In an octahedral complex, if we assume the metal ion to be inside a cube then ligands will approach from its faces. So the axial d orbitals will experience more electronic repulsion as compared to non-axial d orbitals. That's why they are higher in energy. But what I am finding difficult to understand is why non-axial d orbitals decrease their energy below the excited degenerate d orbitals level. Some answers that I found on other sites were mentioning about conservation of energy and that total decrease in t2g level and eg level are equal but still I cannot understand it.

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    $\begingroup$ The crystal field splitting depicts the energy levels in an octahedral complex, relative to one where the ligand charge density is spherically distributed. That is to say, the repulsion is already there, it's just being redistributed (hence the 'conservation of energy'). It's not being compared against a free ion in which there is no external repulsion. $\endgroup$
    – orthocresol
    Oct 25 at 20:02
  • $\begingroup$ In an octahedral complex dx2-y2 and dz2 will experience more repulsion by ligands and their energy will be raised so the extra energy gain is due to repulsion but why the non axial orbitals decrease their energy? In spherical field if they were excited, then when the octahedral complex is formed they will be experiencing more repulsion(not more than that faced by axial orbitals),then going by that logic they should have higher energy than in spherical field but their energy decrease further. Is it so that their energy is being used for exciting dx2-y2 and dz2 orbitals. $\endgroup$ Oct 26 at 2:36
  • $\begingroup$ I don’t follow your train of thought. The xy, yz, and xz orbitals point away from the ligands in an octahedral field, whereas in a spherical field they can’t help but point towards some charge density (since it is uniformly distributed over all directions).So I don’t see why there should be more repulsion. It seems to me that there should be less, which corresponds to the “decrease” in energy. $\endgroup$
    – orthocresol
    Oct 26 at 11:00
  • $\begingroup$ Of course, this is all quite handwavy, and I wouldn’t blame you at all if you didn’t want to take my comment at face value and instead wanted a mathematical proof of the above. But that’s an entirely different question, IMO. $\endgroup$
    – orthocresol
    Oct 26 at 11:01
  • $\begingroup$ In spherical field the whole set of d orbitals gets excited. When the ligands gets closer and closer and they form octahedral complex then there comes a difference in repulsion faced by axial and non axial orbitals. So I get it that the axial orbitals will face more repulsion and non axial will face some less but the magnitude of repulsion faced by dxy, dyz and dxz won't be less than that when they were experiencing a spherically symmetrical field(of course because in spherical field the ligands were far away) $\endgroup$ Oct 26 at 11:51

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