[Wien] Using option Qsplit=6 in qtl to rotate to get t2g and eg

[Wasim Raja Mondal]

Gavin,
         Thank you for your reply. Now, I understand the group table. I am
getting a1g, eg\pi and \eg \sigma as reported in literature for example in
Fig5 of the paper I provided in the link. But, in my DOS a1g, eg\pi and
eg\sigma are still mixed up.

For that, I tried in case.inq file different new z and x axis. But I am not
getting the DOS as reported in the Fig 5 of the paper (link I provided.)

I know I should not ask this type of question here. But I am struggling bit
for many days with this structure. My question is : starting with cif file
, running LAPW, calculating DOS using qtl with option 4, what new z and x
axis should I define in case.inq file to reproduce the LDA dos for this
structure. It is just simple LDA calculation.


Please let me know if you find with just one look.


Thanks
Wasim

On Sun, Apr 5, 2020 at 1:13 AM Gavin Abo <gsabo at crimson.ua.edu> wrote:

> Ok, I think I understand now, in FIG. 1 of [1] the eg\sigma appears to be
> the high energy band while eg\pi the low energy band in the energy diagram.
>
> In FIG. 5 of the reference [2] that you provided, I see eg\sigma peaks at
> high energy (i.e., at about 2 to 4 eV) while the eg\pi is at low energy
> (i.e., about -1 to 1 eV) in the DOS plot.
>
> Thus, I think you will need to plot both (d-xy,dx2-y2) and (d-xz,dyz),
> then you can probably identify which is eg\pi and which is eg\sigma by
> looking at the DOS plot.
>
> Based on Figure 4.2 in [3], (d-xy,dx2-y2) might be eg\sigma while
> (d-xz,dyz) the eg\pi.
> [1] https://arxiv.org/abs/1502.04555v1
> [2] https://arxiv.org/abs/cond-mat/0402133v1 ,
> https://journals.aps.org/prb/abstract/10.1103/PhysRevB.70.205116
> [3] http://ikee.lib.auth.gr/record/129214/files/GRI-2012-8671.pdf
>
> On 4/4/2020 9:29 PM, Wasim Raja Mondal wrote:
>
> Dear Gavin,
>                    I am trying to reproduce simple LDA DOS as reported in
> Fig 5 of this paper.
> https://journals.aps.org/prb/abstract/10.1103/PhysRevB.70.205116
>
>
> I am really struggling. If you can do, please let me know.
>
>
> Thanking you in advance
> Wasim
>
> On Sat, Apr 4, 2020 at 10:58 PM Gavin Abo <gsabo at crimson.ua.edu> wrote:
>
>> According to [1], corundum has point group D3d in Schoenflies notation.
>>
>> Character Tables at [2,3] have for D3d:
>>
>> A1g with x2 + y2, z2 in quadratic notation
>>
>> Eg with (x2 − y2, xy), (xz, yz) in quadratic notation
>>
>> Prof. Blaha at [4] mentioned that with ISPLIT=4, the header of case.qtl
>> is expected to give:
>> s,p,pz,pxy,d,d-z2,(d-xy,dx2-y2),(d-xz,dyz),f
>>
>> Therefore, it looks like A1g is given as d-z2 and Eg is give as
>> (d-xy,dx2-y2) and (d-xz,dyz).
>>
>> At [3], if you click the "Click here to get more detailed information on
>> they symmetry operations" link on the webpage, it gives another webpage
>> with another table having a "Matrix form" column that seems to correspond
>> to the transformation matrices (Identity, Inverse, Rotations, etc. [5])
>> used create the character table [8,9].
>>
>> It is not clear to me what you mean by pi and sigma. Is pi for example
>> when two d-xz orbitals overlap such as that in the image of [6,7]?
>> [1] https://en.wikipedia.org/wiki/Hexagonal_crystal_family
>> [2]
>> https://en.wikipedia.org/wiki/List_of_character_tables_for_chemically_important_3D_point_groups#Antiprismatic_groups_(Dnd)
>> [3]
>> https://www.cryst.ehu.es/cgi-bin/rep/programs/sam/point.py?sg=162&num=20
>> [4]
>> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg19805.html
>> [5]
>> http://w0.rz-berlin.mpg.de/imprs-cs/download/symmetry2011_1_K_Horn.pdf
>> (slide 6)
>> [6] https://www.chemtube3d.com/salc-d-d-orbitaloverlap/
>> [7]
>> https://commons.wikimedia.org/wiki/File:Quintuple_bond_orbital_diagram2.png
>>
>> Informational video with PowerPoint slides on what a Character Table is:
>> [8]
>> https://cosmolearning.org/video-lectures/character-tables-one-application-symmetry/
>> [9] https://www.chem.uci.edu/~lawm/10-2.pdf
>>
>>
>> On 4/4/2020 3:13 PM, Wasim Raja Mondal wrote:
>>
>> Dear expert,
>>                      Can you anyone suggest what rotation matrix for V2O3
>> corundum structure with qsplit=4 should I take to decoupling the d orbital,
>> a1g,eg\pi, eg\sigma?
>>
>> Thanks
>> Wasim
>>
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