[Wien] QTL quantization axis for Y_lm orbitals

Tue Jan 17 11:13:54 CET 2023

a) Yes it is possible to use a "different" local rotation matrix (AFTER 
the SCF cycle, and just for the analysis). This way you get the A_lm,... 
in this frame.

b) Be aware, that this works only inside spheres, so matrix elements 
calculated only from contributions inside spheres will be incomplete 
(the LAPW-basis is NOT a LCAO-basis set !!!), though when interested in 
localized 3d (4f) electrons it could be a good approximation.

c) Be aware that what you get from qtl are "symmetrized" partial 
charges, i.e. the qtl's are averaged over the equivalent k-points in the 
full BZ. Note that the A_lm(k=100) are in general different from 
A_lm(k=010), even in a tetragonal symmetry, where we usually have only 
k=100 in the mesh, but not k=010.

So you probably have to calculate a full k-mesh and sum externally over 
the equivalent k-points.

> Thank you for the quick answer.
>
> I am thinking more of a circular dichroism in photoemission, intuitive 
> approximate orbital-resolved description in some simple cases. For 
> this one needs the quantization axis (the z-axis) along the incoming 
> light (this is possible in QTL, as we discussed in previous emails) 
> and the phases of the coefficients (which, it seems, are not 
> printed-out by QTL).
>
> I will look into -alm option, thank you for letting me know this 
> option. As I understand, lapw2 projects orbitals only according to the 
> coordinate system defined by case.struct file. So I would need to 
> rotate the coordinate frame to get the new z-axis along the 
> experimental light direction (I think might be tedious but quite 
> elementary, I think this is what QTL does).
>
> Best,
> Lukasz
>
>
>
> On 2023-01-16 18:38, Peter Blaha wrote:
>> Hi,
>> In lapw2 there is an input option ALM (use   x lapw2 -alm), which
>> would write the A_lm, B_lm, as well as the radial wf. into a file.
>>
>> optical matrix elements: They are calculated anyway in optics.
>>
>> Regards
>>
>> Am 16.01.2023 um 17:13 schrieb pluto via Wien:
>>> Dear Prof Blaha, dear All,
>>>
>>> I think QTL provides squared wave function coefficients, which are 
>>> real numbers. Can we get the complex coefficients, before squaring? 
>>> The phase might matter in some properties, such as optical matrix 
>>> elements.
>>>
>>> I explain in more detail. We can assume some Psi = A|s> + B|p>. 
>>> Using QTL we will get |A|^2 and |B|^2, and we can plot these to e.g. 
>>> get the "fat bands", i.e. the orbital character of the bands. But in 
>>> general A and B are complex numbers, can we output them before they 
>>> are squared?
>>>
>>> Best,
>>> Lukasz
>>>
>>>
>>>
>>>
>>>
>>>
>>> On 22/12/2022 18:12, Peter Blaha wrote:
>>>> Subject:
>>>> Re: [Wien] QTL quantization axis for Y_lm orbitals
>>>> From:
>>>> Peter Blaha <peter.blaha at tuwien.ac.at>
>>>> Date:
>>>> 22/12/2022, 18:12
>>>> To:
>>>> wien at zeus.theochem.tuwien.ac.at
>>>>
>>>> Hi,
>>>> In your example with (1. 0. 0.) it means that what is plotted in 
>>>> the partial charges (or partial DOS) as pz, points into the 
>>>> crystallographic x-axis (I guess it interchanges px and pz). I'm 
>>>> not sure if such a rotation would ever be necessary.
>>>>
>>>> In your input file you have (1. 1. 1.), which means that pz will 
>>>> point into the 111 direction of the crystal.  This could be a real 
>>>> and meaningful choice.
>>>>
>>>> Such lroc make sense to exploit "approximate" symmetries of eg. of 
>>>> a distorted (and tilted) octahedron, where you want the z-axis to 
>>>> be in the shortest Me-O direction.....
>>>>
>>>> > PS: where can I find the "QTL - technical report by P. Novak"? I 
>>>> don't
>>>> > see it on WIEN2k website.
>>>>
>>>> This pdf file is in SRC_qtl.
>>>>
>>>> Regards
>>>> Peter Blaha
>>>>
>>>> Am 22.12.2022 um 17:52 schrieb pluto via Wien:
>>>>> Dear All,
>>>>>
>>>>> I would like to calculate orbital projections for the Y_lm basis 
>>>>> (spherical harmonics) along some generic quantization axis using 
>>>>> QTL program.
>>>>>
>>>>> Below I paste an exanple case.inq input file from the manual (page 
>>>>> 206). When "loro" is set to 1 one can set a "new axis z".
>>>>>
>>>>> Is that axis the new quantization axis for the Y_lm orbitals? I 
>>>>> just want to make sure.
>>>>>
>>>>> This would mean that if I set the "new axis" to 1. 0. 0., I will 
>>>>> have the basis of |pz+ipy>, |px>, and |pz-ipy>. It that correct?
>>>>>
>>>>> Best,
>>>>> Lukasz
>>>>>
>>>>> PS: where can I find the "QTL - technical report by P. Novak"? I 
>>>>> don't see it on WIEN2k website.
>>>>>
>>>>>
>>>>>
>>>>> ------------------ top of file: case.inq --------------------
>>>>> -7. 2. Emin Emax
>>>>> 2 number of selected atoms
>>>>> 1 2 0 0 iatom1 qsplit1 symmetrize loro
>>>>> 2 1 2 nL1 p d
>>>>> 3 3 1 1 iatom2 qsplit2 symmetrize loro
>>>>> 4 0 1 2 3 nL2 s p d f
>>>>> 1. 1. 1. new axis z
>>>>> ------------------- bottom of file ------------------------
>>>>> _______________________________________________
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>>>>>
>>>>
>>>> -- 
>>>> -------------------------------------------------------------------------- 
>>>>
>>>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
>>>> Phone: +43-1-58801-165300
>>>> Email: peter.blaha at tuwien.ac.at    WIEN2k: http://www.wien2k.at
>>>> WWW:   http://www.imc.tuwien.ac.at
>>>> ------------------------------------------------------------------------- 
>>>>
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>>>
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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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