[Wien] questions about ORB

[Pavel Novak]

Dear Vahid Ghanbarian,

On Mon, 5 Dec 2005, vahid ghanbarian wrote:

> Dear WIEN2k users
>
>
>
> In the ORB section of user's guide, the below statements were written:
>
> If LDA+U is used in an unrestricted, general way, it introduces an orbital
> field in the calculation. 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 LDA+U potential is
> necessary.
>
> I have some questions.
>
> 1. Is this statement true? When we have a system with the centre of
> inversion, all of the component of orbital dependent potential will be real.
Orbital potential is a hermitean matrix, while the diagonal elements are
real, nondiagonal are in general complex.

>
> 2. Dose the real version of LAPW1 put the orbital field equal to zero in a
> system with the centre of inversion that has only real component of orbital
> dependent potential?
Yes, orbital field brings in Hamiltonian term linear in orbital momentum:
B_orb.L, without spin-orbit coupling such term is incompatible with the
space inversion symmetry.

>
> 3. How can we do the extra averaging of the LDA+U potential for system
> without the centre of inversion, when LAPW1 must be complex?
Orbital potential is a matrix in space of sherical harmonics Ylm.
To average orbital potential you put Vmm, V-m-m -> (Vmm + V-m-m)/2.

Regards
Pavel Novak
>
>
>
> Best regards
>
> Vahid Ghanbarian.
>