[Wien] QTL quantization axis for Y_lm orbitals

[Peter Blaha]

It was mentioned several times on the mailing list that

x lapw2 -alm

prints the radial functions into a file (just once) as well as all 
Alm,Blm,... for each k-point and band-index.

For further details search the mailing list.

For the interstitial matrix elements you can get them by the integral 
between two plane wave expansions (times the dipole operator ?) 
multiplied with the "step-function". Such detaisl are well explained in 
D. Singh's book...


Am 12.02.2023 um 20:10 schrieb pluto via Wien:
> Dear Prof. Blaha,
>
> Thank you for your comments.
>
> Are the functions u and u-dot provided in some output file? Manual 
> mentions different types of u and u-dot for the cases of Psi^LO and 
> Psi^lo. Manual also mentions that u and u-dot are obtained by 
> numerical integration of radial Schrodinger equation on the mesh. Are 
> they all tabulated somewhere?
>
> Having all the A_lm, B_lm, C_lm and all the u and u-dot would allow to 
> have the full wave function Psi(r) inside the spheres as a function of 
> wave-vector and energy. That would allow to numerically calculate the 
> matrix elements which I need, with the assumption of my favorite final 
> state, and without any further assumptions. The only remaining problem 
> would be the interstitial region, but it would also be under control 
> by knowing how much charge leaks out of the spheres.
>
> Best,
> Lukasz
>
>
>
>
> On 2023-02-09 18:06, Peter Blaha wrote:
>> Well, I'm not sure I do understand all your problems, but a few 
>> comments:
>>
>> a) XMCD is implemented in   optics !
>>
>> b) I do not see the problem with A_lm, B_lm C_lm,..., because in any
>> case  A_lm (or for semicore a C_lm) will dominate and you can probably
>> neglect the B_lm and the corresponding u-dot radial function.
>>
>> When you chose a good expansion energy for your radial wf., you more
>> or less have this "hydrogenic orbital" with one fixed radial function.
>> Of course, this argument holds only when your states are "localized",
>> otherwise you will have a large interstital (PW) contribution.
>>
>> c) I'm not the real expert of Wannier functions, but I guess the WF
>> might be complicated linear combinations of different l,m ....
>>
>>
>>
>> Am 09.02.2023 um 15:46 schrieb pluto via Wien:
>>> Dear Sylwia, dear Prof. Blaha, dear All,
>>>
>>> Having these A_lm, B_lm etc is of course a problem if one wants to 
>>> estimate interferences in dipole optical matrix element due to 
>>> phases at which different Y_lm orbitals enter the wave function. It 
>>> would be good to have a single complex number per Y_lm.
>>>
>>> For this it would be good to have the LAPW wavefunction projected 
>>> onto hydrogenic orbitals that just have a single radial component. 
>>> Then there would be just one complex coefficient. For a particular l 
>>> (i.e. s, p, or d) one would have a common radial part of the wave 
>>> function, since the radial part does not depend on m. Then one would 
>>> need to assume the final state expansion in Y_lm (can always be done 
>>> even for free-electron final state) and do some estimation of the 
>>> XMCD process within the simplified LCAO way of thinking.
>>>
>>> Is there any tool already existing to project WIEN2k wave function 
>>> onto hydrogenic orbitals?
>>> I was thinking something like this might be a part of the 
>>> WIEN2Wannier, but I wanted to ask here before investing further time 
>>> into this.
>>>
>>> Best,
>>> Lukasz
>>>
>>>
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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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