I'm studying crystal field theory.

In the case of an octahedral complex, why do ligands that approach along the axes raise the energies of orbitals other than $\mathrm{d}_{x^2-y^2}$ and $\mathrm{d}_{z^2}$?

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    $\begingroup$ It's not like ligands approach along the axes, it's the axes are chosen so as to point at the ligands. $\endgroup$ – Ivan Neretin Sep 25 '15 at 12:00
  • $\begingroup$ Yes,that answers it,but all the d orbitals are not identical in shape,aren't they?The d-xy and the d-z^2 orbitals,for example,are,as I happen to understand,significantly different in shape. $\endgroup$ – Aditya Anand Sep 25 '15 at 12:04
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    $\begingroup$ Shape of d-orbitals is somewhat of an abstraction. Anyway, the "true" orbitals are expressed in complex numbers, and these commonly used nice pictures are but linear combinations. They could have been combined differently. $\endgroup$ – Ivan Neretin Sep 25 '15 at 12:55
  1. Crystal field theory assumes negative point charges approaching the central metal along the axes.

  2. Orbitals are wave functions of electrons; their energy corresponds to the energy of the electron within.

Out of 1 and 2 we can follow that the negative charges are approaching other negative charges. Simple physics will tell you that two like charges repulse each other. Therefore, the electrons in all orbitals experience a certain repulsion. Repulsion destabilises their orbitals, i.e. raises their energy.

Note that Crystal field theory is a very basic theory and fails quickly when studying less simple complexes.

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