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    $\begingroup$ The match between cell vectors (abc / xyz) and orbital orientations would need to be asked as a separate question on this StackExchange. This StackExchange does have a one question per post rule. As far as I can tell, I have explained why one can normally see contributions from the same orbitals, such as $d_{z^2}$, both below and above the Fermi level. To be clear, this explanation will hold true even if all orbitals are appropriately aligned. If this does not address the original question, please clarify the original question, or consider accepting the answer. $\endgroup$ Commented Apr 26, 2024 at 19:50
  • $\begingroup$ Yes I am raising this question differently. Can you explain kindly, why sometimes even in octahedral symmetry we get $d_{x^2-y^2}$ or $d_{z}^2$ orbital's contribution in $t_{2g}$ section with other two different $d$ orbitals? $\endgroup$ Commented Apr 26, 2024 at 19:58
  • $\begingroup$ Do you mean you expected all $t_{2g}$ orbitals to be distinguishable from all the $e_g$ orbitals in the PDOS, and are wondering why they are not? Because to me that would sound like a different question that is better asked separately. $\endgroup$ Commented Apr 26, 2024 at 20:03
  • $\begingroup$ Yes, kindly you check PDOS plot section of this paper pubs.rsc.org/en/content/articlelanding/2015/sc/c5sc01251a. I am also raising these questions separately as per your suggestion. $\endgroup$ Commented Apr 26, 2024 at 20:10
  • $\begingroup$ That sounds like a new question. You can try the rotation suggested in Chengcheng's answer to see if it separates $t_{2g}$ from $e_g$ better. To be more clear, I added the specific statement of the current question to my answer. $\endgroup$ Commented Apr 26, 2024 at 20:36