[Wien] Wannier

Sat Feb 17 10:43:10 CET 2024

Hi,

Yes, for sure you can forget the "Blm" and most important are the "Alm".

There are 2 problems:

You may have some "Clm" (local orbitals), which could be dominating ! 
While this is probably less important for real "semicore states" as you 
may not use them for PES, it might be important for something like C or 
O s states or Ti-4s,4p valence states. The problems can be avoided when 
modifying case.in1 and removing the local orbitals for the atoms with 
low valence states like O-2s, ....; and for the atoms with semicore 
states, put the 4s as APW and the 3s as LO (2nd line in case.in1).

The more critical problem is that the ALMs give you only the amplitude 
and phase INSIDE the atomic sphere.

Checkout case.outputst, and you will see how much l-like charge of a 
particular atom is within the atomic sphere.

For instance for Ti (RMT=2.25)

   3D*     -0.355365     -0.246227  2.00  0.00    0.8136  F
   4S      -0.342909     -0.306636  1.00  1.00    0.1495  F

++++++

  it means that 81 % of the 3d charge is inside the sphere, but only 15% 
of 4s charge.

This has the consequence that a pure 3d state might have a 
"alm=sqrt(0.8)", but a PURE 4s state has only alm=sqrt(0.15).

This is the reason, why we introduced the "renormalized partial DOS", 
where the interstital DOS is removed and the 3d PDOS will be slightly, 
the 4s PDOS strongly enhanced. You should probably use a similar concept 
and use the renormalization factors given in the output of a rendos 
calculation.

Regards

Peter Blaha

Am 16.02.2024 um 23:28 schrieb pluto:
> Dear Oleg, Mikhail, dear Prof. Blaha,
>
> Thank you for the quick answers!
>
> It seems that the Alm (related to the "u") coefficient might be what I 
> need, because it refers to the "atomic-like" potential. Perhaps the 
> Blm coefficient, related to the "u-dot", is "small" in most cases, 
> also maybe it somehow represents the non-atomic (i.e. non-LCAO) 
> correction to the electronic state inside the MT sphere? I apologize 
> if calling "u" of LAPW as being "atomic" is wrong, but maybe it is not 
> totally wrong in the spirit of my problem. I am fine with approximate 
> numbers here, everything in the order of 80%-90% (say referring to the 
> final ARPES intensity) would be fine, I think. (The Alm of different 
> atoms would just control the amplitude and phase interference of the 
> spherical waves photoemitted from these atoms.)
>
> Does that way of thinking make some sense?
>
> Perhaps it is also the case, that a very large LCAO basis can explain 
> any band structure, but I think this is not the point, here the goal 
> is to simplify the problem.
>
> In this physical problem, I cannot live without the complex 
> coefficients. This is easily understood in graphene, where the "dark 
> corridor" of ARPES results from the k-dependent phases of the 
> wave-functions on sites A and B.
>
> Best,
> Lukasz
>
>
> On 2024-02-15 08:40, Peter Blaha wrote:
>> Hi,
>> I do not know too much about Wannerization and LCAO models.
>>
>> However, I'd like to mention the  PES  program, which is included in 
>> WIEN2k.
>>
>> It uses the atomic cross sections (as you mentioned), but not the
>> wavefunctions, but the "renormalized" partial DOS. (This will omitt
>> the interstital and renormalize in particular the delocalized
>> orbitals).
>>
>> It does NOT include  phases (interference), but our experience is
>> quite good - although limited. Check out the PES section in the UG and
>> the corresponding paper by Bagheri&Blaha.
>>
>> Regards
>>
>> Am 15.02.2024 um 01:41 schrieb pluto via Wien:
>>> Dear All,
>>>
>>> I am interested to project WIEN2k band structure onto atomic 
>>> orbitals, but getting complex amplitudes. For example, for graphene 
>>> Dirac band (formed primarily by C 2pz) I would get two k-dependent 
>>> complex numbers A_C2pz(k) and B_C2pz(k), where A and B are the two 
>>> inequivalent sites, and these coefficients for other orbitals (near 
>>> the Dirac points) would be nearly zero. Of course, for graphene I 
>>> can write a TB model and get these numbers, but already for WSe2 
>>> monolayer TB model has several bands (TB models for WSe2 are 
>>> published but implementing would be time-consuming), and for a 
>>> generic material there is often no simple TB model.
>>>
>>> Some time ago I looked at the WIEN2k wave functions, but because of 
>>> the way LAPW works, it is not a trivial task to project these onto 
>>> atomic orbitals. This is due to the radial wave functions, each one 
>>> receiving its own coefficient.
>>>
>>> I was wondering if I can somehow get such projection automatically 
>>> using Wien2Wannier, and later with some Wannier program. I thought 
>>> it is good to ask before I invest any time into this.
>>>
>>> And I would need it with spin, because I am interested with systems 
>>> where SOC plays a role.
>>>
>>> The reason I ask:
>>> Simple model of photoemission can be made by assuming coherent 
>>> addition of atomic-like photoionization, with additional k-dependent 
>>> initial band amplitudes/phases. One can assume that radial integrals 
>>> in photoemission matrix elements don't have special structure and 
>>> maybe just take atomic cross sections of Yeh-Lindau. But one still 
>>> needs these complex coefficients to allow for interference of the 
>>> emission from different sites within the unit cell. I think for a 
>>> relatively simple material such as WSe2 monolayer, the qualitative 
>>> result of this might be reasonable. I am not aiming at anything 
>>> quantitative since we have one-step-model codes for quantitative.
>>>
>>> Any suggestion on how to do this projection (even approximately) 
>>> within the realm of WIEN2k would be welcome.
>>>
>>> Best,
>>> Lukasz
>>>
>>>
>>> PD Dr. Lukasz Plucinski
>>> Group Leader, FZJ PGI-6
>>> Phone: +49 2461 61 6684
>>> https://electronic-structure.fz-juelich.de/
>>>
>>> _______________________________________________
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-- 
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Peter Blaha,  Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-158801165300
Email: peter.blaha at tuwien.ac.at
WWW:   http://www.imc.tuwien.ac.at      WIEN2k: http://www.wien2k.at
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