{TAGDEF|LDAUTYPE|1 {{!}} 2 {{!}} 4|2}}
{{TAGDEF|LDAUTYPE|1 {{!}} 2 {{!}} 4|2}}


Description: {{TAG|LDAUTYPE}} specifies which type of L(S)DA+U approach will be used.
Description: {{TAG|LDAUTYPE}} specifies the DFT+U variant that will be used.
----
----
*{{TAG|LDAUTYPE}}=1: The rotationally invariant LSDA+U introduced by Liechtenstein ''et al.''<ref name="liechtenstein:prb:95"/>
The following variants of the [[DFT+U: formalism|DFT+U approach]] are available:
::<math>
E_{\rm HF}=\frac{1}{2} \sum_{\{\gamma\}}
(U_{\gamma_1\gamma_3\gamma_2\gamma_4} -
U_{\gamma_1\gamma_3\gamma_4\gamma_2}){ \hat
n}_{\gamma_1\gamma_2}{\hat n}_{\gamma_3\gamma_4}
</math>
:and is determined by the PAW on site occupancies
::<math>
{\hat n}_{\gamma_1\gamma_2} = \langle \Psi^{s_2} \mid m_2 \rangle
\langle m_1 \mid \Psi^{s_1} \rangle
</math>
:and the (unscreened) on site electron-electron interaction
::<math>
U_{\gamma_1\gamma_3\gamma_2\gamma_4}= \langle m_1 m_3 \mid
\frac{1}{|\mathbf{r}-\mathbf{r}^\prime|} \mid m_2 m_4 \rangle
\delta_{s_1 s_2} \delta_{s_3 s_4}
</math>
:where |''m''&rang; are real spherical harmonics of angular momentum ''L''={{TAG|LDAUL}}.


:The unscreened e-e interaction ''U''<sub>&gamma;<sub>1</sub></sub><sub>&gamma;<sub>3</sub></sub><sub>&gamma;<sub>2</sub></sub><sub>&gamma;<sub>4</sub></sub> can be written in terms of the Slater integrals <math>F^0</math>, <math>F^2</math>, <math>F^4</math>, and <math>F^6</math> (f-electrons). Using values for the Slater integrals calculated from atomic orbitals, however, would lead to a large overestimation of the true e-e interaction, since in solids the Coulomb interaction is screened (especially <math>F^0</math>).
*{{TAG|LDAUTYPE}}=1: The rotationally invariant DFT+U introduced by Liechtenstein ''et al.''{{cite|liechtenstein:prb:95}}


:In practice these integrals are therefore often treated as parameters, ''i.e.'', adjusted to reach agreement with experiment in some sense: equilibrium volume, magnetic moment, band gap, structure. They are normally specified in terms of the effective on site Coulomb- and exchange parameters, ''U'' and ''J'' ({{TAG|LDAUU}} and {{TAG|LDAUJ}}, respectively). ''U'' and ''J'' are sometimes extracted from constrained-LSDA calculations.
*{{TAG|LDAUTYPE}}=2: The simplified (rotationally invariant) approach to DFT+U, introduced by Dudarev ''et al.''{{cite|dudarev:prb:98}}


:These translate into values for the Slater integrals in the following way (as implemented in VASP at the moment):
*{{TAG|LDAUTYPE}}=3: Linear response ansatz of Cococcioni et al. {{cite|cococcioni:2005}} to compute U. See [[Calculate U for LSDA+U|how to calculate U]].
{{NB|mind|For {{TAG|LDAUTYPE}}{{=}}3, the {{TAG|LDAUU}} and {{TAG|LDAUJ}} tags specify the strength of the spherical potential acting on the spin-up and spin-down manifolds, respectively.|:}}


::{| cellpadding="5" cellspacing="0" border="1"
*{{TAG|LDAUTYPE}}=4: Same as {{TAG|LDAUTYPE}}=1, but without exchange splitting.
| <math>L\;</math> || <math>F^0\;</math> || <math>F^2\;</math> || <math>F^4\;</math> || <math>F^6\;</math>
|-
| <math>1\;</math> || <math>U\;</math> || <math>5J\;</math> || - || -
|-
| <math>2\;</math> || <math>U\;</math> || <math>\frac{14}{1+0.625}J</math> || <math>0.625 F^2\;</math> || -
|-
| <math>3\;</math> || <math>U\;</math> || <math>\frac{6435}{286+195 \cdot 0.668+250 \cdot 0.494}J</math> || <math>0.668 F^2\;</math> || <math>0.494 F^2\;</math>
|}


:The essence of the L(S)DA+U method consists of the assumption that one may now write the total energy as:
A method to estimate the parameters for DFT+U is the [[Constrained-random-phase approximation|constrained-random-phase approximation]]. Another method is the linear response ansatz with {{TAG|LDAUTYPE}}=3, mentioned above. On the other hand, in many applications, the DFT+U parameters are used as tuning parameters to fit experimental data.
{{NB|tip|For band-structure calculations, increase {{TAG|LMAXMIX}} to 4 (<math>d</math> elements) or 6 (<math>f</math> elements).}}
This is because the {{FILE|CHGCAR}} file contains only information up to angular momentum quantum number set by {{TAG|LMAXMIX}} for the [[LDAUTYPE#occmat|on-site PAW occupancy matrices]]. When the {{FILE|CHGCAR}} file is read and kept fixed in the course of the calculations ({{TAG|ICHARG}}=11), the results will necessarily not be identical to a self-consistent run. The deviations are often large for DFT+U calculations.
{{NB|warning|The total energy will depend on the parameters <math>U</math> ({{TAG|LDAUU}}) and <math>J</math> ({{TAG|LDAUJ}}). It is, therefore, not meaningful to compare the total energies resulting from calculations with different <math>U</math> and/or <math>J</math>; or <math>U-J</math> in the case of Dudarev's approach ({{TAG|LDAUTYPE}}{{=}}2).}}


