# The Orbital package in wien2k (LDA+U)

## The Orbital package in wien2k (LDA+U)

From the userguide

ORB (Calculate orbital dependent potentials)

This program was contributed by:

All variants are implemented in the rotationally invariant way (Liechtenstein et al. 1995). If LDA+U is used in an unrestricted, general way, it introduces an orbital field in the calculation (in analogy to the exchange field in spin-polarized calculations, but it interacts with the orbital, instead of spin momentum). The presence of such an orbital field may lower the symmetry. In particular the complex version of LAPW1 must be used. Care is needed when dealing with the LDA+U orbital field. It may be quite large, and without specifying its direction it may fluctuate, leading to oscillations of scf procedure or/and to false solutions. It is therefore necessary to use it in combination with the spin-orbit coupling, preferably running first LSDA+(s-o) and then slowly switching on the LDA+U orbital field. If the LDA+U orbital polarization is not needed, it is sufficient to run real version of LAPW1, which then automatically puts the orbital field equal to zero. For systems without the center of inversion, when LAPW1 must be complex, an extra averaging of the LDA+U potential is necessary.

To continue with the other potentiels clik on the link below

http://www.qft.iqfr.csic.es/docs/WIEN2k/7SCF_cycle.html#SECTION05420000000000000000

ORB (Calculate orbital dependent potentials)

This program was contributed by:

**orb**calculates the orbital dependent potentials, i.e. potentials which are nonzero in the atomic spheres only and depend on the orbital state numbers $l, m$. In the present version the potential is assumed to be independent of the radius vector and needs the density matrix calculated in lapwdm. Four different potentials are implemented in this package:**LDA+U**. There are three variants of this method, two of them are discussed in Novák et al. 2001**LDA+U(SIC)**- introduced by Anisimov et al. 1993, with an approximate correction for the self-interaction correction. This is probably best suited for strongly correlated systems and for a full potential method we recommend to use an ``effective'' $U_{eff} = U - J $; setting $J=0$.**LDA+U(AMF)**- introduced by Czyzyk and Sawatzky 1994 as 'Around the Mean Field' method. (In Novák et al. 2001 it is denoted as LDA+U(DFT)). This version is (probably) more suitable for metallic or less strongly correlated systems.**LDA+U(HMF)**- in addition the Hubbard model in the mean field approximation, as introduced by Anisimov et al. 1991 is also implemented. Note, however, that it is to be used with the LDA (not LSDA) exchange-correlation potential in spin polarized calculations!All variants are implemented in the rotationally invariant way (Liechtenstein et al. 1995). If LDA+U is used in an unrestricted, general way, it introduces an orbital field in the calculation (in analogy to the exchange field in spin-polarized calculations, but it interacts with the orbital, instead of spin momentum). The presence of such an orbital field may lower the symmetry. In particular the complex version of LAPW1 must be used. Care is needed when dealing with the LDA+U orbital field. It may be quite large, and without specifying its direction it may fluctuate, leading to oscillations of scf procedure or/and to false solutions. It is therefore necessary to use it in combination with the spin-orbit coupling, preferably running first LSDA+(s-o) and then slowly switching on the LDA+U orbital field. If the LDA+U orbital polarization is not needed, it is sufficient to run real version of LAPW1, which then automatically puts the orbital field equal to zero. For systems without the center of inversion, when LAPW1 must be complex, an extra averaging of the LDA+U potential is necessary.

To continue with the other potentiels clik on the link below

http://www.qft.iqfr.csic.es/docs/WIEN2k/7SCF_cycle.html#SECTION05420000000000000000

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