[Wien] questions about ORB

[Pavel Novak]

Dear Vahid Ghanbarian,

my yesterday answer was incomplete, as it concerned only the diagonal
terms. More complete reasoning goes as follows:
If the system does not have center of inversion in real space, it should
still be invariant with respect to the time inversion T. For the orbital
potential it must be fulfilled:
T Vorb= Vorb
Now  Vorb may be written as
 Vorb = SUM_m SUM_m' Cmm' |l,m><l,m'|
where |l,m>=Ylm
It holds (see any textbook)
 T Ylm= (-1)^(l-m)Yl-m
 then after simple algebra (note that Cmm' must be complex conjugated)
 T Vorb = SUM_m SUM_m' (C-m-m')* (-1)^(m+m') |l,m><l,m'|
so that we arrive to condition
 Cm,m' = (-1)^(m+m') (C-m,-m')*
Averaging is thus performed by substituting
 Cm,m' --> [Cm,m' + (-1)^(m+m') (C-m,-m')*]/2

Averaging is not automatically performed and you have to write your own
small program.

If you do not average, time inversion symmetry may be broken during the
scf procedure and the system then exhibit nonzero orbital momentum.
Even if this does not happen the calculation may be difficult to converge.

Regards
Pavel Novak

On Wed, 7 Dec 2005, vahid ghanbarian wrote:
 There are three questions.
>
> 1.        For the extra averaging of the LDA+U potential for system
> without the centre of inversion, when LAPW1 must be complex, dose the
> WIEN2k put Vmm, V-m-m ->(Vmm+V-m-m)/2 automatically or we must do this
> work by hand? If by hand, how?
>
> *2.        *Is the orbital field equal to zero when Vmm=V-m-m? If no,
> why do we put Vmm, V-m-m ->(Vmm+V-m-m)/2?**
>
> *3.        *When is the orbital field important?**
>
> * *
>
> Thanks
>
> Vahid Ghanbarian
>