::<math>
It is possible to use {{TAG|LDAUTYPE}}=1, 2, and 3 for a non–spin-polarized calculation with {{TAG|ISPIN}}=1.
E_{\mathrm{tot}}(n,\hat n)=E_{\mathrm{DFT}}(n)+E_{\mathrm{HF}}(\hat n)-E_{\mathrm{dc}}(\hat n)
</math>


:where the Hartree-Fock like interaction replaces the L(S)DA on site due to the fact that one subtracts a double counting energy (<math>E_{\mathrm{dc}}</math>) which supposedly equals the on site L(S)DA contribution to the total energy,
== Related tags and articles ==
 
::<math>
E_{\mathrm{dc}}(\hat n) = \frac{U}{2} {\hat n}_{\mathrm{tot}}({\hat n}_{\mathrm{tot}}-1) -
\frac{J}{2} \sum_\sigma {\hat n}^\sigma_{\mathrm{tot}}({\hat n}^\sigma_{\mathrm{tot}}-1).
</math>
 
*{{TAG|LDAUTYPE}}=2: The simplified (rotationally invariant) approach to the LSDA+U, introduced by Dudarev ''et al.''<ref name="dudarev:prb:98"/>
 
*{{TAG|LDAUTYPE}}=4: same as {{TAG|LDAUTYPE}}=1, but LDA+U instead of LSDA+U (i.e. no LSDA exchange splitting).
 
== Related Tags and Sections ==
{{TAG|LDAU}},
{{TAG|LDAU}},
{{TAG|LDAUL}},
{{TAG|LDAUL}},
{{TAG|LDAUU}},
{{TAG|LDAUU}},
{{TAG|LDAUJ}},
{{TAG|LDAUJ}},
{{TAG|LDAUPRINT}}
{{TAG|LDAUPRINT}},
{{TAG|LMAXMIX}},
{{TAG|DFT+U: formalism}}
 
{{sc|LDAUTYPE|Examples|Examples that use this tag}}


== References ==
== References ==
<references>
<references/>
<ref name="liechtenstein:prb:95">[http://link.aps.org/doi/10.1103/PhysRevB.52.R5467 A. I. Liechtenstein, V. I. Anisimov and J. Zaane, Phys. Rev. B 52, R5467 (1995).]</ref>
<ref name="dudarev:prb:98">[http://link.aps.org/doi/10.1103/PhysRevB.57.1505 S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Phys. Rev. B 57, 1505 (1998).]</ref>
</references>
----
----
[[The_VASP_Manual|Contents]]


[[Category:INCAR]][[Category:LDA+U]]
[[Category:INCAR tag]][[Category:Exchange-correlation functionals]][[Category:DFT+U]]

Latest revision as of 08:53, 9 May 2023

LDAUTYPE = 1 | 2 | 4
Default: LDAUTYPE = 2 

Description: LDAUTYPE specifies the DFT+U variant that will be used.

The following variants of the DFT+U approach are available:

  • LDAUTYPE=1: The rotationally invariant DFT+U introduced by Liechtenstein et al.[1]
  • LDAUTYPE=2: The simplified (rotationally invariant) approach to DFT+U, introduced by Dudarev et al.[2]
Mind: For LDAUTYPE=3, the LDAUU and LDAUJ tags specify the strength of the spherical potential acting on the spin-up and spin-down manifolds, respectively.

A method to estimate the parameters for DFT+U is the constrained-random-phase approximation. Another method is the linear response ansatz with LDAUTYPE=3, mentioned above. On the other hand, in many applications, the DFT+U parameters are used as tuning parameters to fit experimental data.

Tip: For band-structure calculations, increase LMAXMIX to 4 ( elements) or 6 ( elements).

This is because the CHGCAR file contains only information up to angular momentum quantum number set by LMAXMIX for the on-site PAW occupancy matrices. When the CHGCAR file is read and kept fixed in the course of the calculations (ICHARG=11), the results will necessarily not be identical to a self-consistent run. The deviations are often large for DFT+U calculations.

Warning: The total energy will depend on the parameters (LDAUU) and (LDAUJ). It is, therefore, not meaningful to compare the total energies resulting from calculations with different and/or ; or in the case of Dudarev's approach (LDAUTYPE=2).

It is possible to use LDAUTYPE=1, 2, and 3 for a non–spin-polarized calculation with ISPIN=1.

Related tags and articles

LDAU, LDAUL, LDAUU, LDAUJ, LDAUPRINT, LMAXMIX, DFT+U: formalism

Examples that use this tag

References

  1. ↑ A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B 52, R5467 (1995).
  2. ↑ S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Phys. Rev. B 57, 1505 (1998).
  3. ↑ M. Cococcioni and S. de Gironcoli, Phys. Rev. B 71, 035105 (2005).
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