My textbook defines $\mathrm{t_{2g}}$ orbitals as

$\mathrm{t_{2g}}$ stands for a set of three orbitals which are asymmetric with respect to $C_2$ axes, perpendicular to the highest $C_n$ axes, but which is symmetric in sign through the centre of inversion.

I know that “$\mathrm{t}$” is a randomly chosen letter as suggested by M. Farooq, “$\mathrm{g}$” comes from gerade (MOT), that's what the last line says. Though “$2$” in subscript must have come from $C_2$, but I didn't get the meaning of

…which are asymmetric with respect to $C_2$ axes, perpendicular to the highest $C_n$ axes.

Please explain what does this line conveys.

  • 1
    $\begingroup$ I have checked the original literature, t or T, does not stand for three or triplet. It was a randomly chosen letter. You are right g is for gerade. In original works, the letter F was used alphabetically, A,B,E, F as symmetry labels. $\endgroup$
    – AChem
    Jan 2, 2020 at 5:28
  • $\begingroup$ Dos this answer your question: What are t2g and eg in CFT? $\endgroup$
    – andselisk
    Jan 2, 2020 at 8:39
  • $\begingroup$ @andselisk But this post does not include the above definition or it's meaning. Wasn't the meaning of "t, e, g" explained in broader essence? $\endgroup$
    – Zenix
    Jan 2, 2020 at 11:30
  • $\begingroup$ @M.Farooq what is the original literature for this? I had always assumed the symmetry labels had some German connection. $\endgroup$
    – Tyberius
    Jan 3, 2020 at 14:37
  • $\begingroup$ Tyberius, actually not. I was planning to write a short historical article. Except for g and u I could not authenticate any other German meaning. The rest are mostly myths including $Entartet$ for degenerate. $\endgroup$
    – AChem
    Jan 3, 2020 at 15:03


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