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On site Coulomb interaction: L(S)DA+U

(Supported as of VASP.4.6.)


LDAUTYPE= 1 | 2 | 4

LDAUL= [0 | 1 | 2 | 3 array] $ \qquad$ LDAUU= [real array] $ \qquad$ LDAUJ= [real array]

LDAUPRINT= 0 | 1 | 2


The L(S)DA often fails to describe systems with localized (strongly correlated) $ d$ and $ f$ electrons (this manifests itself primarily in the form of unrealistic one-electron energies). In some cases this can be remedied by introducing a strong intra-atomic interaction in a (screened) Hartree-Fock like manner, as an on site replacement of the L(S)DA. This approach is commonly known as the L(S)DA+U method.
Setting LDAU=.TRUE. in the INCAR file switches on the L(S)DA+U.

By means of the LDAUTYPE-tag on specifies which type of L(S)DA+U approach will be used:

LDAUL= $ L_1$ $ L_2$ ... specifies the $ l$-quantum number (one number for each species) for which the on-site interaction is added.
(-1=no on-site terms added, 1= p, 2= d, 3= f, Default: LDAUL=2)

LDAUU= $ U_1$ $ U_2$ ... specifies the effective on-site Coulomb interaction parameters.

LDAUJ= $ J_1$ $ J_2$ ... specifies the effective on-site Exchange interaction parameters.

NB: LDAUL, LDAUU, and LDAUJ must be specified for all atomic species!

LDAUPRINT= 0 | 1 | 2 Controls the verbosity of the L(S)DA+U module.
(0: silent, 1: Write occupancy matrix to OUTCAR, 2: idem 1., plus potential matrix dumped to stdout, Default: LDAUPRINT=0)

It is important to be aware of the fact that when using the L(S)DA+U, in general the total energy will depend on the parameters $ U$ and $ J$. It is therefore not meaningful to compare the total energies resulting from calculations with different $ U$ and/or $ J$ (c.q. $ U-J$ in case of Dudarev's approach).

Furthermore, since LDA+U usually results in aspherical charge densities at $ d$ and $ f$ atoms we recommend to set LASPH = .TRUE. in the INCAR file for gradient corrected functionals (see Sec. 6.44). For Ce$ _2$O$ _3$ for instance, identical results to the FLAPW methods can be only obtained setting LASPH = .TRUE.

Note on bandstructure calculation: The CHGCAR file also contains only information up to LMAXMIX (defaulted to 2) 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 be necessarily not identical to a selfconsistent run. The deviations can be (or actually are) large for L(S)DA+U calculations. For the calculation of band structures within the L(S)DA+U approach, it is hence strictly required to increase LMAXMIX to 4 (d elements) and 6 (f elements). (see Sec. 6.63).

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