[Wien] QTL quantization axis for Y_lm orbitals
gutowska at agh.edu.pl
gutowska at agh.edu.pl
Thu Feb 16 14:44:16 CET 2023
Dear Łukasz,
every second column is a small component of relativistic wave function.
You should multiply it by alpha=1/137 in case of relativistic
calculations, otherwise you should neglect it. For reference, you can
look into eg. l2main.F, where eg. overlaps are calculated as:
UA(I)=RRAD1(I,L)*RRAD1(I,L)+ &
CIN*RRAD2(I,L)*RRAD2(I,L)
where RRAD1 is the first column, RRAD2 is the second column and CIN is
specified as:
CIN=1.d0/137.0359895d0**2
IF (.NOT.REL) CIN=4.0*1.0D-22
Best,
Sylwia
W dniu 16.02.2023 14:33, pluto via Wien napisał(a):
> Dear Prof. Blaha,
>
> I looked the case.radwf file. For my test case of bulk-fcc-Al it
> consists to following header:
>
> 1 781 0.0001000000 0.0129828604 2.5000000000
>
> Here "1" seems to indicate the atom number from the case.struct (there
> is only one inequivalent for fcc Al) and "781" indicates the number of
> mesh points between the center of the atom and the radius of the
> sphere (starting at the radius and ending at the center). Radius in
> this case is 2.5 Bohr, as also indicated.
>
> After this there are sections, each with 781 rows. These sections are
> marked by 0, 1, 2, 3...8 which for me seems to be s, p, d, f, ...
>
> Now each of these sections contains up to 10 columns. Can you explain
> the meaning of these columns?
>
> To me it looks as if 2 columns are assigned to each of u, u-dot, u_lo,
> ... But I would expect a single column of real numbers, in the spirit
> of R_nl for the hydrogen.
>
> I plotted some of these columns for check, and the first columns of
> the first section looks like 3s, but the second column looks a bit
> strange.
>
> Best,
> Lukasz
>
>
>
>
>
>
>
>
>
> On 2023-02-13 10:21, Peter Blaha wrote:
>> 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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