In crystal field theory, the average energy of the d-orbitals stays the same after splitting because the model only redistributes the energies among the five d-orbitals and does not consider the actual energy needed to rearrange ligand charges. Your misconception comes from thinking about the physical work required to move charges, but crystal field theory is only concerned with comparing d-orbital energy levels, not the overall system energy.

Expanding on Tomislav Friganović 's absolutely correct answer: within the framework of crystal field theory, you indeed don't go beyond the pure zero-energy redistribution. If you use fully fleshed out molecular orbital theory, however, you get fully mixed orbitals and these will of course due to their mixed nature look different. In that sense the crystal field theory can be considered an approximation in which such combinations are forcibly set to 0, although that's not how this was historically developed.

Both previous points are well-articulated. To build on them: in real coordination complexes, the purely electrostatic picture of CFT often falls short because metal-ligand bonding commonly involves significant covalent character, especially with pi-donor or pi-acceptor ligands. This covalency leads to energy shifts and orbital mixing that directly influence key properties like spin-state preferences, optical spectra, and reactivity patterns, all of which are more accurately described by ligand field or molecular orbital theory.

Dear Nikita,

In crystal field theory, the average energy of the five d--orbitals remains constant when moving from a spherical to an octahedral field because the splitting only redistributes the energies of the orbitals relative to each other, without changing the total energy of the system from the d-electron's point of view. In a perfectly spherical field, all five d-orbitals are degenerate-they have the same energy. When the symmetry is lowered to octahedral, the electrostatic field from the six ligands splits the d-orbitals into two energy levels (eg and t2g), but the weighted average of these new energy levels remains equal to the original spherical field energy. This is because the crystal field splitting is defined relative to this average; it simply shifts some orbitals up and others down in energy, balancing each other out.

The point you raise about the energy needed to gather negative charge into six discrete points is correct from an electrostatic perspective, but this energy cost is not considered in CFT when calculating the d-orbital energies. CFT assumes that the field created by the ligands already exists; it only describes how this field affects the energies of the metal's d-electrons. The energy needed to build or arrange the ligand field itself is part of the total lattice or formation energy of the crystal, not the orbital splitting energy considered by CFT. Therefore, from the viewpoint of the d-electrons alone, the average energy stays the same before and after the splitting.