LDAU= .TRUE. | .FALSE.
LDAUTYPE= 1 | 2 | 4
LDAUL= [0 | 1 | 2 | 3 array] LDAUU= [real array] LDAUJ= [real array]
LDAUPRINT= 0 | 1 | 2
The L(S)DA often fails to describe systems with localized (strongly correlated)
and 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:
The unscreened e-e interaction can be written in terms of Slater's 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, and . ( and 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:
This can be understood as adding a penalty functional to the LSDA total energy expression that forces the on site occupancy matrix in the direction of idempotency, i.e., . (Real matrices are only idempotent when their eigenvalues are either 1 or 0, which for an occupancy matrix translates to either fully occupied or fully unoccupied levels.)
Note: in Dudarev's approach the parameters and do not enter seperately, only the difference is meaningfull.
LDAUL= ... specifies the -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= ... specifies the effective on-site Coulomb interaction parameters.
LDAUJ= ... specifies the effective on-site Exchange interaction parameters.
NB: LDAUL, LDAUU, and LDAUJ must be specified for all
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 and . It is therefore not meaningful to compare the total energies resulting from calculations with different and/or (c.q. in case of Dudarev's approach).
Furthermore, since LDA+U usually results in aspherical charge densities at and atoms we recommend to set LASPH = .TRUE. in the INCAR file for gradient corrected functionals (see Sec. 6.44). For CeO 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).