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<p>According to [1], corundum has point group D3d in Schoenflies
notation.</p>
<p>Character Tables at [2,3] have for D3d:<br>
</p>
<p>A1g with x2 + y2, <font color="#0000ff">z2</font> in quadratic
notation<br>
</p>
<p>Eg with <font color="#ff8000">(x2 − y2, xy)</font>, <font
color="#ff00ff">(xz, yz)</font> in quadratic notation<br>
</p>
<p>Prof. Blaha at [4] mentioned that with ISPLIT=4, the header of
case.qtl is expected to give:<br>
s,p,pz,pxy,d,<font color="#0000ff">d-z2</font>,<font
color="#ff8000">(d-xy,dx2-y2)</font>,<font color="#ff00ff">(d-xz,dyz)</font>,f<br>
</p>
<p>Therefore, it looks like A1g is given as <font color="#0000ff">d-z2</font>
and Eg is give as <font color="#ff8000">(d-xy,dx2-y2)</font> and
<font color="#ff00ff">(d-xz,dyz)</font>.<br>
</p>
<p>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].</p>
<p>It is not clear to me what you mean by <font color="#008000">pi</font>
and <font color="#804000">sigma</font>. Is pi for example when
two d-xz orbitals overlap such as that in the image of [6,7]?<br>
</p>
[1] <a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Hexagonal_crystal_family">https://en.wikipedia.org/wiki/Hexagonal_crystal_family</a><br>
[2]
<a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/List_of_character_tables_for_chemically_important_3D_point_groups#Antiprismatic_groups_(Dnd)">https://en.wikipedia.org/wiki/List_of_character_tables_for_chemically_important_3D_point_groups#Antiprismatic_groups_(Dnd)</a><br>
[3]
<a class="moz-txt-link-freetext" href="https://www.cryst.ehu.es/cgi-bin/rep/programs/sam/point.py?sg=162&num=20">https://www.cryst.ehu.es/cgi-bin/rep/programs/sam/point.py?sg=162&num=20</a><br>
[4]
<a class="moz-txt-link-freetext" href="https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg19805.html">https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg19805.html</a><br>
[5]
<a class="moz-txt-link-freetext" href="http://w0.rz-berlin.mpg.de/imprs-cs/download/symmetry2011_1_K_Horn.pdf">http://w0.rz-berlin.mpg.de/imprs-cs/download/symmetry2011_1_K_Horn.pdf</a>
(slide 6)<br>
[6] <a class="moz-txt-link-freetext" href="https://www.chemtube3d.com/salc-d-d-orbitaloverlap/">https://www.chemtube3d.com/salc-d-d-orbitaloverlap/</a><br>
[7]
<a class="moz-txt-link-freetext" href="https://commons.wikimedia.org/wiki/File:Quintuple_bond_orbital_diagram2.png">https://commons.wikimedia.org/wiki/File:Quintuple_bond_orbital_diagram2.png</a><br>
<p>Informational video with PowerPoint slides on what a Character
Table is:</p>
[8]
<a class="moz-txt-link-freetext" href="https://cosmolearning.org/video-lectures/character-tables-one-application-symmetry/">https://cosmolearning.org/video-lectures/character-tables-one-application-symmetry/</a><br>
[9] <a class="moz-txt-link-freetext" href="https://www.chem.uci.edu/~lawm/10-2.pdf">https://www.chem.uci.edu/~lawm/10-2.pdf</a><br>
<p><br>
</p>
<div class="moz-cite-prefix">On 4/4/2020 3:13 PM, Wasim Raja Mondal
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAGfip2WXYP-z7=q=JZBJMid-JNN2OzSpERRsLc2HA2yOiev8rg@mail.gmail.com">
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<div dir="ltr">Dear expert,
<div> Can you anyone suggest what rotation
matrix for V2O3 corundum structure with qsplit=4 should I take
to decoupling the d orbital, a1g,eg\<font color="#008000">pi</font>,
eg\<font color="#804000">sigma</font>?</div>
<div><br>
</div>
<div>Thanks</div>
<div>Wasim</div>
</div>
</blockquote>
<blockquote type="cite"
cite="mid:CAGfip2WXYP-z7=q=JZBJMid-JNN2OzSpERRsLc2HA2yOiev8rg@mail.gmail.com"></blockquote>
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