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

[Gavin Abo]

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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