LDAUTYPE: Difference between revisions

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: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,
: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,


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Revision as of 20:26, 1 March 2011

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

Description: LDAUTYPE specifies which type of L(S)DA+U approach will be used.


  • LDAUTYPE=1: The rotationally invariant LSDA+U introduced by Liechtenstein et al.[1]
and is determined by the PAW on site occupancies
and the (unscreened) on site electron-electron interaction
where |m⟩ are real spherical harmonics of angular momentum L=LDAUL.
The unscreened e-e interaction Uγ1γ3γ2γ4 can be written in terms of the Slater integrals , , , and (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 ).
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 (LDAUU and LDAUJ, respectively). U and J are sometimes extracted from constrained-LSDA calculations.
These translate into values for the Slater integrals in the following way (as implemented in VASP at the moment):
- -
-
The essence of the L(S)DA+U method consists of the assumption that one may now write the total energy as:
where the Hartree-Fock like interaction replaces the L(S)DA on site due to the fact that one subtracts a double counting energy , which supposedly equals the on site L(S)DA contribution to the total energy,
  • LDAUTYPE=2: The simplified (rotationally invariant) approach to the LSDA+U, introduced by Dudarev et al.[2]
  • LDAUTYPE=4: same as LDAUTYPE=1, but LDA+U instead of LSDA+U (i.e. no LSDA exchange splitting).

Related Tags and Sections

LDAU, LDAUL, LDAUU, LDAUJ, LDAUPRINT

References


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