LDAUTYPE = 1 | 2 | 4
Default: LDAUTYPE = 2
Description: LDAUTYPE specifies which type of L(S)DA+U approach will be used.
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. The first VASP LDA+U calculations, including some additional technical details on the VASP implementation, can be found in Ref.  (the original implementation was done by Olivie Bengone  and Georg Kresse).
- This particular flavour of LSDA+U is of the form
- 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 LSDA+U method consists of the assumption that one may now write the total energy as:
- where the Hartree-Fock like interaction replaces the LSDA on site due to the fact that one subtracts a double counting energy , which supposedly equals the on-site LSDA contribution to the total energy,
- LDAUTYPE=2: The simplified (rotationally invariant) approach to the LSDA+U, introduced by Dudarev et al.
- This flavour of LSDA+U is of the following form:
- 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,
- 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 U and J do not enter seperately, only the difference (U-J) is meaningful.
- In the LDA+U case the double counting energy is given by,
Warning: 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 (LDAUU and LDAUJ, respectively). It is therefore not meaningful to compare the total energies resulting from calculations with different U and/or J, or U-J in case of Dudarev's approach (LDAUTYPE=2).
Note on bandstructure calculation: the CHGCAR file contains only information up to angular momentum quantum number L=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 be necessarily not identical to a selfconsistent run. The deviations are often 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).
Related Tags and Sections
- ↑ A Rohrbach, J Hafner and G Kresse J. Phys.: Condens. Matter 15, 979–996 (2003).
- ↑ O. Bengone, M. Alouani, P. Blöchl, and J. Hugel, Phys. Rev. B 62, 16392 (2000).
- ↑ A. I. Liechtenstein, V. I. Anisimov and J. Zaane, Phys. Rev. B 52, R5467 (1995).
- ↑ S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys and A. P. Sutton, Phys. Rev. B 57, 1505 (1998).