Description of the procedure to be used to do LDA+U Calculations.
This feature is available only in PAW. The LDA+U framework is described in
the paper [1] and [2].
Two choices of double counting are provided: the Full Localized limit
and the Around Mean Field approximation.
Our implementation is described in [5].
It follows the main lines of the paper [4].
Forces and stress are implemented.
For details on keywords (lpawu,upawu,jpawu,usedmatpu,dmatpuopt,dmatudiag) see keyword usepawu in input variables.
In both the output and log files, we can find:
- The LDA+U contribution of energy which is contained inside the PAW Spherical terms in the output file.
- The Decomposition of the LDA+U energy is given (Interaction energy, Double
counting term, and sum of the two) in the log file.
- The orbital density matrix (n_{m,m'}^{\sigma}), also called occupation
matrix (corresponding to eq 9 of ref [4] and eq 1 of ref [2], see also
[5] and variable dmapuopt) is also
given for each atom in the basis of real spherical harmonics.
It is given at each SCF step in the log file: one can thus check the
convergency of the calculation.
Consistency between total energy and forces in LDA+U have been checked.
The reader can find somes examples in the directory Test_v5 (t08.in, t19.in, t11.in, t53.in..)
[1] V. I. Anisimov, J. Zaanen, and O. K. Andersen PRB 44, 943 (1991)

[2] A.I. Lichtenstein, V.I. Anisimov and J. Zaanen PRB 52, 5467 (1995)

[3] M. T. Czyzyk and G. A. Sawatzky PRB 49, 14211 (1994)

[4] O. Bengone, M. Alouani, P. Blöchl, and J. Hugel PRB 62, 16392 (2000)

[5] B. Amadon, F. Jollet and M. Torrent Phys. Rev. B 77, 155104 (2008).