[Wien] QTL quantization axis for Y_lm orbitals
gutowska at agh.edu.pl
gutowska at agh.edu.pl
Tue Jan 17 20:02:52 CET 2023
Dear Lukasz,
the reason is that the (radial part) of the wave function is actually
the sum of 5 terms.
As mentioned at http://www.wien2k.at/lapw/index.html in sector
"LAPW+LO", the wave function is the sum of the atomic radial wave
function and its energy derivative multiplied by the factors A_lm(k) and
B_lm(k) respectively.
There is also an additional radial wave function called the local
orbital with the coefficient C_lm(k).
Then comes the APW+lo method, where the local orbital is the sum of the
new radial wave function and its energy derivative multiplied by the new
coefficients A'_lm(k) and B'_lm(k), respectively.
This gives 5 coefficients: A_lm(k), B_lm(k), C_lm(k), A'_lm(k), B'_lm(k)
in the case.almblm file. Each of them has a real and an imaginary part.
This is explained in Chapter 2 of the User's Guide.
what's best
Sylwia
W dniu 17.01.2023 19:47, pluto via Wien napisał(a):
> Dear Prof. Blaha, dear All,
>
> I tried x lapw2 -alm (instead of x lapw2 -band -qtl). For me this
> works if I set TEMP in case.in2 (with TETRA and GAUSS I am getting an
> error when running x lapw2 -alm, but it might be some problem with my
> WIEN2k compilation on iMac - I will soon recompile on a new Linux
> machine.)
>
> Anyway, this produces case.almblm file. I paste the beginning of the
> file below (this is some simple test Ag bulk calculation).
>
> Is there some documentation of this case.almblm file? To me it seems
> the first column is l and the second column is m. The third column
> seems to be just the index.
>
> Then there are 10 columns, grouped in pairs (so 5 pairs in total).
> Are those real and imaginary coefficients of the wavefunctions? I
> would expect one complex number per orbital per eigenvalue per
> k-point, why is there 5 of them?
>
> I understand that it goes beyond the routine use of the lapw2, but
> perhaps you have simple answers...
>
> I there a way to limit the case.almblm to inlcude only s,p,d, and f
> orbitals?
>
> Best,
> Lukasz
>
>
>
>
> K-POINT: 1.0000000000 0.5000000000 0.0000000000 112 12 W
> 1 1 8 jatom,nemin,nemax
> 1 ATOM
> 1 1.8018018018018018E-002 NUM, weight
> 0 0 1 2.60221268E-16 0.00000000E+00 -5.40303983E-16
> 0.00000000E+00 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 1 -1 2 2.86916281E-16 -4.69385598E-03 -2.00999914E-15
> 1.39370083E-02 0.00000000E+00 0.00000000E+00 3.39480612E-14
> -6.74796430E-01 0.00000000E+00 0.00000000E+00
> 1 0 3 -0.00000000E+00 -2.00964551E-03 0.00000000E+00
> 5.96704418E-03 0.00000000E+00 0.00000000E+00 -0.00000000E+00
> -2.88909932E-01 0.00000000E+00 0.00000000E+00
> 1 1 4 2.86916281E-16 4.69385598E-03 -2.00999914E-15
> -1.39370083E-02 0.00000000E+00 0.00000000E+00 3.39480612E-14
> 6.74796430E-01 0.00000000E+00 0.00000000E+00
> 2 -2 5 -2.42907691E-16 2.49342676E-03 -1.73032916E-16
> -5.78839244E-03 -0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 2 -1 6 1.82264517E-16 -7.54868519E-04 -4.65058419E-17
> 1.75239766E-03 -0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 2 0 7 -4.15664411E-16 0.00000000E+00 2.83273479E-16
> -0.00000000E+00 -0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 2 1 8 -1.82264517E-16 -7.54868519E-04 4.65058419E-17
> 1.75239766E-03 -0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 2 2 9 -2.42907691E-16 -2.49342676E-03 -1.73032916E-16
> 5.78839244E-03 -0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 -3 10 -5.25533553E-18 -5.74114831E-04 -3.70079029E-16
> 2.64701447E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 -2 11 1.14832148E-16 -7.09955076E-04 5.94043515E-16
> 2.38542576E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 -1 12 1.09946596E-16 -2.52160001E-03 1.69024006E-15
> 7.91632710E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 0 13 0.00000000E+00 4.66796968E-04 0.00000000E+00
> -1.17957558E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 1 14 1.09946596E-16 2.52160001E-03 1.69024006E-15
> -7.91632710E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 2 15 -1.14832148E-16 -7.09955076E-04 -5.94043515E-16
> 2.38542576E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 3 3 16 -5.25533553E-18 5.74114831E-04 -3.70079029E-16
> -2.64701447E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 4 -4 17 4.94473493E-17 8.06437880E-04 -9.23437474E-16
> -2.37542253E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 4 -3 18 4.68841179E-17 -2.84229742E-04 8.36550189E-17
> 1.08576915E-03 0.00000000E+00 0.00000000E+00 0.00000000E+00
> 0.00000000E+00 0.00000000E+00 0.00000000E+00
>
> --
> PD Dr. Lukasz Plucinski
> Group Leader, FZJ PGI-6
> https://electronic-structure.fz-juelich.de/
> Phone: +49 2461 61 6684
> (sent from 9600K)
>
>
> --
> This email has been checked for viruses by Avast antivirus software.
> www.avast.com
>
>
>
>
>
>
> On 17/01/2023 11:13, Peter Blaha wrote:
>> 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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