[Wien] Definition of directions in QTL band character calculations

[Peter Blaha]

Your points (A,B,C) are correct.

The qtl code was contributed by P.Novak, and I would have to dig into 
the code to find all details.

For the hexagonal system I'd expect that the hex-y axis coincides with 
the cartesian y-axis (at least this is standard WIEN2k convention), and 
I guess also in R lattices the same convention with hex is used. 
However, as I said before, this is just a "guess".

To find this out uniquely, select in the qtl-file (generated with the 
desired coordinate system) a state of interest (with eigenvalue e1) 
which has predominantly one character (eg. pz or d-xy or ...) on one of 
the atoms.

Then run    x lapw2 -all emin emax       (such that emin/emax brackets 
your e1 closely) and plot the corresponding charge density with xcrysden 
(lapw5) or 3ddens. This gives you uniquely the form of the orbital and 
you can see if it agrees with your "pz" assignment.

Regards


Am 15.02.2023 um 00:53 schrieb pluto via Wien:
> Dear All,
>
> I am interested in calculating different types of orbital characters.
>
> When calculating a TMDC of 1T type (space group 164) I experience the 
> following:
>
> (A). When using regular commands (x lapw2 -band -qtl -up/dn -so) I am 
> having x swapped with z. Perhaps also other things happen, according 
> to Loc-Rot matrices in case.struct. This is explained in UG, page 277.
>
> (B). When using QTL to calculate characters, with loro=0 I have the 
> same result as in point (A).
>
> (C). When using QTL to calculate characters with loro=1, and setting 
> the "new-z-axis" to "0 0 1", I am having the pz orbital facing out of 
> plane of the layers (i.e. along the hexagonal c-axis). This is of 
> course a good starting point for anyone who compares bands to ARPES data.
>
> I just want to make sure, if I understand the logic of this. I 
> understand that with "lapw2 -qtl" and with "qtl, loro=0" the 
> coordinate system is rotated according to the Loc-Rot matrices from 
> the case.struct. I also understand that these Loc-Rot matrices can be 
> in principle different for each inequivalent atom, so in principle 
> setting "pz" for atom 1 can be physically a different direction than 
> "pz" for atom 2.
>
> Now I am not sure to which axis the program QTL refers when loro=1 (or 
> loro=2). It seems to me that it somehow refers to the hexagonal 
> coordinate system defined in the case.struct. For a layered hexagonal 
> system, conventionally this would mean a-b-c, with c being 
> out-of-plane of the layers, and with 120 deg between a and b. Lets say 
> that a-b-c transforms into h-k-l in the reciprocal space. Then l (and 
> c) are out-of-plane, so in Cartesian system it is parallel to z=(001). 
> But what are x and y of the Cartesian system? For "qtl, loro=2", "new 
> z-axis 0 0 1", "new x axis 1 0 0" is x=(100) direction parallel to a? 
> Or maybe parallel to h? (y would be determined this way).
>
> In other words, with "qtl loro=2', "new z-axis 0 0 1", "new x axis 1 0 
> 0", would the new x-axis be along Gamma-M or along Gamma-K?
>
> How would this work for the rhombohedral system (layered 2D system)? 
> Because for the k-list of the rhombohedral system one needs to use the 
> rhombohedral reciprocal vectors, while in the case.struct file one 
> provides hexagonal lattice parameters (this was discussed many times 
> in the forum), and for real orbitals we need Cartesian system... Would 
> QTL with loro=1 again set the z-axis out of plane of the layers 
> according to the hexagonal abc (or hkl)?
>
> 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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