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

[Wasim Raja Mondal]

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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