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

[Gavin Abo]

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 
> <mailto: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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